Association Rules
Association_Rule
Support: 2/8
Confidence: 1/3
Milk Bread
Support: 2/8 Confidence: 2/3
Frequent Itemsets and Strong Rules
Support and Confidence are bounded by thresholds:
C3 {{1, 2,3}}
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Lk Ck+1
{X Yk | X , Y Lk , X i Yi , i [1, k 1], X k Yk }
Ordered List
L2 {{1, 2},{2,3}} L2 {{1,3},{2,3}} L2 {{1, 2},{1,3},{2,3}} L2 {{1, 2},{1,3}}
Searching for rules in the form of: Bread Butter
6
7
Support of an Itemset
Itemset
Bread
Butter Chips Jelly
Support
6/8
3/8 2/8 3/8
Itemset
Bread, Butter
Support
Minimum support σ
Minimum confidence Φ A frequent (large) itemset is an itemset with support larger than σ. A strong rule is a rule that is frequent and its confidence is higher than Φ. Association Rule Problem Given I, D, σ and Φ, to find all strong rules in the form of XY. The number of all possible association rules is huge. Brute force strategy is infeasible. A smart way is to find frequent itemsets first.
关于规则的英语作文
Rules are an integral part of our daily lives,providing structure and order to society. They exist in various forms and are essential for maintaining harmony and ensuring the smooth functioning of communities,organizations,and even nations.Importance of Rules1.Safety and Security:Rules are designed to protect individuals from harm.For instance, traffic laws ensure that roads are safe for all users,reducing the risk of accidents.2.Order and Organization:In schools,rules help maintain discipline and a conducive learning environment.Without rules,chaos could ensue,making it difficult for students to focus and learn effectively.3.Fairness and Equality:Rules often serve to create a level playing field,ensuring that everyone is treated equally.This is particularly important in competitive environments, such as sports or academic settings.4.Efficiency and Productivity:In the workplace,rules and regulations help streamline processes,leading to increased efficiency and productivity.Types of Rulesws:These are formal rules set by the government and enforced by legal systems. They govern a wide range of activities,from criminal behavior to taxation.2.Social Norms:These are unwritten rules that dictate appropriate behavior in social situations.They can vary greatly between cultures and are learned through observation and experience.3.Institutional Rules:These are the rules set by organizations,such as schools, companies,or clubs.They are designed to ensure the smooth operation of the institution and the wellbeing of its members.4.Personal Rules:Individuals may have their own set of rules that guide their behavior and decisionmaking.These can be based on personal values,beliefs,or goals. Adhering to Rules1.Understanding the Purpose:Its important to understand why a rule exists before deciding to follow it.This can help in accepting the necessity of the rule and adhering toit willingly.2.Respecting Authority:Rules are often set by those in authority,and respecting this authority is crucial for maintaining social order.3.Consequences of Noncompliance:Being aware of the potential consequences of breaking a rule can be a strong motivator for compliance.4.Personal Responsibility:Each individual has a responsibility to follow rules,not just for their own benefit but for the benefit of the community as a whole.Challenges with Rules1.Rigidity:Sometimes,rules can be too rigid,not allowing for flexibility in certain situations,which may lead to frustration or conflict.2.Inequality:Rules can sometimes be biased or unfair,favoring certain groups over others,leading to social injustice.plexity:In some cases,the complexity of rules can make it difficult for individuals to understand and comply with them,leading to unintentional rulebreaking.ConclusionWhile rules are necessary for the functioning of society,its also important to periodically review and update them to ensure they remain relevant and fair.As members of society, we have a role to play in both following and contributing to the development of rules that benefit everyone.By doing so,we can create a more harmonious and efficient world.。
数据挖掘方法——关联规则(自己整理)
小结：Apriori算法可以分为频繁项集的生成和关联规则的生成两 大步骤；FP-Growth算法可以分成FP-Tree的生成，频繁项集的生成和 关联规则的生成3大步骤。
Copyright © 2009, MANAGEMENT SCIENCE ASSOCIATES, INC.
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五、关联规则挖掘的相关算法
Copyright © 2009, MANAGEMENT SCIENCE ASSOCIATES, INC.
Copyright © 2009, MANAGEMENT SCIENCE ASSOCIATES, INC.
