Data-mining massive time series astronomical data sets - a case study

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Course Objectives
To teach the fundamental concepts of data mining
To provide hands‐on experience in
applying the concepts to real‐world applications.
From: R. Grossman, C. Kamath, V. Kumar, “Data Mining for Scientific and Engineering Applications”
Scale of Data
Organization
Walmart Google Yahoo NASA satellites NCBI GenBank France Telecom UK Land Registry AT&T Corp
– remote sensors on a satellite – telescopes scanning the skies – microarrays generating gene expression data – scientific simulations generating terabytes of data
Fraud Detection & Mining Unusual Patterns
• Approaches: Clustering & model construction for frauds, outlier analysis • Applications: Health care, retail, credit card service, …
Data Mining: Confluence of Multiple Disciplines

Bursty and Hierarchical Structure in Streams_ACM_2002

Bursty and Hierarchical Structure in Streams∗Jon Kleinberg†AbstractA fundamental problem in text data mining is to extract meaningful structure from document streams that arrive continuously over time.E-mail and news articles are two natural examples of such streams,each characterized by topics that appear, grow in intensity for a period of time,and then fade away.The published literature in a particular researchﬁeld can be seen to exhibit similar phenomena over a much longer time scale.Underlying much of the text mining work in this area is the following intuitive premise—that the appearance of a topic in a document stream is signaled by a“burst of activity,”with certain features rising sharply in frequency as the topic emerges.The goal of the present work is to develop a formal approach for modeling such “bursts,”in such a way that they can be robustly and eﬃciently identiﬁed,and can provide an organizational framework for analyzing the underlying content.The ap-proach is based on modeling the stream using an inﬁnite-state automaton,in which bursts appear naturally as state transitions;it can be viewed as drawing an analogy with models from queueing theory for bursty network traﬃc.The resulting algorithms are highly eﬃcient,and yield a nested representation of the set of bursts that imposes a hierarchical structure on the overall stream.Experiments with e-mail and research paper archives suggest that the resulting structures have a natural meaning in terms of the content that gave rise to them.1IntroductionDocuments can be naturally organized by topic,but in many settings we also experience their arrival over time.E-mail and news articles provide two clear examples of such docu-ment streams:in both cases,the strong temporal ordering of the content is necessary for making sense of it,as particular topics appear,grow in intensity,and then fade away again. Over a much longer time scale,the published literature in a particular researchﬁeld can be meaningfully understood in this way as well,with particular research themes growing and diminishing in visibility across a period of years.Work in the areas of topic detection and tracking[2,3,6,67,68],text mining[39,62,63,64],and visualization[29,47,66]has explored techniques for identifying topics in document streams comprised of news stories, using a combination of content analysis and time-series modeling.Underlying a number of these techniques is the following intuitive premise—that the appearance of a topic in a document stream is signaled by a“burst of activity,”with certain features rising sharply in frequency as the topic emerges.The goal of the present work is to develop a formal approach for modeling such“bursts,”in such a way that they can be robustly and eﬃciently identiﬁed,and can provide an organizational framework for analyzing the underlying content.The approach presented here can be viewed as drawing an analogy with models from queueing theory for bursty network traﬃc(see e.g.[4,18,35]).In addition, however,the analysis of the underlying burst patterns reveals a latent hierarchical structure that often has a natural meaning in terms of the content of the stream.My initial aim in studying this issue was a very concrete one:I wanted a better organizing principle for the enormous archives of personal e-mail that I was accumulating.Abundant anecdotal evidence,as well as academic research[7,46,65],suggested that my own experience with“e-mail overload”corresponded to a near-universal phenomenon—a consequence of both the rate at which e-mail arrives,and the demands of managing volumes of saved personal correspondence that can easily grow into tens and hundreds of megabytes of pure text content.And at a still larger scale,e-mail has become the raw material for legal proceedings[37]and historical investigation[9,41,48]—with the National Archives,for example,agreeing to accept tens of millions of e-mail messages from the Clinton White House [50].In sum,there are several settings where it is a crucial problem toﬁnd structures that can help in making sense of large volumes of e-mail.An active line of research has applied text indexing and classiﬁcation to develop e-mail interfaces that organize incoming messages into folders on speciﬁc topics,sometimes recom-mending further actions on the part of a user[5,10,14,32,33,42,51,52,54,55,56,59,60]—in eﬀect,this framework seeks to automate a kind ofﬁling system that many users im-plement manually.There has also been work on developing query interfaces to fully-indexed collections of e-mail[8].My interest here is in exploring organizing structures based more explicitly on the role of time in e-mail and other document streams.Indeed,even theﬂow of a single focused topicis modulated by the rate at which relevant messages or documents arrive,dividing naturally into more localized episodes that correspond to bursts of activity of the type suggested above.For example,my saved e-mail contains over a thousand messages relevant to the topic “grant proposals”—announcements of new funding programs,planning of proposals,and correspondence with co-authors.While one could divide this collection into sub-topics based on message content—certain people,programs,or funding agencies form the topics of some messages but not others—an equally natural and substantially orthogonal organization for this topic would take into account the sequence of episodes reﬂected in the set of messages —bursts that surround the planning and writing of certain proposals.Indeed,certain sub-topics(e.g.“the process of gathering people together for our large NSF ITR proposal”) may be much more easily characterized by a sudden conﬂuence of message-sending over a particular period of time than by textual features of the messages themselves.One can easily argue that many of the large topics represented in a document stream are naturally punctuated by bursts in this way,with theﬂow of relevant items intensifying in certain key periods.A general technique for highlighting these bursts thus has the potential to expose a great deal ofﬁne-grained structure.Before moving to a more technical overview of the methodology,let me suggest one further perspective on this issue,quite distant from computational concerns.If one were to view a particular folder of e-mail not simply as a document stream but also as something akin to a narrative that unfolds over time,then one immediately brings into play a body of work that deals explicitly with the bursty nature of time in narratives,and the way in which particular events are signaled by a compression of the time-sense.In an early concrete reference to this idea,E.M.Forster,lecturing on the structure of the novel in the1920’s, asserted that...there seems something else in life besides time,something which may conve-niently be called“value,”something which is measured not by minutes or hoursbut by intensity,so that when we look at our past it does not stretch back evenlybut piles up into a few notable pinnacles,and when we look at the future it seemssometimes a wall,sometimes a cloud,sometimes a sun,but never a chronologicalchart[20].This role of time in narratives is developed more explicitly in work of Genette[22,23],Chat-man[12],and others on anisochronies,the non-uniform relationships between the amount of time spanned by a story’s events and the amount of time devoted to these events in the actual telling of the story.Modeling Bursty Streams.Suppose we were presented with a document stream—for concreteness,consider a large folder of e-mail on a single broad topic.How should we go about identifying the main bursts of activity,and how do they help impose additional structure on the stream?The basic point emerging from the discussion above is that suchbursts correspond roughly to points at which the intensity of message arrivals increases sharply,perhaps from once every few weeks or days to once every few hours or minutes. But the rate of arrivals is in general very“rugged”:it does not typically rise smoothly to a crescendo and then fall away,but rather exhibits frequent alternations of rapidﬂurries and longer pauses in close proximity.Thus,methods that analyze gaps between consecutive message arrivals in too simplistic a way can easily be pulled into identifying large numbers of short spurious bursts,as well as fragmenting long bursts into many smaller ones.Moreover, a simple enumeration of close-together sets of messages is only aﬁrst step toward more intricate structure.The broader goal is thus to extract global structure from a robust kind of data reduction—identifying bursts only when they have suﬃcient intensity,and in a way that allows a burst to persist smoothly across a fairly non-uniform pattern of message arrivals.My approach here is to model the stream using an inﬁnite-state automaton A,which at any point in time can be in one of an underlying set of states,and emits messages at diﬀerent rates depending on its state.Speciﬁcally,the automaton A has a set of states that correspond to increasingly rapid rates of emission,and the onset of a burst is signaled by a state transition—from a lower state to a higher state.By assigning costs to state transitions, one can control the frequency of such transitions,preventing very short bursts and making it easier to identify long bursts despite transient changes in the rate of the stream.The overall framework is developed in Section2.It draws on the formalism of Markov sources used in modeling bursty network traﬃc[4,18,35],as well as the formalism of hidden Markov models [53].Using an automaton with states that correspond to higher and higher intensities provides an additional source of analytical leverage—the bursts associated with state transitions form a naturally nested structure,with a long burst of low intensity potentially containing several bursts of higher intensity inside it(and so on,recursively).For a folder of related e-mail messages,we will see in Sections2and3that this can provide a hierarchical decomposition of the temporal order,with long-running episodes intensifying into briefer ones according to a natural tree structure.This tree can thus be viewed as imposing aﬁne-grained organization on the sub-episodes within the message stream.Following this development,Section4focuses on the problem of enumerating all signif-icant bursts in a document stream,ranked by a measure of“weight.”Applied to a case in which the stream is comprised not of e-mail messages but of research paper titles over the past several decades,the set of bursts corresponds roughly to the appearance and disappear-ance of certain terms of interest in the underlying research area.The approach makes sense for many other datasets of an analogousﬂavor;in Section4,I also discuss an example based on U.S.Presidential State of the Union Addresses from1790to2002.Section5discusses the connections to related work in a range of areas,particularly the striking recent work of Swan,Allan,and Jensen[62,63,64]on overview timelines,which forms the body of research closest to the approach here.Finally,Section6discusses some further applications of themethodology—how burstiness in arrivals can help to identify certain messages as“land-marks”in a large corpus of e-mail;and how the overall framework can be applied to logs of Web usage.2A Weighted Automaton ModelPerhaps the simplest randomized model for generating a sequence of message arrival times is based on an exponential distribution:messages are emitted in a probabilistic manner,so that the gap x in time between messages i and i+1is distributed according to the“memoryless”exponential density function f(x)=αe−αx,for a parameterα>0.(In other words,the probability that the gap exceeds x is equal to e−αx.)The expected value of the gap in this model isα−1,and hence one can refer toαas the rate of message arrivals.Intuitively,a“bursty”model should extend this simple formulation by exhibiting periods of lower rate interleaved with periods of higher rate.A natural way to do this is to construct a model with multiple states,where the rate depends on the current state.Let us start with a basic model that incorporates this idea,and then extend it to the models that will primarily be used in what follows.A two-state model.Arguably the most basic bursty model of this type would be con-structed from a probabilistic automaton A with two states q0and q1,which we can think of as corresponding to“low”and“high.”When A is in state q0,messages are emitted at a slow rate,with gaps x between consecutive messages distributed independently according to a density function f0(x)=α0e−α0x When A is in state q1,messages are emitted at a faster rate,with gaps distributed independently according to f1(x)=α1e−α1x,whereα1>α0. Finally,between messages,A changes state with probability p∈(0,1),remaining in its current state with probability1−p,independently of previous emissions and state changes.Such a model could be used to generate a sequence of messages in the natural way.A begins in state q0.Before each message(including theﬁrst)is emitted,A changes state with probability p.A message is then emitted,and the gap in time until the next message is determined by the distribution associated with A’s current state.One can apply this generative model toﬁnd a likely state sequence,given a set of mes-sages.Suppose there is a given set of n+1messages,with speciﬁed arrival times;this determines a sequence of n inter-arrival gaps x=(x1,x2,...,x n).The development here will use the basic assumption that all gaps x i are strictly positive.We can use the Bayes procedure(as in e.g.