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五、关联规则挖掘的相关算法
1.Apriori算法：使用候选项集找频繁项集 Apriori算法是一种最有影响的挖掘布尔关联规则频繁项集的算法。其核心是 基于两阶段频集思想的递推算法。该关联规则在分类上属于单维、单层、布尔关 联规则。在这里，所有支持度大于最小支持度的项集称为频繁项集，简称频集。 该算法的基本思想是：首先找出所有的频集，这些项集出现的频繁性至少和 预定义的最小支持度一样。然后由频集产生强关联规则，这些规则必须满足最小 支持度和最小可信度。然后使用第1步找到的频集产生期望的规则，产生只包含集 合的项的所有规则，其中每一条规则的右部只有一项，这里采用的是中规则的定 义。一旦这些规则被生成，那么只有那些大于用户给定的最小可信度的规则才被 留下来。为了生成所有频集，使用了递推的方法。 Apriori算法可以产生相对较小的候选项目集，扫描数据库的次数由最大频繁 项目集的项目数决定。因此，该算法适合于最大频繁项目集相对较小的数据集中 的关联规则挖掘问题。 Apriori算法的两大缺点:1.可能产生大量的候选集；2.可能需要重复扫描数据库。
关联分析的目的：找出数据库中隐藏的关联网。一般用Support(支 持度)和Confidence(可信度)两个阀值来度量关联规则的相关性，引入 lift(提高度或兴趣度）、相关性等参数，使得所挖掘的规则更符合需求。
公平恪守道德的英语作文
Adherence to morality is a cornerstone of a fair society.In an essay that emphasizes the importance of moral integrity,one might explore various aspects of how moral principles guide our actions and decisions,leading to a just and equitable environment.Title:Upholding Morality for a Fair SocietyIn the pursuit of fairness,morality plays an indispensable role.It is the compass that guides our actions and decisions,ensuring that we treat others with respect and dignity.A society that is grounded in moral principles is one where justice is not just a concept,but a reality that is lived and breathed by its citizens.The Foundation of MoralityMorality is the set of principles or rules that distinguish right from wrong.It is the ethical framework that we use to evaluate our actions and the actions of others.In a fair society, these principles are not just personal beliefs but are collectively agreed upon and upheld by all members of the community.Integrity and TrustIntegrity is a key component of morality.It is the quality of being honest and having strong moral principles.When individuals act with integrity,they build trust within their community.This trust is essential for a fair society,as it fosters cooperation and collaboration,allowing for the equitable distribution of resources and opportunities.Justice and FairnessJustice is the fair and impartial treatment of all members of a society.It is closely linked to morality,as moral principles guide our understanding of what is fair and just.A society that is committed to justice ensures that all individuals have equal access to opportunities and are protected under the law,regardless of their background or status. The Role of EducationEducation is a powerful tool in instilling moral values.Through education,we can teach the principles of fairness,respect,and empathy.By learning about different cultures and perspectives,we can develop a deeper understanding of the importance of treating others with dignity and respect.The Impact of Moral LeadershipLeaders play a crucial role in setting the moral tone of a society.When leaders act with integrity and fairness,they inspire others to do the same.This sets a standard for behavior that permeates throughout the community,creating a culture of moral responsibility and ethical conduct.Challenges and SolutionsDespite the importance of morality,there are challenges in maintaining a fair society. Corruption,discrimination,and inequality can undermine moral principles.To combat these issues,societies must implement strong legal frameworks,promote transparency, and encourage active citizen participation in governance.ConclusionIn conclusion,the adherence to moral principles is essential for creating a fair society.It is through our collective commitment to integrity,justice,and education that we can build a world where fairness is not just an ideal,but a lived experience for all.By embracing our moral responsibilities,we can work towards a future where every individual is treated with the respect and dignity they deserve.。
Top Down FP-Growth for Association Rule Mining
M.-S. Chen, P.S. Yu, and B. Liu (Eds.): PAKDD 2002, LNAI 2336, pp. 334-340, 2002.© Springer-Verlag Berlin Heidelberg 2002Top Down FP-Growth for Association Rule MiningKe Wang, Liu Tang, Jiawei Han, and Junqiang LiuSchool of Computing Science, Simon Fraser University {wangk, llt, han, jliui}@cs.sfu.caAbstract. In this paper, we propose an efficient algorithm, called TD-FP-Growth (the shorthand for Top-Down FP-Growth), to mine frequent patterns.TD-FP-Growth searches the FP-tree in the top-down order, as opposed to the bottom-up order of previously proposed FP-Growth. The advantage of the top-down search is not generating conditional pattern bases and sub-FP-trees, thus,saving substantial amount of time and space. We extend TD-FP-Growth to mine association rules by applying two new pruning strategies: one is to push multiple minimum supports and the other is to push the minimum confidence.Experiments show that these algorithms and strategies are highly effective in reducing the search space.1 IntroductionAssociation rule mining has many important applications in real life. An association rule represents an interesting relationship written as B A ⇒, read as “if A occurs,then B likely occurs”. The probability that both A and B occur is called the support ,and written as count (AB). The probability that B occurs given that A has occurred is called the confidence . The association rule mining problem is to find all association rules above the user-specified minimum support and minimum confidence. This is done in two steps: step 1, find all frequent patterns ; step 2, generate association rules from frequent patterns .This two-step mining approach suffers from several drawbacks. First, only a single uniform minimum support is used, though the distribution of data in reality is not uniform. Second, the two-step process does not consider the confidence constraint at all during the first step. Pushing the confidence constraint into the first step can further reduce search space and hence improve efficiency.In this paper, we develop a family of algorithms, called TD-FP-Growth , for mining frequent patterns and association rules. Instead of exploring the FP-tree in the bottom-up order as in [5], TD-FP-Growth explores the FP-tree in the top-down order. The advantage of the top-down search is not constructing conditional pattern bases and sub-trees as in [5]. We then extend TD-FP-Growth to mine association rules by applying two new pruning strategies: TD-FP-Growth(M) pushes multiple minimum supports and TD-FP-Growth(C) pushes the minimum confidence.2 Related WorkSince its introduction [1], the problem of mining association rules has been the subject of many studies [8][9][10][11]. The most well known method is the Apriori’s anti-monotone strategy for finding frequent patterns [3]. However, this method suffersTop Down FP-Growth for Association Rule Mining 335 from generating too many candidates. To avoid generating many candidates, [4] proposes to represent the database by a frequent pattern tree (called the FP-tree). The FP-tree is searched recursively in a bottom-up order to grow longer patterns from shorter ones. This algorithm needs to build conditional pattern bases and sub-FP-trees for each shorter pattern in order to search for longer patterns, thus, becomes very time and space consuming as the recursion goes deep and the number of patterns goes large.As far as we know, [7][8] are the only works to explicitly deal with non-uniform minimum support. In [7], a minimum item support (MIS) is associated with each item. [8] bins items according to support and specifies the minimum support for combinations of bins. Unlike those works, our specification of minimum support is associated with the consequent of a rule, not with an arbitrary item or pattern.3 TD-FP-Growth for Frequent Pattern MiningAs in [5], TD-FP-Growth first constructs the FP-tree in two scans of the database. In the first scan, we accumulate the count for each item. In the second scan, only the frequent items in each transaction are inserted as a node into the FP-tree. Two transactions share the same upper path if their first few frequent items are same. Each node in the tree is labeled by an item. An I_node refers to a node labeled by item I. For each item I, all I_nodes are linked by a side-link. Associated with each node v is a count, denoted by count(v), representing the number of transactions that pass through the node. At the same time, a header table H(Item, count, side-link) is built. An entry (I, H(I),ptr) in the header table records the total count and the head of the side-link for item I, denoted by H(I) and ptr respectively. Importantly, the items in each transaction are lexicographically ordered, and so are the labels on each path in FP-tree and the entries in a header table. We use Example 3.1 to illustrate the idea of TD-FP-Growth.Example 3.1 A transaction database is given as in the following Figure 3.1. Suppose that the minimum support is 2. After two scans of transaction database, the FP-tree and the header table H is built as Figure 3.1.The top-down mining of FP-tree is described below. First, entry a at the top of H is frequent. Since a_node only appears on the first level of the FP-tree, we just need to output {aFigure 3.1 Transaction table, FP-tree and HThen, for entry b in H, following the side-link of b, we walk up the paths starting from b_node in the FP-tree once to build a sub-header-table for b, denoted H_b.336 Ke Wang et al.These paths are in bold face in Figure 3.2. During the walk up, we link up encountered nodes of the same label by a side-link, and accumulate the count for such nodes. In Figure 3.2, there are two paths starting with b_node: root-b and root-a-b. By walking up these paths, we accumulate the count of the a_node to 1 because path root-a-b only occurs once in the database. We also create an entry a in the sub-header table H_b. The count of entry a is 1 since the count of a is actually the count of pattern {a, b}.a_node is now linked by the side-link for entry a in H_b and the count is modified to 1. Since the minimum support is 2, pattern {a, b} is infrequent. This finishes mining patterns with b as the last item. H_b now can be deleted from the memory. If pattern {a, b} is frequent, we will continue to build sub-header-table H_ab and mine FP-tree recursively. In general, when we consider an entry I in H_x, we will mine all frequent patterns that end up with Ix. In this way, TD-FP-GrowthSimilarly, we find frequent patterns: {c}, {b, c} and {a, c} for entry c, and {e}, {b, e}, {c, e} and {b, c, e} for entry e.Algorithm 1: TD-FP-GrowthInput: a transaction database, with items in each transaction sorted in the lexicographic order, a minimum support: minsup. Output: frequent patterns above the minimum support. Method: build the FP-tree; then call mine-tree (∅, H); Procedure mine-tree(X, H)(1) for each entry I (top down order) in H do(2)if H(I) >= minsup, then(3)output IX;(4)create a new header table H I by call buildsubtable(I);(5)mine-tree(IX, H I);Procedure buildsubtable(I)(1) for each node u on the side-link of I do(2)walk up the path from u once do if encounter a J_node v then(3)link v into the side-link of J in H I;(4)count(v) = count(v) + count(u);(5)H I (J) = H I (J) + count(u);Unlike FP-Growth, TD-FP-Growth processes nodes at upper levels before processing those at lower levels. This is important to ensure that any modificationTop Down FP-Growth for Association Rule Mining 337 made at upper levels would not affect lower levels. Indeed, as we process a lower level node, all its ancestor nodes have already been processed. Thus, to obtain the “conditional pattern base” of a pattern (as named in [5]), we simply walk up the paths above the nodes on the current side-link and update the counts on the paths. In this way, we update the count information on these paths “in place” without creating a copy of such paths. As a result, during the whole mining process, no additional conditional pattern bases and sub-trees are built. This turns out to be a big advantage over the bottom-up FP-Growth that has to build a conditional pattern base and sub-tree for each pattern found. Our experiments confirm this performance gain.4 TD-FP-Growth for Association Rule MiningIn this section, we extend TD-FP-Growth for frequent pattern mining to association rule mining. We consider two new strategies for association rule mining problem: push multiple minimum supports and push the confidence constraint.In the discussion below, we assume that items are divided into class items and non-class items. Each transaction contains exactly one class item and several non-class items. We consider only rules with one class item on the right-hand side. Class items are denoted by C1,…,C m.4.1 TD-FP-Growth(M) for Multiple Minimum SupportsIn a ToyotaSale database, suppose that Avalon appears in fewer transactions, say 10%, whereas Corolla appears in more transactions, say 50%. If a large uniform minimum support, such as 40%, is used, the information about Avalon will be lost. On the contrary, if a small uniform minimum support, such as 8%, is used, far too many uninteresting rules about Corolla will be found. A solution is to adopt different minimum supports for rules of different classes.We adopt TD-FP-Growth to mine association rules using non-uniform minimum supports. The input to the algorithm is one minsup i for each class C i, and the minimum confidence minconf. The output is all association rules X ⇒C i satisfying minsup i and minconf. The algorithm is essentially TD-FP-Growth with the following differences. (1) We assume that the class item C i in each transaction is the last item in the transaction. (2) Every frequent pattern XC i must contain exactly one class item C I, where X contains no class item. The support of X is represented by H(I) and the support of XC i is represented by H(i, I). (3) The minimum support for XC i is minsup i.