[15])to determine the conditional probability of a state sequence ,...,q i n);note that this must be done in terms of the underlying density functions, q=(q i1since the gaps are not drawn from discrete distributions.Each state sequence q induces a density function f q over sequences of gaps,which has the form f q(x1,...,x n)= n t=1f i t(x t). If b denotes the number of state transitions in the sequence q—that is,the number ofindices i t so that q i t =q i t +1—then the (prior)probability of q is equal to( i t =i t +1p )(i t =i t +11−p )=p b (1−p )n −b = pq Pr [q ]f q (x )=11−p b (1−p )nn t =1f i t (x t ),where Z is the normalizing constant q Pr [q ]f q (x ).Finding a state sequence q maximizing this probability is equivalent to ﬁnding one that minimizes−ln Pr [q |x ]=b ln 1−pp + n t =1−ln f i t (x t )Finding a state sequence to minimize this cost function is a problem that can be motivated intuitively on its own terms,without recourse to the underlying probabilistic model.The ﬁrst of the two terms in the expression for c (q |x )favors sequences with a small number of state transitions,while the second term favors state sequences that conform well to the sequence x of gap values.Thus,one expects the optimum to track the global structure of bursts in the gap sequence,while holding to a single state through local periods of non-uniformity.Varying the coeﬃcient on b controls the amount of “inertia”ﬁxing the automaton in its current state.The next step is to extend this simple “high-low”model to one with a richer state set,using a cost model;this will lead to a method that also extracts hierarchical structure from the pattern of bursts.An inﬁnite-state model.Consider a sequence of n +1messages that arrive over a period of time of length T .If the messages were spaced completely evenly over this time interval,then they would arrive with gaps of size ˆg =T/n .Bursts of greater and greater intensity would be associated with gaps smaller and smaller than ˆg .This suggests focusing on an inﬁnite-state automaton whose states correspond to gap sizes that may be arbitrarily small,so as to capture the full range of possible bursts.The development here will use a cost model0132γln n per state 2013tree representation0132burstsb)optimal state sequence a)q q q q 0123q itransition costtransition cost 0emissions at rate -1s ig Figure 1:An inﬁnite-state model for bursty sequences.(a)The inﬁnite-state automaton A ∗s,γ;in state q i ,messages are emitted at a spacing in time that is distributed according to f (x )=αi e −αi x ,where αi =ˆg −1s i .There is a cost to move to states of higher index,but not to states of lower index.(b)Given a sequence of gaps between message arrivals,an optimal state sequence in A ∗s,γis computed.This gives rise to a set of nested bursts :intervals of time in which the optimal state has at least a certain index.The inclusions among the set of bursts can be naturally represented by a tree structure.as in the two-state case,where the underlying goal is to ﬁnd a state sequence of minimum cost.Thus,consider an automaton with a “base state”q 0that has an associated exponential density function f 0with rate α0=ˆg −1=n/T —consistent with completely uniform message arrivals.For each i >0,there is a state q i with associated exponential density f i having rate αi =ˆg −1s i ,where s >1is a scaling parameter.(i will be referred to as the index of the state q i .)In other words,the inﬁnite sequence of states q 0,q 1,...models inter-arrival gaps that decrease geometrically from ˆg ;there is an expected rate of message arrivals that intensiﬁes for larger and larger values of i .Finally,for every i and j ,there is a cost τ(i,j )associated with a state transition from q i to q j .The framework allows considerable ﬂexibility in formulating the cost function;for the work described here,τ(·,·)is deﬁned so that the cost of moving from a lower-intensity burst state to a higher-intensity one is proportional to the number of intervening states,but there is no cost for the automaton to end a higher-intensityburst and drop down to a lower-intensity one.Speciﬁcally,when j>i,moving from q i to q j incurs a cost of(j−i)γln n,whereγ>0is a parameter;and when j<i,the cost is0.See Figure1(a)for a schematic picture.This automaton,with its associated parameters s andγ,will be denoted A∗s,γ.Given a sequence of positive gaps x=(x1,x2,...,x n)between message arrivals,the goal—by analogy with the two-state model above—is toﬁnd a state sequence q=(q i,...,q i n)that1minimizes the cost functionc(q|x)= n−1 t=0τ(i t,i t+1) + n t=1−ln f i t(x t) .(Let i0=0in this expression,so that A∗s,γstarts in state q0.)Since the set of possible q is inﬁnite,one cannot automatically assert that the minimum is even well-deﬁned;but this will be established in Theorem2.1below.As before,minimizing theﬁrst term is consistent with having few state transitions—and transitions that span only a few distinct states—while minimizing the second term is consistent with passing through states whose rates agree closely with the inter-arrival gaps.Thus,the combined goal is to track the sequence of gaps as well as possible without changing state too much.Observe that the scaling parameter s controls the“resolution”with which the discrete rate values of the states are able to track the real-valued gaps;the parameterγcontrols the ease with which the automaton can change states.In what follows,γwill often be set to a default value of1;we can use A∗s to denote A∗s,1.Computing a minimum-cost state sequence.Given a a sequence of positive gaps x=(x1,x2,...,x n)between message arrivals,consider the algorithmic problem ofﬁnding a,...,q i n)in A∗s,γthat minimizes the cost c(q|x);such a sequence state sequence q=(q i1will be called optimal.To establish that the minimum is well-deﬁned,and to provide a means of computing it,it is useful toﬁrst deﬁne a naturalﬁnite restriction of the automaton:for a natural number k,one simply deletes all states but q0,q1,...,q k−1from A∗s,γ,and denotes the resulting k-state automaton by A k s,γ.Note that the two-state automaton A2s,γis essentially equivalent(by an amortization argument)to the probabilistic two-state model described earlier.It is not hard to show that computing an optimal state sequence in A∗s,γis equivalent to doing so in one of itsﬁnite restrictions.x i andTheorem2.1Letδ(x)=min ni=1k= 1+log s T+log sδ(x)−1 .(Note thatδ(x)>0,since all gaps are positive.)If q∗is an optimal state sequence in A k s,γ, then it is also an optimal state sequence in A∗s,γ.Proof.Let q∗=(q1,...,q n)be an optimal state sequence in A k s,γ,and let q=(q i1,...,q i n)be an arbitrary state sequence in A∗s,γ.As before,set 0=i0=0,since both sequences start in state q0;for notational purposes,it is useful to deﬁne n+1=i n+1=0as well.The goal is to show that c(q∗|x)≤c(q|x).If q does not contain any states of index greater than k−1,this inequality follows from the fact that q∗is an optimal state sequence in A k s,γ.Otherwise,consider the state sequenceq =(q i1,...,q in)where i t=min(i t,k−1).It is straightforward to verify thatn−1t=0τ(i t,i t+1)≤n−1 t=0τ(i t,i t+1).Now,for a particular choice of t between1and n,consider the expression−ln f j(x t)=αj x t−lnαj;what is the value of j for which it is minimized?The function h(α)=αx t−lnαis concave upwards over the interval(0,∞),with a global minimum atα=x−1t.Thus,if j∗is such thatαj∗≤x−1t≤αj∗+1,then the minimum of−ln f j(x t)is achieved at one of j∗or j∗+1;moreover,if j ≥j ≥j∗+1,then−ln f j (x t)≥−ln f j (x).Since k= 1+log s T+log sδ(x)−1 ,one hasαk−1=ˆg−1s k−1=nT·s log s T+log sδ(x)−1=1δ(x)=1In view of the theorem,it is enough to give an algorithm that computes an optimal state sequence in an automaton of the form A k s,γ.This can be done by adapting the standard forward dynamic programming algorithm used for hidden Markov models[53]to the model and cost function deﬁned here:One deﬁnes C j(t)to be the minimum cost of a state sequence for the input x1,x2,...,x t that must end with state q j,and then iteratively builds up the values of C j(t)in order of increasing t using the recurrence relation C j(t)=−ln f j(x t)+ min (C (t−1)+τ( ,j))with initial conditions C0(0)=0and C j(0)=∞for j>0.Inall the experiments here,an optimal state sequence in A∗s,γcan be found by restricting to a number of states k that is a very small constant,always at most25.Note that although theﬁnal computation of an optimal state sequence is carried out by recourse to aﬁnite-state model,working with the inﬁnite model has the advantage that a number of states k is notﬁxed a priori;rather,it emerges in the course of the computation, and in this way the automaton A∗s,γessentially“conforms”to the particular input instance. 3Hierarchical Structure and E-mail StreamsExtracting hierarchical structure.From an algorithm to compute an optimal state sequence,one can then deﬁne the basic representation of a set of bursts,according to a hierarchical structure.For a set of messages generating a sequence of positive inter-arrival gaps x=(x1,x2,...,x n),suppose that an optimal state sequence q=(q i1,q i2,...,q i n)in A∗s,γhas been determined.Following the discussion of the previous section,we can formally deﬁne a burst of intensity j to be a maximal interval over which q is in a state of index j or higher.More precisely, it is an interval[t,t ]so that i t,...,i t ≥j but i t−1and i t +1are less than j(or undeﬁned if t−1<0or t +1>n).It follows that bursts exhibit a natural nested structure:a burst of intensity j may contain one or more sub-intervals that are bursts of intensity j+1;these in turn may contain sub-intervals that are bursts of intensity j+2;and so forth.This relationship can be represented by a rooted treeΓ,as follows.There is a node corresponding to each burst;and node v is a child of node u if node u represents a burst B u of intensity j(for some value of j),and node v represents a burst B v of intensity j+1such that B v⊆B u.Note that the root ofΓcorresponds to the single burst of intensity0,which is equal to the whole interval[0,n].Thus,the treeΓcaptures hierarchical structure that is implicit in the underlying stream. Figure1(b)shows the transformation from an optimal state sequence,to a set of nested bursts,to a tree.Hierarchy in an e-mail stream.Let us now return to one of the initial motivations for this model,and consider a stream of e-mail messages.What does the hierarchical structure of bursts look like in this setting?I applied the algorithm to my own collection of saved e-mail,consisting of messages sent and received between June9,1997and August23,2001.(The cut-oﬀdates are chosen here so as to roughly cover four academic years.)First,here is a brief summary of this collection. Every piece of mail I sent or received during this period of time,using my e-mail address,can be viewed as belonging to one of two categories:ﬁrst,messages consisting of one or more largeﬁles,such as drafts of papers mailed between co-authors(essentially, e-mail asﬁle transfer);and second,all other messages.The collection I am considering here consists simply of all messages belonging to the second,much larger category;thus,to arough approximation,it is all the mail I sent and received during this period,unﬁltered by content but excluding longﬁles.It contains34344messages in UNIX mailbox format, totaling41.7megabytes of ascii text,excluding message headers.1Subsets of the collection can be chosen by selecting all messages that contain a particular string or set of strings;this can be viewed as an analogue of a“folder”of related messages, although messages in the present case are related not because they were manuallyﬁled together but because they are the response set to a particular query.Studying the stream induced by such a response set raises two distinct but related questions.First,is it in fact the case that the appearance of messages containing particular words exhibits a“spike,”in some informal sense,in the(temporal)vicinity of signiﬁcant times such as deadlines,scheduled events,or unexpected developments?And second,do the algorithms developed here provide a means for identifying this phenomenon?In fact such spikes appear to be quite prevalent,and also rich enough that the algo-rithms of the previous section can extract hierarchical structure that in many cases is quite deep.Moreover,the algorithms are eﬃcient enough that computing a representation for the bursts on a query to the full e-mail collection can be done in real-time,using a simple implementation on a standard PC.To give a qualitative sense for the kind of structure one obtains,Figures2and3show the results of computing bursts for two diﬀerent queries using the automaton A∗2.Figure2shows an analysis of the stream of all messages containing the word“ITR,”which is prominent in my e-mail because it is the name of a large National Science Foundation program for which my colleagues and I wrote two proposals in1999-2000.There are many possible ways to organize this stream of messages,but one general backdrop against which to view the stream is the set of deadlines imposed by the NSF for theﬁrst run of the rge proposals were submitted in a three-phase process,with deadlines of11/15/99,1/5/00,and 4/17/00for letters of intent,pre-proposals,and full proposals respectively.Small proposals were submitted in a two-phase process,with deadlines of1/5/00and2/14/00for letters of intent and full proposals respectively.I participated in a group writing a proposal of each kind.Turning to theﬁgure,part(a)is a plot of the raw input to the automaton A∗2,showing the arrival time of each message in the response set.Part(b)shows a nested interval representation of the set of bursts for the optimal state sequence in A∗2;the intervals are annotated with theﬁrst and last dates of the messages they contain,and the dates of the NSF deadlines are lined up with the intervals that contain them.Note that this is a schematic representation,designed to show the inclusions that give rise to the treeΓ;the lengths and centering of the intervals in the drawing are not signiﬁcant.Part(c)shows a drawing of the resulting treeΓ.The root corresponds to the single burst of intensity0that is present in any state sequence.One sees that the two children of the root span intervals surrounding the。

数据挖掘导论英文版

数据挖掘导论英文版Data Mining IntroductionData mining is the process of extracting valuable insights and patterns from large datasets. It involves the application of various techniques and algorithms to uncover hidden relationships, trends, and anomalies that can be used to inform decision-making and drive business success. In today's data-driven world, the ability to effectively harness the power of data has become a critical competitive advantage for organizations across a wide range of industries.One of the key strengths of data mining is its versatility. It can be applied to a wide range of domains, from marketing and finance to healthcare and scientific research. In the marketing realm, for example, data mining can be used to analyze customer behavior, identify target segments, and develop personalized marketing strategies. In the financial sector, data mining can be leveraged to detect fraud, assess credit risk, and optimize investment portfolios.At the heart of data mining lies a diverse set of techniques and algorithms. These include supervised learning methods, such asregression and classification, which can be used to predict outcomes based on known patterns in the data. Unsupervised learning techniques, such as clustering and association rule mining, can be employed to uncover hidden structures and relationships within datasets. Additionally, advanced algorithms like neural networks and decision trees have proven to be highly effective in tackling complex, non-linear problems.The process of data mining typically involves several key steps, each of which plays a crucial role in extracting meaningful insights from the data. The first step is data preparation, which involves cleaning, transforming, and integrating the raw data into a format that can be effectively analyzed. This step is particularly important, as the quality and accuracy of the input data can significantly impact the reliability of the final results.Once the data is prepared, the next step is to select the appropriate data mining techniques and algorithms to apply. This requires a deep understanding of the problem at hand, as well as the strengths and limitations of the available tools. Depending on the specific goals of the analysis, the data mining practitioner may choose to employ a combination of techniques, each of which can provide unique insights and perspectives.The next phase is the actual data mining process, where the selectedalgorithms are applied to the prepared data. This can involve complex mathematical and statistical calculations, as well as the use of specialized software and computing resources. The results of this process may include the identification of patterns, trends, and relationships within the data, as well as the development of predictive models and other data-driven insights.Once the data mining process is complete, the final step is to interpret and communicate the findings. This involves translating the technical results into actionable insights that can be easily understood by stakeholders, such as business leaders, policymakers, or scientific researchers. Effective communication of data mining results is crucial, as it enables decision-makers to make informed choices and take appropriate actions based on the insights gained.One of the most exciting aspects of data mining is its continuous evolution and the emergence of new techniques and technologies. As the volume and complexity of data continue to grow, the need for more sophisticated and powerful data mining tools and algorithms has become increasingly pressing. Advances in areas such as machine learning, deep learning, and big data processing have opened up new frontiers in data mining, enabling practitioners to tackle increasingly complex problems and extract even more valuable insights from the data.In conclusion, data mining is a powerful and versatile tool that has the potential to transform the way we approach a wide range of challenges and opportunities. By leveraging the power of data and the latest analytical techniques, organizations can gain a deeper understanding of their operations, customers, and markets, and make more informed, data-driven decisions that drive sustainable growth and success. As the field of data mining continues to evolve, it is clear that it will play an increasingly crucial role in shaping the future of business, science, and society as a whole.。

时间序列数据挖掘算法的研究及应用

时间序列数据挖掘算法的研究及应用时间序列数据（Time Series Data）是指按时间顺序采样或测量得到的数据。

在现代社会中，我们所接触的各种数据普遍伴随着时间的因素，因此，对时间序列数据的处理和分析成为了一个非常重要的研究方向。

随着计算机技术的不断发展，时间序列数据挖掘的方法和算法也不断得到了优化和改进，从而推动了时间序列数据挖掘的应用范围不断扩大。

为了更好地进行时间序列数据的处理和分析，我们需要使用一些专门的算法和方法。

下面，我们将介绍几种常用的时间序列数据挖掘算法。

一、时间序列预测算法时间序列预测算法是指根据已知的时间序列数据，通过建立合适的模型，来预测未来一段时间内的时间序列趋势。

常见的时间序列预测算法包括 ARIMA 模型、神经网络模型、支持向量机模型等。

这些模型在时间序列数据的预测和预警方面有着非常广泛的应用。

例如，在股票市场中，我们可以使用时间序列预测算法来构建模型，预测未来一段时间内股票的价格走势。

在能源领域中，我们可以使用时间序列预测算法来预测未来一段时间内的能源需求量，从而为能源供应和调度提供依据。

在医疗领域中，我们可以使用时间序列预测算法来预测不同种类疾病的发病率，帮助医疗机构制定相应的疾病预防措施。

二、时间序列聚类算法时间序列聚类算法是指将时间序列数据分为若干个类别，并使得同一类别内的时间序列具有相似性，而不同类别的时间序列具有明显的差异性。

时间序列聚类算法的目的是为了在时间序列数据中发现潜在的模式和异常，并帮助我们更好地理解时间序列数据的性质和结构。

常见的时间序列聚类算法包括 K-means 算法、基于密度的 DBSCAN 算法、层次聚类算法等。

时间序列聚类算法在许多领域都有着广泛的应用。

例如，在气候领域中，我们可以使用时间序列聚类算法来将气候变化数据分为若干个类别，并发现各类别内的相似性和差异性，从而更好地理解气候变化的规律和趋势。

在智能交通领域中，我们可以使用时间序列聚类算法来将车辆轨迹数据分为不同的类别，并帮助我们更好地了解车辆运行的规律和特点。

Data Mining是什么意思

简单来说Data Mining就是在庞大的数据库中寻找出有价值的隐藏事件，籍由统计及人工智能的科学技术，将资料做深入分析，找出其中的知识，并根据企业的问题建立不同的模型，以提供企业进行决策时的参考依据。

举例来说，银行和信用卡公司可籍由Data Mining的技术将庞大的顾客资料做筛选、分析、推演及预测，找出哪些是最有贡献的顾客，哪些是高流失率族群，或是预测一个新的产品或促销活动可能带来的响应率，能够在适当的时间提供适当适合的产品及服务。

也就是说，透过Data Mining企业可以了解它的顾客，掌握他们的喜好，满足他们的需要。

近年来，Data Mining已成为企业热门的话题。

愈来愈多的企业想导入Data Mining的技术，美国的一项研究报告更是将Data Mining 视为二十一世纪十大明星产业，可见它的重要性。

一般Data Mining 较长被应用的领域包括金融业、保险业、零售业、直效行销业、通讯业、制造业以及医疗服务业等。

高二英语科技词汇单选题40题(带答案)

高二英语科技词汇单选题40题(带答案)1.The new smartphone has a large _____.A.screenB.keyboardC.mouseD.printer答案：A。