(4) We prune XC i immediately if its confidence computed by by H(i, I)/H(I) is below the minimum confidence.4.2 TD-FP-Growth(C) for Confidence PruningA nice property of the minimum support constraint is the anti-monotonicity: if a pattern is not frequent, its supersets are not frequent either. All existing frequent pattern mining algorithms have used this property to prune infrequent patterns. However, the minimum confidence constraint does not have a similar property. This is the main reason that most association rule mining algorithms ignore the confidence requirement in the step of finding frequent patterns. However, if we choose a proper338 Ke Wang et al.definition of support, we can still push the confidence requirement inside the search of patterns. Let us consider the following modified notion of support.Definition 4.1: The (modified) support of a rule A ⇒ B is count(A).We rewrite the minimum confidence constraint C: count(AB)/count(A)>=minconf to count(AB)>=count(A)*minconf. From the support requirement count(A)>=minsup, we have a new constraint C’: count(AB) >= minsup * minconf. Notice that C’ is anti-monotone with respect to the left-hand side A. Also, C’ is not satisfied, neither is C. This gives rise to the following pruning strategy.Theorem 4.1: (1) If A ⇒B does not satisfy C’, A ⇒ B does not satisfy the minimum confidence either. (2) If A ⇒ B does not satisfy C’, no rule AX ⇒B satisfies the minimum confidence, where X is any set of items.Now, we can use both the minimum support constraint and the new constraint C’to prune the search space: if a rule A ⇒ B fails to satisfy both the minimum support and C’, we prune all rules AX ⇒ B for any set of items X. In this way, the search space is tightened up by intersecting the search spaces of the two constraints.5 Experiment ResultsAll experiments are performed on a 550MHz AMD PC with 512MB main memory, running on Microsoft Windows NT4.0. All programs are written in Microsoft Visual C++ 6.0. We choose several data sets from UC_Irvine Machine Learning Database Repository: /~mlearn/MLRepository.html.dataset# of trans # of itemsper transclass distribution# of distinctitemsDna-train200061C1=23.2%, C2=24.25%, C3= 52.55%240 Connect-46755743C1=65.83%, C2= 24.62%, C3= 9.55%126Forest58101213C1= 36.36%, C2= 48.76%, C3= 6.15%, C4:0.47%, C5= 1.63%, C6= 2.99%, C7= 3.53%15916 Table 5.1 data sets tableTable 5.1 shows the properties for the three data sets. C onnect-4 is the densest, meaning that there are a lot of long frequent patterns. Dna-train comes the next in density. Forest is relatively sparse comparing with the other two data sets, however, it is a large data set with 581012 transactions.5.1 Frequent Pattern MiningIn this experiment, we evaluate the performance gain of TD-FP-Growth on mining frequent patterns. We compare it with Apriori and FP-Growth. Figure 5.1 shows a set of curves on the scalability with respect to different minimum supports (minsup). These experiments show that TD-FP-Growth is the most efficient algorithm for all data sets and minimum supports tested.Top Down FP-Growth for Association Rule Mining 3395.2 TD-FP-Growth for Multiple Minimum SupportsIn this experiment, we evaluate the performance gain of using multiple minimum supports. We compare three algorithms: TD-FP-Growth(M), TD-FP-Growth(U), and Apriori. TD-FP-Growth(U) is TD-FP-Growth(M) in the special case that there is only a single minimum support equal to the smallest minimum supports specified. To specify the minimum support for each class, we multiply a reduction factor to the percentage of each class. For example, if there are two classes in a data set and the percentage of them is 40% and 60%, with the reduction factor of 0.1, the minimum supports for the two classes are 4% and 6% respectively. And the uniform minimum support is set to 4%.As shown in Figure 5.2, TD-FP-Growth(M) scales best for all data sets. Take C onnect-4 as the example. As we try to mine rules for the rare class draw, which occurs in 9.55% of the transactions, the uniform minimum support at reduction factor of 0.95 is 9.55% * 95%, TD-FP-Growth(U) ran for more than 6 hours and generated more 115 million rules. However, with the same reduction factor, TD-FP-Growth(M) generated only 2051 rules and took only 5 seconds. That’s why in Figure 5.2 for C onnect-4, the run time for the two algorithms with uniform minimum support is not included.5.3 TD-FP-Growth for Confidence PruningIn this experiment, we evaluate the effectiveness of confidence pruning. The results are reported in Figure 5.3. TD-FP-Growth(NC) is TD-FP-Growth(C) with confidence pruning turned off. We fix the minimum support and vary the minimum confidence. As shown in Figure 5.3, TD-FP-Growth(C) is more efficient than Apriori and TD-FP-Growth(NC), for all data sets, minimum supports, and minimum confidences tested.340 Ke Wang et al.Figure 5.3 confidence-pruning results—time comparison6 ConclusionIn this paper, we proposed an efficient algorithm for frequent pattern mining, calledTD-FP-Growth . The main advantage of TD-FP-Growth is not building conditional pattern bases and conditional FP-tree as the previously proposed FP-Growth does.We extended this algorithm to mine association rules by applying two new pruning strategies. We studied the effectiveness of TD-FP-Growth and the new pruning strategies on several representative data sets. The experiments show that the proposed algorithms and strategies are highly effective and outperform the previously proposed FP-Growth .Reference[1] R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. ACM-SIGMOD 1993, 207-216.[2] H. Toivonen. Sampling large databases for association rules. VLDB 1996, 134-145.[3] R. Agrawal and S. Srikant. Mining sequential patterns. ICDE 1995, 3-14.[4] J. Han, J. Pei and Y. Yin. Mining Frequent patterns without candidate generation. SIGMOD 2000, 1-12.[5] R. Srikant and R. Agrawal. Mining generalized association rules. VLDB 1995, 407-419.[6] R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item constraints. VLDB 1996, 134-145.[7] B. Liu, W. Hsu, and Y. Ma. Mining association rules with multiple minimum supports.KDD 1999, 337-341[8] K. Wang, Y. He and J. Han. Mining frequent patterns using support constraints. VLDB 2000, 43-52.。
R-Agrawalg关于关联规则的开创性论文
X =) Y , where X I, Y I, and X \ Y = .
The rule X =) Y holds in the transaction set D with
con dence c if c% of transactions in D that contain
X also contain Y . The rule X =) Y has support s
An algorithm for nding all association rules, henceforth referred to as the AIS algorithm, was presented in 4]. Another algorithm for this task, called the SETM algorithm, has been proposed in 13]. In this paper, we present two new algorithms, Apriori and AprioriTid, that di er fundamentally from these algorithms. We present experimental results showing
PSarnotcieaegdoi,nCgshoilfe,th1e99240th VLDB Conference
tires and auto accessories also get automotive services done. Finding all such rules is valuable for crossmarketing and attached mailing applications. Other applications include catalog design, add-on sales, store layout, and customer segmentation based on buying patterns. The databases involved in these applications are very large. It is imperative, therefore, to have fast algorithms for this task.
关联规则挖掘AssociationRuleMining背景简介
Brute-force approach:
– List all possible association rules – Compute the support and confidence for each rule – Prune rules that fail the minsup and minconf thresholds Computationally prohibitive!