“screen”是屏幕，新智能手机有一个大屏幕，符合常理。

“keyboard”是键盘，“mouse”是鼠标，“printer”是打印机，都与智能手机不匹配。

2.We can use a _____ to take pictures.puterB.cameraC.televisionD.radio答案：B。

“camera”是相机，可以用来拍照。

“computer”是电脑，“television”是电视，“radio”是收音机，都不能用来拍照。

3.The _____ can play music and videos.ptopB.speakerC.projectorD.scanner答案：A。

“laptop”是笔记本电脑，可以播放音乐和视频。

“speaker”是扬声器，“projector”是投影仪，“scanner”是扫描仪，都不能播放音乐和视频。

4.My father bought a new _____.A.tabletB.bookC.penD.pencil答案：A。

“tablet”是平板电脑。

“book”是书，“pen”是钢笔，“pencil”是铅笔，只有平板电脑是科技设备。

5.The _____ is very useful for online meetings.A.headphoneB.microphoneC.speakerD.camera答案：D。

“camera”摄像头在在线会议中很有用。

“headphone”是耳机，“microphone”是麦克风，“speaker”是扬声器，都不如摄像头在在线会议中的作用直接。

6.We can store a lot of data in a _____.A.flash driveB.penC.pencilD.book答案：A。

《大数据专业英语》课件—09Data Mining

obtain solicitation exclude
[əbˈteɪn] [ˌsəlɪsɪ'teɪʃn] [ɪkˈsklu:d]
vt.构建，建造；构成；创立 n.电子表格 n.关系；联系 vt.隐藏，隐匿 adj.凭经验的；以观察或实验为依据的 adj.可识别的；可辨别的 n.行动，活动；功能，作用；手段 n.行为；态度 n.解决方案，答案 vt.构想出，规划；确切地阐述；用公式表示
平面文件知道；意识到市场战略，营销战略直接邮件，直接邮寄广告无论如何，至少聚焦于实施计划，实施方案把... ...转换为... ...，把... ...翻译为... ... 最佳值，最优值知识部署决策树
vt.插入 n.评估；估价 vt.校准；使标准化，使合标准 adj.最佳的，最优的 n.洞察力，洞悉；直觉，眼光；领悟 n.仪表板，仪表盘 n.可能，可能性 n.欺诈；骗子；伪劣品，冒牌货
Phrases
automatic discovery data mining model high-value customer in order to ... statistical method rely on data mining algorithm be defined as multidimensional data cost allocation time series analysis computational learning be integrated in ...
大数据专业英语教程
Unit 9
Data Mining
Contents
New Words Abbreviations
Phrases 参考译文
New Words

如何使用随机森林进行时间序列数据挖掘(七)

随机森林是一种强大的机器学习算法，常被用于分类和回归问题。

然而，很少有人知道随机森林也可以用于时间序列数据挖掘。

在本文中，我们将探讨如何使用随机森林进行时间序列数据挖掘。

时间序列数据是按时间顺序排列的数据点，通常用于分析和预测未来的趋势。

随机森林是一种集成学习算法，利用多个决策树进行预测，然后取平均值或多数投票结果。

在时间序列数据挖掘中，随机森林可以用于预测未来的趋势，识别周期性模式，以及发现隐藏的关联关系。

首先，我们来看看如何用随机森林进行时间序列数据的预测。

对于一个给定的时间序列数据集，我们可以将其分为训练集和测试集。

然后，我们可以利用训练集来构建一个随机森林模型，并用测试集来评估模型的性能。

在构建随机森林模型时，我们可以使用一些技巧来处理时间序列数据的特性，比如滞后特征，移动平均等。

这些技巧可以帮助模型更好地捕捉时间序列数据的模式，提高预测的准确性。

除了预测，随机森林还可以用于识别时间序列数据中的周期性模式。

周期性模式在时间序列数据中很常见，比如每周的销售额波动，每年的季节性变化等。

利用随机森林，我们可以构建一个模型来识别这些周期性模式，并用于未来的预测。

通过识别周期性模式，我们可以更好地理解时间序列数据的变化规律，从而更好地预测未来的趋势。

此外，随机森林还可以用于发现时间序列数据中的隐藏关联关系。

时间序列数据通常包含大量的信息，但这些信息可能是隐藏的，需要一些技巧来发现。

随机森林可以帮助我们发现不同时间序列之间的关联关系，从而更好地理解数据的内在结构。

通过发现隐藏的关联关系，我们可以更好地利用时间序列数据做出预测，或者发现新的商业机会。

综上所述，随机森林是一种强大的机器学习算法，在时间序列数据挖掘中也有很大的潜力。

通过预测、识别周期性模式和发现隐藏关联关系，我们可以更好地理解时间序列数据的特性，从而做出更准确的预测和发现新的商业机会。

因此，随机森林是一种非常值得探索的算法，在时间序列数据挖掘中有着广阔的应用前景。

如何使用随机森林进行时间序列数据挖掘(Ⅲ)

随机森林是一种强大的机器学习算法，它可以用于时间序列数据挖掘。

在本文中，我们将深入探讨如何使用随机森林来处理时间序列数据。

首先，我们将介绍时间序列数据及其特点，然后将讨论随机森林算法的基本原理和如何将其应用于时间序列数据挖掘。

最后，我们将讨论一些常见的应用和挑战，并提出一些建议。

时间序列数据是按时间顺序排列的数据序列，通常用于描述某一变量随时间变化的情况。

时间序列数据的特点包括趋势性、季节性、周期性和随机性。

趋势性指的是数据在长期内呈现出的总体上升或下降的趋势；季节性指的是数据在短期内呈现出的周期性波动；周期性指的是数据在较长时间内呈现出的重复性波动；随机性指的是数据的不确定性和随机波动。

随机森林是一种集成学习算法，它由多个决策树组成，每棵树都使用不同的子样本和特征集进行训练，最后将它们的预测结果进行平均或投票。

随机森林具有较强的泛化能力和抗过拟合能力，适用于各种类型的数据和问题。

在使用随机森林进行时间序列数据挖掘时，有一些特殊的考虑和技巧。

首先，我们需要对时间序列数据进行预处理，包括平稳化、去除趋势和季节性、差分等。

其次，我们需要将时间序列数据转化为监督学习问题，即将时间序列数据转化为特征和标签的形式。

然后，我们可以使用随机森林算法进行训练和预测。

在训练过程中，我们可以使用交叉验证等技术来选择合适的模型参数，如树的数量、最大深度、最小叶子节点数等。

在预测过程中，我们可以利用随机森林的特性来获取模型的不确定性估计，如特征重要性、置信区间等。

随机森林在时间序列数据挖掘中有许多应用。

例如，它可以用于预测股票价格、销售额、气温等时间序列数据；它还可以用于异常检测、信号处理、数据压缩等。

然而，随机森林在处理时间序列数据时也面临一些挑战，如对长期依赖关系的建模、处理缺失值和异常值、处理非平稳和非线性数据等。

为了更好地应用随机森林进行时间序列数据挖掘，我们可以采取一些策略和技巧。

例如，我们可以利用滑动窗口法来获取更多的历史信息，以提高模型的预测准确性；我们还可以尝试集成不同模型和特征，以提高模型的稳定性和泛化能力。

From Data Mining to Knowledge Discovery in Databases

s Data mining and knowledge discovery in databases have been attracting a signiﬁcant amount of research, industry, and media atten-tion of late. What is all the excitement about?This article provides an overview of this emerging ﬁeld, clarifying how data mining and knowledge discovery in databases are related both to each other and to related ﬁelds, such as machine learning, statistics, and databases. The article mentions particular real-world applications, speciﬁc data-mining techniques, challenges in-volved in real-world applications of knowledge discovery, and current and future research direc-tions in the ﬁeld.A cross a wide variety of ﬁelds, data arebeing collected and accumulated at adramatic pace. There is an urgent need for a new generation of computational theo-ries and tools to assist humans in extracting useful information (knowledge) from the rapidly growing volumes of digital data. These theories and tools are the subject of the emerging ﬁeld of knowledge discovery in databases (KDD).At an abstract level, the KDD ﬁeld is con-cerned with the development of methods and techniques for making sense of data. The basic problem addressed by the KDD process is one of mapping low-level data (which are typically too voluminous to understand and digest easi-ly) into other forms that might be more com-pact (for example, a short report), more ab-stract (for example, a descriptive approximation or model of the process that generated the data), or more useful (for exam-ple, a predictive model for estimating the val-ue of future cases). At the core of the process is the application of speciﬁc data-mining meth-ods for pattern discovery and extraction.1This article begins by discussing the histori-cal context of KDD and data mining and theirintersection with other related ﬁelds. A briefsummary of recent KDD real-world applica-tions is provided. Deﬁnitions of KDD and da-ta mining are provided, and the general mul-tistep KDD process is outlined. This multistepprocess has the application of data-mining al-gorithms as one particular step in the process.The data-mining step is discussed in more de-tail in the context of speciﬁc data-mining al-gorithms and their application. Real-worldpractical application issues are also outlined.Finally, the article enumerates challenges forfuture research and development and in par-ticular discusses potential opportunities for AItechnology in KDD systems.Why Do We Need KDD?The traditional method of turning data intoknowledge relies on manual analysis and in-terpretation. For example, in the health-careindustry, it is common for specialists to peri-odically analyze current trends and changesin health-care data, say, on a quarterly basis.The specialists then provide a report detailingthe analysis to the sponsoring health-care or-ganization; this report becomes the basis forfuture decision making and planning forhealth-care management. In a totally differ-ent type of application, planetary geologistssift through remotely sensed images of plan-ets and asteroids, carefully locating and cata-loging such geologic objects of interest as im-pact craters. Be it science, marketing, ﬁnance,health care, retail, or any other ﬁeld, the clas-sical approach to data analysis relies funda-mentally on one or more analysts becomingArticlesFALL 1996 37From Data Mining to Knowledge Discovery inDatabasesUsama Fayyad, Gregory Piatetsky-Shapiro, and Padhraic Smyth Copyright © 1996, American Association for Artificial Intelligence. All rights reserved. 0738-4602-1996 / $2.00areas is astronomy. Here, a notable success was achieved by SKICAT ,a system used by as-tronomers to perform image analysis,classiﬁcation, and cataloging of sky objects from sky-survey images (Fayyad, Djorgovski,and Weir 1996). In its ﬁrst application, the system was used to process the 3 terabytes (1012bytes) of image data resulting from the Second Palomar Observatory Sky Survey,where it is estimated that on the order of 109sky objects are detectable. SKICAT can outper-form humans and traditional computational techniques in classifying faint sky objects. See Fayyad, Haussler, and Stolorz (1996) for a sur-vey of scientiﬁc applications.In business, main KDD application areas includes marketing, ﬁnance (especially in-vestment), fraud detection, manufacturing,telecommunications, and Internet agents.Marketing:In marketing, the primary ap-plication is database marketing systems,which analyze customer databases to identify different customer groups and forecast their behavior. Business Week (Berry 1994) estimat-ed that over half of all retailers are using or planning to use database marketing, and those who do use it have good results; for ex-ample, American Express reports a 10- to 15-percent increase in credit-card use. Another notable marketing application is market-bas-ket analysis (Agrawal et al. 1996) systems,which ﬁnd patterns such as, “If customer bought X, he/she is also likely to buy Y and Z.” Such patterns are valuable to retailers.Investment: Numerous companies use da-ta mining for investment, but most do not describe their systems. One exception is LBS Capital Management. Its system uses expert systems, neural nets, and genetic algorithms to manage portfolios totaling $600 million;since its start in 1993, the system has outper-formed the broad stock market (Hall, Mani,and Barr 1996).Fraud detection: HNC Falcon and Nestor PRISM systems are used for monitoring credit-card fraud, watching over millions of ac-counts. The FAIS system (Senator et al. 1995),from the U.S. Treasury Financial Crimes En-forcement Network, is used to identify ﬁnan-cial transactions that might indicate money-laundering activity.Manufacturing: The CASSIOPEE trou-bleshooting system, developed as part of a joint venture between General Electric and SNECMA, was applied by three major Euro-pean airlines to diagnose and predict prob-lems for the Boeing 737. To derive families of faults, clustering methods are used. CASSIOPEE received the European ﬁrst prize for innova-intimately familiar with the data and serving as an interface between the data and the users and products.For these (and many other) applications,this form of manual probing of a data set is slow, expensive, and highly subjective. In fact, as data volumes grow dramatically, this type of manual data analysis is becoming completely impractical in many domains.Databases are increasing in size in two ways:(1) the number N of records or objects in the database and (2) the number d of ﬁelds or at-tributes to an object. Databases containing on the order of N = 109objects are becoming in-creasingly common, for example, in the as-tronomical sciences. Similarly, the number of ﬁelds d can easily be on the order of 102or even 103, for example, in medical diagnostic applications. Who could be expected to di-gest millions of records, each having tens or hundreds of ﬁelds? We believe that this job is certainly not one for humans; hence, analysis work needs to be automated, at least partially.The need to scale up human analysis capa-bilities to handling the large number of bytes that we can collect is both economic and sci-entiﬁc. Businesses use data to gain competi-tive advantage, increase efﬁciency, and pro-vide more valuable services to customers.Data we capture about our environment are the basic evidence we use to build theories and models of the universe we live in. Be-cause computers have enabled humans to gather more data than we can digest, it is on-ly natural to turn to computational tech-niques to help us unearth meaningful pat-terns and structures from the massive volumes of data. Hence, KDD is an attempt to address a problem that the digital informa-tion era made a fact of life for all of us: data overload.Data Mining and Knowledge Discovery in the Real WorldA large degree of the current interest in KDD is the result of the media interest surrounding successful KDD applications, for example, the focus articles within the last two years in Business Week , Newsweek , Byte , PC Week , and other large-circulation periodicals. Unfortu-nately, it is not always easy to separate fact from media hype. Nonetheless, several well-documented examples of successful systems can rightly be referred to as KDD applications and have been deployed in operational use on large-scale real-world problems in science and in business.In science, one of the primary applicationThere is an urgent need for a new generation of computation-al theories and tools toassist humans in extractinguseful information (knowledge)from the rapidly growing volumes ofdigital data.Articles38AI MAGAZINEtive applications (Manago and Auriol 1996).Telecommunications: The telecommuni-cations alarm-sequence analyzer (TASA) wasbuilt in cooperation with a manufacturer oftelecommunications equipment and threetelephone networks (Mannila, Toivonen, andVerkamo 1995). The system uses a novelframework for locating frequently occurringalarm episodes from the alarm stream andpresenting them as rules. Large sets of discov-ered rules can be explored with ﬂexible infor-mation-retrieval tools supporting interactivityand iteration. In this way, TASA offers pruning,grouping, and ordering tools to reﬁne the re-sults of a basic brute-force search for rules.Data cleaning: The MERGE-PURGE systemwas applied to the identiﬁcation of duplicatewelfare claims (Hernandez and Stolfo 1995).It was used successfully on data from the Wel-fare Department of the State of Washington.In other areas, a well-publicized system isIBM’s ADVANCED SCOUT,a specialized data-min-ing system that helps National Basketball As-sociation (NBA) coaches organize and inter-pret data from NBA games (U.S. News 1995). ADVANCED SCOUT was used by several of the NBA teams in 1996, including the Seattle Su-personics, which reached the NBA ﬁnals.Finally, a novel and increasingly importanttype of discovery is one based on the use of in-telligent agents to navigate through an infor-mation-rich environment. Although the ideaof active triggers has long been analyzed in thedatabase ﬁeld, really successful applications ofthis idea appeared only with the advent of theInternet. These systems ask the user to specifya proﬁle of interest and search for related in-formation among a wide variety of public-do-main and proprietary sources. For example, FIREFLY is a personal music-recommendation agent: It asks a user his/her opinion of several music pieces and then suggests other music that the user might like (<http:// www.fﬂ/>). CRAYON(/>) allows users to create their own free newspaper (supported by ads); NEWSHOUND(<http://www. /hound/>) from the San Jose Mercury News and FARCAST(</> automatically search information from a wide variety of sources, including newspapers and wire services, and e-mail rele-vant documents directly to the user.These are just a few of the numerous suchsystems that use KDD techniques to automat-ically produce useful information from largemasses of raw data. See Piatetsky-Shapiro etal. (1996) for an overview of issues in devel-oping industrial KDD applications.Data Mining and KDDHistorically, the notion of ﬁnding useful pat-terns in data has been given a variety ofnames, including data mining, knowledge ex-traction, information discovery, informationharvesting, data archaeology, and data patternprocessing. The term data mining has mostlybeen used by statisticians, data analysts, andthe management information systems (MIS)communities. It has also gained popularity inthe database ﬁeld. The phrase knowledge dis-covery in databases was coined at the ﬁrst KDDworkshop in 1989 (Piatetsky-Shapiro 1991) toemphasize that knowledge is the end productof a data-driven discovery. It has been popular-ized in the AI and machine-learning ﬁelds.In our view, KDD refers to the overall pro-cess of discovering useful knowledge from da-ta, and data mining refers to a particular stepin this process. Data mining is the applicationof speciﬁc algorithms for extracting patternsfrom data. The distinction between the KDDprocess and the data-mining step (within theprocess) is a central point of this article. Theadditional steps in the KDD process, such asdata preparation, data selection, data cleaning,incorporation of appropriate prior knowledge,and proper interpretation of the results ofmining, are essential to ensure that usefulknowledge is derived from the data. Blind ap-plication of data-mining methods (rightly crit-icized as data dredging in the statistical litera-ture) can be a dangerous activity, easilyleading to the discovery of meaningless andinvalid patterns.The Interdisciplinary Nature of KDDKDD has evolved, and continues to evolve,from the intersection of research ﬁelds such asmachine learning, pattern recognition,databases, statistics, AI, knowledge acquisitionfor expert systems, data visualization, andhigh-performance computing. The unifyinggoal is extracting high-level knowledge fromlow-level data in the context of large data sets.The data-mining component of KDD cur-rently relies heavily on known techniquesfrom machine learning, pattern recognition,and statistics to ﬁnd patterns from data in thedata-mining step of the KDD process. A natu-ral question is, How is KDD different from pat-tern recognition or machine learning (and re-lated ﬁelds)? The answer is that these ﬁeldsprovide some of the data-mining methodsthat are used in the data-mining step of theKDD process. KDD focuses on the overall pro-cess of knowledge discovery from data, includ-ing how the data are stored and accessed, howalgorithms can be scaled to massive data setsThe basicproblemaddressed bythe KDDprocess isone ofmappinglow-leveldata intoother formsthat might bemorecompact,moreabstract,or moreuseful.ArticlesFALL 1996 39A driving force behind KDD is the database ﬁeld (the second D in KDD). Indeed, the problem of effective data manipulation when data cannot ﬁt in the main memory is of fun-damental importance to KDD. Database tech-niques for gaining efﬁcient data access,grouping and ordering operations when ac-cessing data, and optimizing queries consti-tute the basics for scaling algorithms to larger data sets. Most data-mining algorithms from statistics, pattern recognition, and machine learning assume data are in the main memo-ry and pay no attention to how the algorithm breaks down if only limited views of the data are possible.A related ﬁeld evolving from databases is data warehousing,which refers to the popular business trend of collecting and cleaning transactional data to make them available for online analysis and decision support. Data warehousing helps set the stage for KDD in two important ways: (1) data cleaning and (2)data access.Data cleaning: As organizations are forced to think about a uniﬁed logical view of the wide variety of data and databases they pos-sess, they have to address the issues of map-ping data to a single naming