Apriori principle:
– If an itemset is frequent, then all of its subsets must also be frequent
Apriori principle holds due to the following property of the support measure:
TID Items
– k-itemset
An itemset that contains k items
1 2 3 4 5
Bread, Milk Bread, Diaper, Beer, Eggs Milk, Diaper, Beer, Coke Bread, Milk, Diaper, Beer Bread, Milk, Diaper, Coke
Frequent Itemset Generation
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A
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AC
AD
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BD
BE
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关联规则(associationrule)
关联规则（Association Rules）是数据挖掘领域中的一种重要技术，用于发现数据集中的不显而易见的模式和关系。
它通过分析数据中的项目集合之间的频繁项集，来找出这些项集之间的关联规则，从而揭示数据之间的潜在联系和趋势。
关联规则反映了一个事物与其他事物之间的相互依存性和关联性。
关联规则的应用非常广泛，常见的应用包括购物篮分析。
通过发现顾客放入其购物篮中的不同商品之间的联系，可以分析顾客的购买习惯，从而帮助零售商了解哪些商品频繁地被顾客同时购买。
这种关联的发现有助于零售商制定更有效的营销策略和促销方案。
此外，关联规则还可以应用于价目表设计、商品促销、商品的排放和基于购买模式的顾客划分等领域。
在关联规则分析中，常用的评估标准包括支持度、置信度和提升度。
支持度表示几个关联的数据在数据集中出现的次数占总数据集的比重。
置信度则是指一个数据出现后，另一个数据出现的概率，或者说是数据的条件概率。
提升度则用于衡量关联规则的效果，即使用规则后的效果相对于不使用规则的效果的提升程度。
挖掘关联规则的方法之一是使用Apriori算法。
该算法基于频繁项集的子集也必须是频繁项集的概念，通过迭代的方式生成候选频繁项集，并计算其支持度和置信度，从而找出满足预设阈值的关联规则。
总的来说，关联规则是一种强大的数据挖掘技术，可以帮助企业和研究者从大量数据中发现隐藏的模式和关联，从而制定更有效的决策和策略。
On the Complexity ofMiningQuantitative Association Rules
which may be denoted:
Toothbrush :
Editor: Raymond Ng, Jiawei Han, and Laks Lakshmanan
interesting and important research problem. Recently, di erent aspects of the problem have been studied, and several algorithms have been presented in the literature, among others in (Srikant and Agrawal, 1996 Fukuda et al., 1996a Fukuda et al., 1996b Yoda et al., 1997 Miller and Yang, 1997). An aspect of the problem that has so far been ignored, is its computational complexity. In this paper, we study the computational complexity of mining quantitative association rules.
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关于rules 的英语作文
In any society,rules are essential to maintain order and ensure the smooth functioning of daily life.They are the guidelines that individuals must follow to coexist harmoniously.This essay will explore the importance of rules,the different types of rules, and how they contribute to a wellordered community.The Importance of RulesRules are the cornerstone of social order.They provide a framework within which individuals can interact without causing chaos or harm to one another.Without rules, society would descend into anarchy,with each person acting in their own selfinterest, leading to potential conflicts and a breakdown of social cohesion.1.Safety and Security:One of the primary reasons for having rules is to ensure the safety and security of individuals.For example,traffic laws are designed to prevent accidents and ensure that everyone can travel safely on the roads.2.Fairness and Justice:Rules also serve to promote fairness and justice.They provide a standard against which actions can be judged,ensuring that everyone is treated equally under the law.3.Efficiency:In many cases,rules are put in place to increase efficiency.For instance, rules in a workplace can streamline processes and ensure that tasks are completed in a timely manner.Types of RulesRules can be categorized into several types,each serving a specific purpose within society:1.Legal Rules:These are the laws that are enforced by the government and carry legal consequences for noncompliance.They cover a wide range of areas,from criminal law to civil law.2.Social Rules:These are the unwritten codes of conduct that govern how people interact with one another.They include etiquette,manners,and social norms that are expected to be followed in various social situations.3.Institutional Rules:These are the rules that are specific to an organization or institution, such as a school,workplace,or club.They are designed to maintain order within the institution and ensure that its objectives are met.4.Personal Rules:These are the selfimposed rules that individuals set for themselves to guide their behavior and decisionmaking.They can be based on personal values,beliefs, or goals.The Role of Rules in SocietyRules play a crucial role in shaping society and influencing the behavior of individuals. They are not static they evolve over time as society changes and new challenges arise. The enforcement of rules is also a dynamic process,with different methods being used to ensure compliance,such as education,persuasion,and legal sanctions.cation and Awareness:One of the most effective ways to ensure that rules are followed is through education.By teaching individuals about the importance of rules and the consequences of breaking them,society can foster a culture of compliance.2.Persuasion and Influence:Social norms and peer pressure can also be powerful tools in encouraging individuals to follow rules.When people see others around them adhering to the rules,they are more likely to do the same.3.Legal Sanctions:For legal rules,the threat of punishment serves as a deterrent to noncompliance.This can range from fines and community service to imprisonment, depending on the severity of the offense.ConclusionIn conclusion,rules are an integral part of society,providing structure and ensuring the wellbeing of individuals.They are necessary for maintaining safety,promoting fairness, and increasing efficiency.As society evolves,so too must our understanding and application of rules,ensuring that they remain relevant and effective in guiding our behavior.It is the collective responsibility of all members of society to understand, respect,and adhere to these rules,thereby contributing to a harmonious and orderly community.。
俱乐部管理制度模板英语
俱乐部管理制度模板英语1.1 These regulations are established to regulate the management and operation of the club, to standardize member behavior, and to create a harmonious environment for club activities.1.2 All club members shall abide by these regulations and any other rules and guidelines set by the club.1.3 Any violation of these regulations may result in disciplinary action, including but not limited to warnings, fines, suspension of membership, or expulsion from the club.1.4 These regulations are subject to amendment by the club's board of directors, with the approval of the majority of club members.2. Membership2.1 Membership in the club is open to individuals who meet the membership criteria set by the club, pay the required membership fees, and agree to abide by the club's regulations.2.2 Members shall be entitled to participate in club activities, use club facilities, and enjoy other benefits as specified by the club.2.3 Members shall pay their membership fees in a timely manner, as determined by the club.2.4 Members who wish to resign from the club must notify the club in writing, and their membership fees will not be refunded.3. Club Activities3.1 The club shall organize regular activities, such as meetings, workshops, training sessions, and social events, for the benefit of its members.3.2 Members are encouraged to participate in club activities and contribute to the success of the club.3.3 Members who wish to organize their own activities within the club must seek approval from the club's board of directors and comply with any guidelines set by the club.3.4 Members shall conduct themselves in a respectful and responsible manner during club activities, and shall not engage in any behavior that may disrupt or harm the club.4. Use of Club Facilities4.1 Club facilities, such as meeting rooms, gyms, and sports fields, may be used by members for approved club activities.4.2 Members shall follow any rules and guidelines set by the club for the use of its facilities.4.3 Members shall be responsible for the care and maintenance of club facilities and equipment, and shall report any damage or issues to the club management.4.4 Members shall not use club facilities for any commercial or illegal activities.5. Disciplinary Action5.1 Any member who violates these regulations or engages in behavior that is harmful to the club may be subject to disciplinary action.5.2 Disciplinary action may include warnings, fines, suspension of membership, or expulsion from the club, as determined by the club's board of directors.5.3 Members who are subject to disciplinary action shall have the right to appeal to the club's board of directors.6. Code of Conduct6.1 Members shall conduct themselves in a professional and respectful manner at all times, both within the club and in their interactions with others.6.2 Members shall not engage in any behavior that is discriminatory, harassing, or disrespectful towards others.6.3 Members shall adhere to the principles of fairness, honesty, and integrity in all their dealings within the club.6.4 Any grievances or complaints should be brought to the attention of the club's management in a timely manner, and will be handled in a fair and impartial manner.7. Amendments7.1 These regulations may be amended by the club's board of directors, with the approval of the majority of club members.7.2 Any amendments to these regulations shall be communicated to all members in a timely manner.7.3 Members who do not agree with the amendments may resign from the club in accordance with the club's rules.8. Effective Date8.1 These regulations shall take effect on the date of approval by the club's board of directors.8.2 Members shall be notified of these regulations and shall be required to abide by them from the effective date.I have kept the sample document concise for you. Let me know if you need assistance in expanding on any specific sections.。
英语作文象棋俱乐部规则七年级
Chess Club Rules for Seventh GradeStudentsWelcome to our chess club, where chess enthusiasts can come together to share their passion for this ancient and strategic game. As a member of our club, it is important to adhere to certain rules and regulations to ensure a fun and respectful environment for all. Here are the rules that every seventh-grade student should follow:**1. Attendance and Punctuality**Attendance is crucial in maintaining the momentum and camaraderie within the club. Members are expected to arrive on time for all scheduled meetings and events. Unexplained absences or tardiness may result in warnings, and repeated occurrences may lead to removal from the club.**2. Respect and Courtesy**All members are required to show respect and courtesy to each other, the coaches, and the facilities. This includes maintaining a positive attitude, refraining from using inappropriate language, and respecting the decisions made by the club leadership.**3. Chess Etiquette**During games, members should adhere to proper chess etiquette. This includes waiting for your opponent to make their move, not touching the pieces without permission, and accepting defeat gracefully. Cheating or using unfair tactics is strictly prohibited.**4. Participation and Engagement**Active participation and engagement are encouraged. Members are expected to participate in club activities, including tournaments, practice sessions, and discussions. Sharing strategies, asking questions, and offering feedback are all ways to contribute to the club's growth.**5. Club Property**All chess sets, boards, and other equipment provided by the club must be treated with care. Members are responsible for returning borrowed items in good condition. Damage to club property may result in disciplinary action.**6. Safety and Hygiene**The club expects members to maintain a safe and hygienic environment. This includes washing hands beforeand after playing, respecting personal space, andrefraining from eating or drinking within the playing area. By following these rules, we can ensure that our chess club remains a fun and enriching experience for all. We look forward to a successful and enjoyable year of chess with all our seventh-grade members!**七年级象棋俱乐部规则**欢迎加入我们的象棋俱乐部，这里是象棋爱好者的聚集地，大家可以一起分享对这个古老而富有策略性的游戏的热爱。
社团的规则英语作文
社团的规则英语作文Student clubs are an integral part of the educational experience, providing opportunities for students to explore their interests, develop leadership skills, and build a sense of community. However, for these clubs to function effectively, it is essential to have a set of well-defined rules and guidelines that govern their operations. These rules serve to ensure the smooth running of the club, promote fairness, and protect the rights and responsibilities of all members.One of the primary rules that should be established for student clubs is the membership policy. This policy should clearly outline the criteria for joining the club, such as academic standing, attendance requirements, and any necessary skills or qualifications. Additionally, the policy should address the process for terminating membership, including the grounds for dismissal and the procedures for appeal. By having a well-defined membership policy, the club can ensure that it is accessible to all interested students while maintaining a level of consistency and accountability.Another crucial aspect of club rules is the leadership structure. Thisshould include the roles and responsibilities of the club's executive team, such as the president, vice-president, treasurer, and secretary. The rules should specify the process for electing or appointing these positions, as well as the term limits and any eligibility requirements. Additionally, the rules should outline the decision-making processes, such as how votes are cast and what constitutes a quorum for making important decisions.Closely related to the leadership structure is the issue of club meetings. The rules should establish the