convention,uniformly representing and handling missing data, and handling noise and errors when possible.Data access: Uniform and well-deﬁned methods must be created for accessing the da-ta and providing access paths to data that were historically difﬁcult to get to (for exam-ple, stored ofﬂine).Once organizations and individuals have solved the problem of how to store and ac-cess their data, the natural next step is the question, What else do we do with all the da-ta? This is where opportunities for KDD natu-rally arise.A popular approach for analysis of data warehouses is called online analytical processing (OLAP), named for a set of principles pro-posed by Codd (1993). OLAP tools focus on providing multidimensional data analysis,which is superior to SQL in computing sum-maries and breakdowns along many dimen-sions. OLAP tools are targeted toward simpli-fying and supporting interactive data analysis,but the goal of KDD tools is to automate as much of the process as possible. Thus, KDD is a step beyond what is currently supported by most standard database systems.Basic DeﬁnitionsKDD is the nontrivial process of identifying valid, novel, potentially useful, and ultimate-and still run efﬁciently, how results can be in-terpreted and visualized, and how the overall man-machine interaction can usefully be modeled and supported. The KDD process can be viewed as a multidisciplinary activity that encompasses techniques beyond the scope of any one particular discipline such as machine learning. In this context, there are clear opportunities for other ﬁelds of AI (be-sides machine learning) to contribute to KDD. KDD places a special emphasis on ﬁnd-ing understandable patterns that can be inter-preted as useful or interesting knowledge.Thus, for example, neural networks, although a powerful modeling tool, are relatively difﬁcult to understand compared to decision trees. KDD also emphasizes scaling and ro-bustness properties of modeling algorithms for large noisy data sets.Related AI research ﬁelds include machine discovery, which targets the discovery of em-pirical laws from observation and experimen-tation (Shrager and Langley 1990) (see Kloes-gen and Zytkow [1996] for a glossary of terms common to KDD and machine discovery),and causal modeling for the inference of causal models from data (Spirtes, Glymour,and Scheines 1993). Statistics in particular has much in common with KDD (see Elder and Pregibon [1996] and Glymour et al.[1996] for a more detailed discussion of this synergy). Knowledge discovery from data is fundamentally a statistical endeavor. Statistics provides a language and framework for quan-tifying the uncertainty that results when one tries to infer general patterns from a particu-lar sample of an overall population. As men-tioned earlier, the term data mining has had negative connotations in statistics since the 1960s when computer-based data analysis techniques were ﬁrst introduced. The concern arose because if one searches long enough in any data set (even randomly generated data),one can ﬁnd patterns that appear to be statis-tically signiﬁcant but, in fact, are not. Clearly,this issue is of fundamental importance to KDD. Substantial progress has been made in recent years in understanding such issues in statistics. Much of this work is of direct rele-vance to KDD. Thus, data mining is a legiti-mate activity as long as one understands how to do it correctly; data mining carried out poorly (without regard to the statistical as-pects of the problem) is to be avoided. KDD can also be viewed as encompassing a broader view of modeling than statistics. KDD aims to provide tools to automate (to the degree pos-sible) the entire process of data analysis and the statistician’s “art” of hypothesis selection.Data mining is a step in the KDD process that consists of ap-plying data analysis and discovery al-gorithms that produce a par-ticular enu-meration ofpatterns (or models)over the data.Articles40AI MAGAZINEly understandable patterns in data (Fayyad, Piatetsky-Shapiro, and Smyth 1996).Here, data are a set of facts (for example, cases in a database), and pattern is an expres-sion in some language describing a subset of the data or a model applicable to the subset. Hence, in our usage here, extracting a pattern also designates ﬁtting a model to data; ﬁnd-ing structure from data; or, in general, mak-ing any high-level description of a set of data. The term process implies that KDD comprises many steps, which involve data preparation, search for patterns, knowledge evaluation, and reﬁnement, all repeated in multiple itera-tions. By nontrivial, we mean that some search or inference is involved; that is, it is not a straightforward computation of predeﬁned quantities like computing the av-erage value of a set of numbers.The discovered patterns should be valid on new data with some degree of certainty. We also want patterns to be novel (at least to the system and preferably to the user) and poten-tially useful, that is, lead to some beneﬁt to the user or task. Finally, the patterns should be understandable, if not immediately then after some postprocessing.The previous discussion implies that we can deﬁne quantitative measures for evaluating extracted patterns. In many cases, it is possi-ble to deﬁne measures of certainty (for exam-ple, estimated prediction accuracy on new data) or utility (for example, gain, perhaps indollars saved because of better predictions orspeedup in response time of a system). No-tions such as novelty and understandabilityare much more subjective. In certain contexts,understandability can be estimated by sim-plicity (for example, the number of bits to de-scribe a pattern). An important notion, calledinterestingness(for example, see Silberschatzand Tuzhilin [1995] and Piatetsky-Shapiro andMatheus [1994]), is usually taken as an overallmeasure of pattern value, combining validity,novelty, usefulness, and simplicity. Interest-ingness functions can be deﬁned explicitly orcan be manifested implicitly through an or-dering placed by the KDD system on the dis-covered patterns or models.Given these notions, we can consider apattern to be knowledge if it exceeds some in-terestingness threshold, which is by nomeans an attempt to deﬁne knowledge in thephilosophical or even the popular view. As amatter of fact, knowledge in this deﬁnition ispurely user oriented and domain speciﬁc andis determined by whatever functions andthresholds the user chooses.Data mining is a step in the KDD processthat consists of applying data analysis anddiscovery algorithms that, under acceptablecomputational efﬁciency limitations, pro-duce a particular enumeration of patterns (ormodels) over the data. Note that the space ofArticlesFALL 1996 41Figure 1. An Overview of the Steps That Compose the KDD Process.methods, the effective number of variables under consideration can be reduced, or in-variant representations for the data can be found.Fifth is matching the goals of the KDD pro-cess (step 1) to a particular data-mining method. For example, summarization, clas-siﬁcation, regression, clustering, and so on,are described later as well as in Fayyad, Piatet-sky-Shapiro, and Smyth (1996).Sixth is exploratory analysis and model and hypothesis selection: choosing the data-mining algorithm(s) and selecting method(s)to be used for searching for data patterns.This process includes deciding which models and parameters might be appropriate (for ex-ample, models of categorical data are differ-ent than models of vectors over the reals) and matching a particular data-mining method with the overall criteria of the KDD process (for example, the end user might be more in-terested in understanding the model than its predictive capabilities).Seventh is data mining: searching for pat-terns of interest in a particular representa-tional form or a set of such representations,including classiﬁcation rules or trees, regres-sion, and clustering. The user can signiﬁcant-ly aid the data-mining method by correctly performing the preceding steps.Eighth is interpreting mined patterns, pos-sibly returning to any of steps 1 through 7 for further iteration. This step can also involve visualization of the extracted patterns and models or visualization of the data given the extracted models.Ninth is acting on the discovered knowl-edge: using the knowledge directly, incorpo-rating the knowledge into another system for further action, or simply documenting it and reporting it to interested parties. This process also includes checking for and resolving po-tential conﬂicts with previously believed (or extracted) knowledge.The KDD process can involve signiﬁcant iteration and can contain loops between any two steps. The basic ﬂow of steps (al-though not the potential multitude of itera-tions and loops) is illustrated in ﬁgure 1.Most previous work on KDD has focused on step 7, the data mining. However, the other steps are as important (and probably more so) for the successful application of KDD in practice. Having deﬁned the basic notions and introduced the KDD process, we now focus on the data-mining component,which has, by far, received the most atten-tion in the literature.patterns is often inﬁnite, and the enumera-tion of patterns involves some form of search in this space. Practical computational constraints place severe limits on the sub-space that can be explored by a data-mining algorithm.The KDD process involves using the database along with any required selection,preprocessing, subsampling, and transforma-tions of it; applying data-mining methods (algorithms) to enumerate patterns from it;and evaluating the products of data mining to identify the subset of the enumerated pat-terns deemed knowledge. The data-mining component of the KDD process is concerned with the algorithmic means by which pat-terns are extracted and enumerated from da-ta. The overall KDD process (ﬁgure 1) in-cludes the evaluation and possible interpretation of the mined patterns to de-termine which patterns can be considered new knowledge. The KDD process also in-cludes all the additional steps described in the next section.The notion of an overall user-driven pro-cess is not unique to KDD: analogous propos-als have been put forward both in statistics (Hand 1994) and in machine learning (Brod-ley and Smyth 1996).The KDD ProcessThe KDD process is interactive and iterative,involving numerous steps with many deci-sions made by the user. Brachman and Anand (1996) give a practical view of the KDD pro-cess, emphasizing the interactive nature of the process. Here, we broadly outline some of its basic steps:First is developing an understanding of the application domain and the relevant prior knowledge and identifying the goal of the KDD process from the customer’s viewpoint.Second is creating a target data set: select-ing a data set, or focusing on a subset of vari-ables or data samples, on which discovery is to be performed.Third is data cleaning and preprocessing.Basic operations include removing noise if appropriate, collecting the necessary informa-tion to model or account for noise, deciding on strategies for handling missing data ﬁelds,and accounting for time-sequence informa-tion and known changes.Fourth is data reduction and projection:ﬁnding useful features to represent the data depending on the goal of the task. With di-mensionality reduction or transformationArticles42AI MAGAZINEThe Data-Mining Stepof the KDD ProcessThe data-mining component of the KDD pro-cess often involves repeated iterative applica-tion of particular data-mining methods. This section presents an overview of the primary goals of data mining, a description of the methods used to address these goals, and a brief description of the data-mining algo-rithms that incorporate these methods.The knowledge discovery goals are deﬁned by the intended use of the system. We can distinguish two types of goals: (1) veriﬁcation and (2) discovery. With veriﬁcation,the sys-tem is limited to verifying the user’s hypothe-sis. With discovery,the system autonomously ﬁnds new patterns. We further subdivide the discovery goal into prediction,where the sys-tem ﬁnds patterns for predicting the future behavior of some entities, and description, where the system ﬁnds patterns for presenta-tion to a user in a human-understandableform. In this article, we are primarily con-cerned with discovery-oriented data mining.Data mining involves ﬁtting models to, or determining patterns from, observed data. The ﬁtted models play the role of inferred knowledge: Whether the models reﬂect useful or interesting knowledge is part of the over-all, interactive KDD process where subjective human judgment is typically required. Two primary mathematical formalisms are used in model ﬁtting: (1) statistical and (2) logical. The statistical approach allows for nondeter-ministic effects in the model, whereas a logi-cal model is purely deterministic. We focus primarily on the statistical approach to data mining, which tends to be the most widely used basis for practical data-mining applica-tions given the typical presence of uncertain-ty in real-world data-generating processes.Most data-mining methods are based on tried and tested techniques from machine learning, pattern recognition, and statistics: classiﬁcation, clustering, regression, and so on. The array of different algorithms under each of these headings can often be bewilder-ing to both the novice and the experienced data analyst. It should be emphasized that of the many data-mining methods advertised in the literature, there are really only a few fun-damental techniques. The actual underlying model representation being used by a particu-lar method typically comes from a composi-tion of a small number of well-known op-tions: polynomials, splines, kernel and basis functions, threshold-Boolean functions, and so on. Thus, algorithms tend to differ primar-ily in the goodness-of-ﬁt criterion used toevaluate model ﬁt or in the search methodused to ﬁnd a good ﬁt.In our brief overview of data-mining meth-ods, we try in particular to convey the notionthat most (if not all) methods can be viewedas extensions or hybrids of a few basic tech-niques and principles. We ﬁrst discuss the pri-mary methods of data mining and then showthat the data- mining methods can be viewedas consisting of three primary algorithmiccomponents: (1) model representation, (2)model evaluation, and (3) search. In the dis-cussion of KDD and data-mining methods,we use a simple example to make some of thenotions more concrete. Figure 2 shows a sim-ple two-dimensional artiﬁcial data set consist-ing of 23 cases. Each point on the graph rep-resents a person who has been given a loanby a particular bank at some time in the past.The horizontal axis represents the income ofthe person; the vertical axis represents the to-tal personal debt of the person (mortgage, carpayments, and so on). The data have beenclassiﬁed into two classes: (1) the x’s repre-sent persons who have defaulted on theirloans and (2) the o’s represent persons whoseloans are in good status with the bank. Thus,this simple artiﬁcial data set could represent ahistorical data set that can contain usefulknowledge from the point of view of thebank making the loans. Note that in actualKDD applications, there are typically manymore dimensions (as many as several hun-dreds) and many more data points (manythousands or even millions).ArticlesFALL 1996 43Figure 2. A Simple Data Set with Two Classes Used for Illustrative Purposes.。