frequency and format of club meetings, including whether they will be held in person, virtually, or a combination of both. The rules should also address the procedures for calling special meetings, the process for setting the agenda, and the expectations for member participation and attendance. By having clear guidelines for club meetings, the club can ensure that all members are informed and engaged in the decision-making process.Another crucial aspect of club rules is the management of club finances. The rules should outline the procedures for handling club funds, including the process for approving budgets, making purchases, and maintaining financial records. The rules should also address the issue of fundraising, including any restrictions or guidelines on the types of fundraising activities that are permitted. Additionally, the rules should specify the process for allocating anddistributing club funds, ensuring that all members have a fair and transparent understanding of how the club's resources are being used.Club events and activities are another area that should be addressed in the club rules. The rules should outline the process for planning and executing club events, including the approval process, the allocation of responsibilities, and the expectations for member participation. Additionally, the rules should address any safety or liability concerns, such as the use of club funds for event-related expenses, the requirement for event insurance, and the procedures for addressing any incidents or emergencies that may occur during club events.Finally, the club rules should address the issue of discipline and conflict resolution. The rules should outline the procedures for addressing violations of club rules, including the process for filing complaints, the investigation of alleged infractions, and the imposition of appropriate sanctions. Additionally, the rules should specify the process for appealing disciplinary decisions and the mechanisms for conflict resolution within the club.In conclusion, the establishment of clear and well-defined rules is essential for the successful operation of student clubs. These rules serve to promote fairness, ensure accountability, and protect therights and responsibilities of all club members. By having a comprehensive set of rules in place, student clubs can foster a sense of community, encourage active participation, and provide a meaningful and enriching experience for all involved.。
association_rules参数
association_rules参数
association_rules参数是什么？在机器学习中，关联规则挖掘是一种常见的技术，用于发现数据集中的有趣规律和模式。
在Python 中，我们可以使用mlxtend库中的association_rules函数来进行关联规则挖掘。
association_rules函数有几个重要参数：
1. transactions：一个数据框或一个列表，其中每一行代表一个交易。
每个交易中包含若干个项目，可以是文本、数字等。
2. metric：用于测量规则表现的度量，例如支持度(support)、置信度(confidence)、提升度(lift)等。
3. min_support：最小支持度阈值，用于筛选出支持度大于该阈值的项集。
4. min_threshold：最小置信度或最小提升度阈值，用于筛选出置信度或提升度大于该阈值的关联规则。
5. max_len：关联规则中的最大项集数量。
通过调整这些参数，我们可以探索不同的关联规则，并根据我们的需求选择最优的规则。
- 1 -。
公平维护秩序的英语作文
Upholding fairness and maintaining order are fundamental principles in any society. Here is a detailed English composition on the importance of these concepts:Title:The Importance of Fairness and Order in SocietyIn the intricate tapestry of human society,the threads of fairness and order weave together to create a harmonious and stable environment.These two principles are the bedrock upon which a just and peaceful society is built.Let us delve into the significance of fairness and the necessity of order,and how they contribute to the overall wellbeing of a community.Fairness:The Heart of JusticeFairness is the cornerstone of justice.It ensures that every individual is treated equally under the law and in social interactions.When fairness is upheld,it fosters a sense of trust and respect among people.It is the assurance that hard work and merit will be recognized, regardless of ones background or social status.This principle is vital in educational settings,workplaces,and legal systems,where it prevents favoritism and discrimination.In schools,for instance,fair grading systems ensure that students are assessed based on their abilities and efforts,not on their personal connections or wealth.In the workplace, fair hiring practices and promotions based on performance rather than nepotism create an environment where employees are motivated to excel.Order:The Structure of SocietyOrder is the framework that keeps society functioning smoothly.It is the set of rules, regulations,and norms that guide behavior and maintain social cohesion.Without order, chaos would reign,and the very fabric of society would unravel.Order is essential for the smooth functioning of institutions,from traffic systems that prevent accidents to legal frameworks that protect citizens rights.For example,traffic laws create order on the roads,ensuring that vehicles move in an organized manner,reducing congestion and the risk of accidents.Similarly,the rule of law provides a structured approach to resolving disputes and maintaining peace.The Interplay of Fairness and OrderFairness and order are interdependent.Fairness can only be achieved within a framework of order,as rules must be established to ensure that everyone is treated equally. Conversely,order is more readily accepted and adhered to when it is perceived as fair.If people believe that the rules are unjust,they are less likely to follow them,leading to disorder.Challenges and SolutionsDespite the importance of fairness and order,challenges arise when these principles are compromised.Corruption,for example,undermines fairness by allowing certain individuals to bend the rules for personal gain.To combat this,transparent systems and strong institutions are needed to hold those in power accountable.Moreover,education plays a crucial role in instilling a sense of fairness and respect for order from an early age.By teaching children the value of these principles,we can cultivate a society that values justice and stability.ConclusionIn conclusion,fairness and order are the twin pillars of a wellfunctioning society.They provide the foundation for a just and peaceful coexistence among individuals.It is the collective responsibility of every citizen to uphold these principles,ensuring that our communities remain strong,cohesive,and prosperous.By doing so,we can build a future where every person has the opportunity to thrive and contribute to the common good.This composition highlights the significance of fairness and order in maintaining a stable and just society,and it underscores the importance of each individuals role in upholding these values.。
试论英语词典的义项排列原则
试论英语词典的义项排列原则黄群英词典的义项是词条中释义的最小单位，是对多义词所作的分项解释。
(黄建华，陈楚祥，1997：67)一个多义词，有几个、十几个甚至几十个不同的意义，这些不同的意义放在同一个词条里，就必然产生一个孰先孰后的排列次序的问题。
词典的义项通常按一定的次序排列。