Machine Learning and Data Mining

Machine Learning and Data Mining Machine learning and data mining are two of the most important fields in computer science today. With the increasing amount of data being generated every day, it has become essential to develop tools and techniques that can help us extract meaningful insights from this data. Both machine learning and data mining are concerned with using algorithms and statistical models to analyze data and make predictions based on patterns and trends. Machine learning is a subset of artificial intelligence that focuses on developing algorithms that can learn from data. These algorithms are designed to automatically improve their performance over time as they are exposed to more data. Machine learning is used in a wide range of applications, from image recognition and natural language processing to fraud detection and recommendation systems. Data mining, on the other hand, is the process of discovering patterns and relationships in large datasets. It involves using statistical techniques and machine learning algorithms to identify hidden patterns and trends in data that can be used to make predictions or inform decision-making. Data mining is used in a variety of fields, including marketing, finance, healthcare, and social sciences. One of the main challenges in both machine learning and data mining is dealing with the sheer volume of data that is generated every day. With the rise of big data, it has become increasinglydifficult to process and analyze data using traditional methods. This has led to the development of new techniques and algorithms that are designed to handle large datasets and extract insights from them. Another challenge in both fields is ensuring the accuracy and reliability of the results. Machine learning algorithms are only as good as the data they are trained on, so it is important to ensurethat the data is representative and unbiased. Similarly, data mining algorithms can produce misleading results if the data is not properly cleaned and preprocessed. Despite these challenges, machine learning and data mining have the potential to revolutionize many industries and fields. In healthcare, for example, machine learning algorithms can be used to analyze medical images and identify early signs of disease. In finance, data mining can be used to detect fraudulent transactions and identify patterns in financial data that can be used to make better investment decisions. Overall, machine learning and data mining are two ofthe most exciting and rapidly evolving fields in computer science today. While there are still many challenges to overcome, the potential benefits are enormous, and we can expect to see many new applications and breakthroughs in the coming years. As we continue to generate more data, the need for these tools and techniques will only continue to grow, making machine learning and data mining essential skills for anyone working in technology or data-driven fields.。

如何使用随机森林进行时间序列数据挖掘(Ⅱ)

时间序列数据挖掘在当今的数据分析领域中扮演着至关重要的角色。

随机森林是一种强大的机器学习算法，它在时间序列数据挖掘中也有着广泛的应用。

本文将介绍如何使用随机森林进行时间序列数据挖掘，包括数据准备、模型训练和评估等方面。

1. 时间序列数据简介时间序列数据是按时间顺序排列的一系列数据点的集合。

在时间序列数据挖掘中，我们通常关心的是数据点随时间变化的规律和趋势。

比如股票价格、气温变化、销售额等都可以看作时间序列数据。

为了更好地理解时间序列数据，我们需要先对其进行可视化和描述性统计分析，从而更好地把握数据的特点和规律。

2. 随机森林简介随机森林是一种集成学习算法，它通过集成多个决策树来进行预测。

在随机森林中，每棵决策树都是基于随机选择的数据子集和特征子集进行训练的。

这种随机性的引入可以有效地减少过拟合，提高模型的泛化能力。

随机森林在处理高维数据和大规模数据时表现出色，同时也对缺失值和异常值具有较强的鲁棒性。

3. 时间序列数据预处理在使用随机森林进行时间序列数据挖掘之前，我们需要对数据进行预处理。

首先，我们要对时间序列数据进行平稳性检验，确保数据的平稳性。

平稳性是时间序列分析的基本假设，平稳的时间序列数据更容易建立模型和进行预测。

其次，我们需要对数据进行差分处理，将非平稳时间序列数据转化为平稳时间序列数据。

最后，我们还需要对数据进行缺失值和异常值的处理，确保数据的完整性和准确性。

4. 时间序列数据特征提取在进行时间序列数据挖掘时，我们通常需要提取一些特征来描述数据的规律和趋势。

常用的时间序列数据特征包括均值、方差、自相关系数、滞后相关系数等。

这些特征可以帮助我们更好地理解数据的性质和结构，为模型训练提供有力支持。

5. 随机森林模型训练在进行随机森林模型训练时，我们首先需要将时间序列数据转化为监督学习的数据集。

通常采用滑动窗口法或者特征滞后法来构建监督学习数据集。

然后，我们可以使用Python中的scikit-learn库来构建随机森林模型，并进行模型训练。

时间序列数据挖掘中相似性和趋势预测的研究

时间序列数据挖掘中相似性和趋势预测的研究时间序列是指按照时间顺序进行排列的一组数据，具有非常广泛的应用，包括经济预测、环境监测、医疗诊断等领域。

时间序列数据挖掘是指通过机器学习、数据挖掘等方法，对于时间序列数据进行分析和处理，以达到对数据的深度理解、事件预测、系统优化等目的。

其中，相似性分析和趋势预测是时间序列数据挖掘中的两个重要方面，本文将着重对这两个方面进行综述和分析。

一、相似性分析相似性分析是对于时间序列中的不同数据进行比较和匹配，以寻找数据之间的相似性和相关性。

在时间序列数据挖掘中，相似性分析有非常广泛的应用，包括图像和声音识别、交通流量预测等。

下面我们将从数据表示、距离度量、相似性度量、采样率和插值等几个方面来讨论相似性分析的方法和技术。

1.数据表示对于时间序列数据的表示，常见的方式包括时间区间和时间点。

时间区间表示是指将时间序列数据分段表示，每一段代表一个时间区间的数据；时间点表示则是在时间轴上标注数据采集的时间戳，随着采集时间的增加，时间序列也在不断地增加。

时间区间表示的优点在于可以更好地处理时序数据的不确定性和噪声，但需要更多的计算资源；时间点表示则更直观和易于理解，但需要特殊处理不规则或不完整的数据。

根据具体应用场景和数据的特点，选择合适的数据表示方法非常重要。

2.距离度量距离度量是指对于两个时间序列的距离进行计算的方法。

常见的距离度量包括欧氏距离、曼哈顿距离、切比雪夫距离等，具体选择方法要根据数据特征进行处理。

例如，在处理具有线性关系的数据时可以使用欧氏距离；而在处理非线性数据时则可以使用切比雪夫距离。

3.相似性度量相似性度量是指对于两个时间序列相似性程度进行计算的方法。

常见的相似性分析方法包括最近邻方法、K-Means聚类和模式匹配等。

最近邻方法是指寻找与目标时间序列最相似的历史序列，并将其作为预测结果的依据。

K-Means聚类是指对于时间序列进行聚类分析，确定各个聚类中心，以此来寻找相似性更高的时间序列。

如何使用随机森林进行时间序列数据挖掘

随机森林是一种强大的机器学习算法，它可以被用来进行时间序列数据挖掘。

在本文中，我们将深入探讨如何使用随机森林这一算法来处理时间序列数据，并解释其中的原理和方法。

### 1. 介绍随机森林随机森林是一种集成学习方法，它结合了多个决策树来进行预测。

每个决策树都是基于不同的随机样本和特征进行训练的，然后通过投票或取平均值的方式来进行预测。

这使得随机森林能够有效地避免过拟合，并且对于大规模数据具有很高的准确性和鲁棒性。

### 2. 应用随机森林进行时间序列数据挖掘在时间序列数据挖掘中，我们通常需要预测未来的数值或者趋势。

随机森林可以很好地应用在这个领域，以下是一些使用随机森林进行时间序列数据挖掘的步骤和技巧：#### 数据准备首先，我们需要准备我们的时间序列数据。

这包括收集历史数据、对数据进行清洗和预处理等步骤。

确保数据的质量和完整性对于建立准确的模型非常重要。

#### 特征选择在时间序列数据中，通常会有很多特征，但并非所有的特征都对于预测具有重要性。

因此，我们需要对特征进行选择和筛选，以便提高模型的准确性和效率。

随机森林可以通过特征重要性评估来帮助我们选择最重要的特征。

#### 构建模型接下来，我们可以使用随机森林算法来构建预测模型。

在这一步骤中，我们需要将数据集分为训练集和测试集，然后使用训练集来训练模型。

随机森林可以轻松处理大规模数据，并且不需要对数据进行太多的预处理，因此非常适合时间序列数据挖掘。

#### 参数调优随机森林有一些参数需要进行调优，例如树的数量、最大深度、特征选择等。

通过交叉验证和网格搜索等方法，我们可以找到最佳的参数组合，以提高模型的性能和鲁棒性。

#### 模型评估最后，我们需要对模型进行评估。

通过对测试集的预测结果进行比较和分析，我们可以得出模型的准确性、精确度和召回率等指标，从而判断模型的优劣，并对其进行改进和优化。

### 3. 随机森林在时间序列数据挖掘中的优势相比于其他传统的时间序列数据挖掘方法，随机森林具有一些明显的优势：- 对缺失值和异常值具有很好的鲁棒性，不需要过多的数据预处理- 能够自动处理特征之间的相关性和非线性关系- 不需要对数据进行平稳性处理，适用于非平稳的时间序列数据- 能够处理大规模和高维度的数据，速度快且准确度高### 4. 结论通过本文的介绍，我们了解到了随机森林在时间序列数据挖掘中的应用方法和优势。

数据挖掘多元时间序列概念

数据挖掘多元时间序列概念数据挖掘多元时间序列概念随着信息技术的发展，人们对于数据的需求也越来越高。

在海量数据中，时间序列数据是一种非常重要的数据类型。

时间序列是按照时间顺序排列的一组连续观测值，它反映了某个现象随时间变化的规律性。

而多元时间序列则是指在同一个时间点上，有多个变量同时被观测到。

因此，如何对多元时间序列进行挖掘和分析成为了当前研究的热点之一。

一、多元时间序列概述1.1 时间序列定义时间序列是指按照固定频率或不规则频率记录下来的某个现象在不同时刻的取值。

1.2 多元时间序列定义多元时间序列是指在同一个时刻上，对于不止一个变量进行观测并记录下来。

1.3 多元时间序列特点（1）具有高维度：每个时刻都有不止一个变量被观测到。

（2）具有相关性：不同变量之间存在着相关关系。

（3）具有动态性：随着时间推移，每个变量都会发生变化。

二、多元时间序列分析方法2.1 传统分析方法传统的多元时间序列分析方法主要包括时间序列分解、平稳性检验、自回归移动平均模型（ARMA）等。

时间序列分解是将一个时间序列拆分成趋势、季节和随机成分三个部分，以便更好地理解和预测数据。

平稳性检验是判断一个时间序列是否平稳的方法，如果不平稳，则需要对其进行差分或者其他预处理方式。

ARMA模型则是一种常用的预测模型，它将时间序列看作是自回归和移动平均两个过程的组合。

2.2 数据挖掘方法数据挖掘方法主要包括聚类、分类、关联规则挖掘等。

这些方法可以对多元时间序列进行分类和预测，并发现其中隐藏的规律。

聚类是将相似的数据点划分到同一组中，可以帮助我们发现多元时间序列中不同变量之间存在的相似性。

分类则是将样本划分到不同的类别中，可以用于预测未来发展趋势。

关联规则挖掘则可以发现多元时间序列中变量之间存在的关系，例如某个变量增加时其他变量是否也会跟着增加。

三、多元时间序列应用领域3.1 金融领域在金融领域，多元时间序列可以用于股票价格预测、风险控制等方面。

对恒星进行数据挖掘：改变天文学的虚拟化望远镜

斯隆数字巡天计划生成的超过15TB的可查询数据使天文学家能够在研究项目上少花数年的时间。

在20世纪90年代，天体物理学家Alex Szalay博士和计算机科学家Jim Gray博士集展开了这样一项头脑风暴：如果数据库可以变成一个数据望远镜，这个望远镜可以进行数据挖掘会怎么样?如果可以自由使用这样的数据，天文学领域将发生彻底的改变。

随着时间的推移，这个想法变成了斯隆数字巡天(SDSS)，这是一个由数十家机构的数百名科学家组成的国际合作组织。

斯隆数字巡天的目标是使用位于新墨西哥州Apache Point天文台的专用2.5米望远镜对星空编制索引。

配备 1.2亿像素摄像头的望远镜可拍摄超过四分之一的夜空，一次拍摄1.5平方度(1.5 square degrees at a time)。

该项目使用Microsoft SQL Server作为后端数据库。

大数据从1998年到2009年间，望远镜同时在成像模式和光谱模式下运行。

斯隆数字巡天于2009年停止使用成像相机，但望远镜仍继续以光谱模式进行观测活动。

数据可通过SkyServer数据库(在线门户网站)公开获取。

如今，该数据库拥有15TB可查询的公共数据集，以及大约150TB的额外原始文件和校准文件。

将恒星数字化约翰霍普金斯大学文理学院和惠廷工程学院的彭博物理学、天文学和计算机科学教授Szalay解释说：“在传统的天文学中，项目的想法是由天文学家提出来的，但首先，他们需要找到目标。

”在斯隆数字巡天还没有成立之前，这是一个耗时的过程。

天文学家必须写提案并选择大面积的空域来探索可能的目标，对想法进行测试。

如果提案被接受，天文学家就可以预约使用望远镜的时间。

Szalay说：“在长达半年的时间里，你只要有空就会去山顶的天文台。

如果你很幸运，适逢那天天晴且无云，你就能将一些数据带回去。

”Szalay说，自此，天文学家可能要花几个月的时间对这些数据进行图像处理，也许会发现几百个目标。

恒星初始质量函数

恒星初始质量函数1. 引言恒星初始质量函数（Initial Mass Function，简称IMF）是指在星际物质坍缩形成恒星时，不同质量范围内恒星的数量分布函数。

研究恒星初始质量函数对于理解星际物质形成和演化过程以及了解星系结构和演化有着重要的意义。

本文将详细探讨恒星初始质量函数的定义、研究方法、主要结果及其意义。

2. 恒星初始质量函数的定义恒星初始质量函数是指在一个星团或星系中，恒星在形成时的初始质量分布。

它描述了不同质量范围内恒星的数量分布，通常以某种形式的概率密度函数来表示。

恒星初始质量函数的表达式可以采用不同形式，如光学和红外观测可用于计算的Kroupa IMF、Salpeter IMF等。

3. 研究方法研究恒星初始质量函数的方法通常采用观测、数值模拟和理论分析相结合的方式。

3.1 观测方法观测方法是通过对星际物质中的恒星进行观测和统计分析来得到恒星初始质量函数。

光学、红外和射电波段的观测提供了测量星等和光谱信息的手段，从而获得恒星质量的估计。

此外，通过对星团和星系的成员进行观测和成员筛选，可以得到不同质量范围内的恒星数量。

3.2 数值模拟方法数值模拟方法通过对星云坍缩和恒星形成过程进行数值模拟，模拟初始质量函数的形成机制。

这种方法基于物理方程和初始条件，通过数值计算来模拟星际物质的演化过程，包括重力坍缩、物质输运和恒星形成等过程。

通过对模拟结果的统计分析，可以得到模拟的恒星初始质量函数。

3.3 理论分析方法理论分析方法通过建立恒星形成理论模型，将星际物质的性质与恒星初始质量函数联系起来。

通过分析不同物理过程的作用，可以得到恒星初始质量函数的理论预测。

这种方法依赖于对恒星形成过程的理解和对星际物质性质的研究。

4. 主要结果研究表明，恒星初始质量函数在不同星团和星系中具有相似的形式，即质量范围内恒星数量随质量的幂律分布。

4.1 Kroupa IMFKroupa IMF是一种常用的恒星初始质量函数，它采用分段的形式，分别描述了低质量和高质量范围内的恒星数量分布。

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FFT coefficient vlaues.
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Australian National University, Canberra, ACT 0200, Australia CRC for Advanced Computational Systems, CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra, ACT 2601, Australia
Fig. 1.
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The color magnitude diagram of 20383 stars from the MACHO database. Each dot represents a star. The crosses are the candidates of variable stars determined by the variable index. The circles are the identified variable stars.
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The graph on the left side shows the plots of the FFT coefficients of stars in 3 clusters. The graph on the right side shows the plots of the FFT coefficients of stars in a randomly selected group.
Data-Mining Massive Time Series Astronomical Data Sets a Case Study
Michael K. Ng1 Zhexue Huang2 Markus Hegland3
1 Department of Mathematics, The University of Hong Kong, Pokfulam Road, H.K. 2 CRC for Advanced Computational Systems, Computer Sciences Laboratory, The 3
Fig. 2.
Acknowledgments: The authors wish to acknowledge that this work was carried out within the Cooperative Research Centre for Advanced Computational Systems established under the Australian Government's Cooperative Research Centres Program. The authors thank Dr T. Axelrod at MSSSO for providing us the sample data
In this paper we present a new application of data mining techniques to massive astronomical data sets. Previous data mining applications deal with time-independent multiple spectral astronomical data 2 . We are concerned with time series astronomical data. More precisely, our data consists of N time series, each with a duration of M days. The data set can be viewed as an N M matrix in which rows are di erent time series and the ordered columns correspond to consecutive time points when measurements were made. Our primary objective of mining such data is to classify the time series according to their morphology and to identify classes which may carry some special signature of morphology. The real data in this application consists of 40 million time series, each representing a sequence of brightness light curve of a star measured in one of two spectral bands on a daily basis in the MACHO project 1 . Totally, about 20 million stars i.e., N 2 107 have been measured in the past four years. More than half a terabyte of time series data has resulted. The scienti c discovery tasks in our data mining exercise are to discover new variable stars and to identify microlensing events represented in some star light curves. There are a number of big challenges in mining such a large time series database. The size of the data is an obvious one which is always of concern. The time dimension is another challenge which is not concerned in the other astronomical data mining applications 2 . The high dimensionality i.e., M 1500 and the varying phase factor of the time series make it hard to mine the data in the time domain. The potentially costly transformation of a large number of time series to some feature domain is inevitable. Selection of suitable features for appropriate representation of these time series in terms of conciseness and accuracy is one of the research problems. The data is far from error-free. Noise, invalid measurements and missing values exist in every time series. The burden of preprocessing and massaging the data is tremendous. All these problems have to be solved with di erent techniques before classi cation is performed. The classi cation is based on dissimilarity of the star light curves. The distance measure in the frequency domain between two stars is used. After star light curves are converted to vectors in the feature spaces, we run the k-means algorithm hierarchically over a set of star feature vectors. We use some visual techniques to verify our clusters. To verify the similarity of stars within clusters and the dissimilarity of stars among clusters in the feature space, we display
the FFT coe cients of all stars in di erent clusters. The graph on the left side of Figure 1 shows three clusters produced based on the FFT coe cients. Each cluster is represented as a smooth surface which indicates that stars are similar in the clusters. One can also see that the three surfaces are quite distinguishable, which means that the stars in di erent clusters are quite dissimilar. The graph on the right side of Figure 1 shows a group of stars which were randomly selected from the variable stars. Because the stars in this group are not clustered according to dissimilarity measure, the surface of this group is very rough, which implies that the stars in this group belong to di erent clusters. We have also implemented other visualization tools to show star light curves in the time domain and found these tools are very useful in verifying clustering results and identifying variable stars. Figure 2 shows some variable stars identi ed using our clustering method and visualization tools from 360 variable candidates selected from about 20000 stars according to the variable de ned by astronomers.