一、英语词典义项排列的三种基本原则根据词典学家们的概括，在英语词典中，义项的排列大体可分为三种基本原则，它们是： 1.历史发展原则这种原则按词义发展的先后时间顺序编排词的各个义项：先出现的词义排在后出现的词义前面，每个词义都注明其在文献中最早以及最后出现的年代，展示词义演变的全过程。
根据李荫华的《英语词典初探》一书(第78页)：所谓历史主义的编写原则，是指对收录的词作详尽的历史描述，即从形体、含义、用法等角度，全面揭示各词的起源、历史演变和现状。
《牛津英语大词典》(The Oxford English Dictionary ，第二版)就是以这种原则排列义项的典型例子。
该词典在揭示词义发展时，最早产生的意义列为第一义，其余照出现的先后顺序编排。
然而，由于词义常衍生出许多分支，它们有时平行，但往往是各自分开，因而显然无法做到单凭一条线索就能将词义变化全面地表述清楚。
所以，对于词义比较丰富的词，该词典在释义开始部分，先用罗马数字介绍该词主要的义项分类，再于每一类中用1，2，3……按历史顺序列举义项，义项下的子项以a，b，c等标注，子项可再分出(a)，(b)，(c)等小项。
下面列举的就是从名词club中引来的例子：club...I. A thick stick，and related senses. ...II. In cards. ...III. A combination，association. ...IV. attrib. and Comb. ...声称按历史发展原则排列义项的词典还有《韦氏新世界词典》(Webster’s New World Dictionary ，第三版)和《韦氏大学词典》(Merriam Webster’s Collegiate Dictionary ，第十版)等等。
给国际交流生介绍象棋俱乐部的规则英语作文
给国际交流生介绍象棋俱乐部的规则英语作文全文共3篇示例，供读者参考篇1Introduction to the Rules of Chess Club for International Exchange StudentsWelcome to our chess club! We are excited to have international exchange students join us and learn the rules of chess. Chess is a timeless game that requires strategy, critical thinking, and patience. By learning and practicing the rules of chess, you will improve your skills and enjoy friendly competition with fellow club members.1. Objective of the Game: The main objective of chess is to checkmate your opponent's king. This means that the opponent's king is in a position to be captured and cannot escape capture on the next move.2. Setting up the Board: The board consists of 64 squares, arranged in an 8x8 grid. Each player has 16 pieces, including one king, one queen, two rooks, two knights, two bishops, and eight pawns. The pieces are set up in a specific formation on the board.3. Movement of Pieces: Each piece moves in a specific way. The king can move one square in any direction. The queen can move in any direction along a straight line. Rooks can move in straight lines vertically or horizontally. Bishops can move diagonally. Knights move in an L-shape, two squares in one direction and then one square in a perpendicular direction. Pawns move forward one square, but capture diagonally.4. Special Moves: There are two special moves in chess. Castling allows the king to move two squares towards a rook and the rook to move to the square next to the king. En passant allows a pawn to capture an opponent's pawn that has moved forward two squares from its starting position.5. Ending the Game: The game ends when a player's king is in checkmate, or when a player resigns. Checkmate occurs when the king is in a position to be captured and cannot escape capture on the next move.6. Etiquette: It is important to follow proper etiquette when playing chess. This includes shaking hands before and after the game, maintaining good sportsmanship, and respecting your opponent.We hope that you enjoy learning and playing chess with us! If you have any questions or need clarification on the rules,please feel free to ask. Let's have a great time playing chess together!篇2Introduction to Chess Club Rules for International Exchange StudentsWelcome to our Chess Club! As an international exchange student, we are excited to have you join us and learn more about the wonderful game of chess. To help you get started, we have put together a guide to our club rules and expectations.1. Club Membership: To join the Chess Club, all members must complete a registration form and pay a small membership fee. This fee helps cover the cost of equipment, tournament entry fees, and other club expenses. As an international exchange student, you may be eligible for a discounted rate or waiver of the membership fee – please inquire with our club administrator for more information.2. Club Meetings: Our Chess Club meets every Monday and Wednesday evening from 6:00 PM to 8:00 PM in the school library. During these meetings, members have the opportunity to participate in friendly games, practice drills, and receive coachingfrom experienced players. We encourage all members to attend regularly and participate in club activities.3. Tournament Participation: Throughout the year, our Chess Club hosts several tournaments and competitions for members to participate in. These events are a great opportunity to test your skills, meet other players, and earn recognition for your accomplishments. We strongly encourage all members to take part in these events and strive for excellence in their chess playing.4. Code of Conduct: As a member of the Chess Club, we expect all players to conduct themselves in a respectful and sportsmanlike manner. This includes treating fellow members with kindness and respect, following the rules of the game, and accepting defeat graciously. Any instances of poor sportsmanship or unsportsmanlike conduct will not be tolerated and may result in disciplinary action.5. Equipment: Our Chess Club provides all necessary equipment, including chess boards, pieces, clocks, and score sheets. Members are responsible for taking care of this equipment and returning it in good condition after each use. If you have your own chess set that you prefer to use, you are welcome to bring it to club meetings.6. Coaching and Training: Our Chess Club offers coaching and training sessions for players of all skill levels. Whether you are a beginner looking to learn the basics or an experienced player seeking to improve your game, we have resources and support available to help you achieve your goals. Please speak with our club administrator to learn more about coaching opportunities.We hope that this guide to our Chess Club rules and expectations will help you feel more comfortable and confident as a new member. If you have any questions or concerns, please do not hesitate to reach out to our club administrator or a club officer for assistance. We look forward to seeing you at our next meeting and wish you great success in your chess playing journey!Welcome to the Chess Club and happy playing!篇3Introduction to Chess Club Rules for International Exchange StudentsWelcome to our chess club! We are delighted to have you as part of our international community and we hope that you will enjoy your time with us. In order to ensure that everyone has apositive and fulfilling experience, we have put together a set of rules and guidelines for you to follow during your time at the club. Please take a moment to familiarize yourself with these rules:1. Respect for Others: Always treat your fellow club members with respect and kindness. Everyone comes from different backgrounds and cultures, so it is important to be open-minded and understanding towards others.2. Punctuality: Please arrive on time for all club meetings and events. We have a busy schedule and it is important that we all respect each other's time.3. Fair Play: In chess, fair play is essential. Always play by the rules and avoid any form of cheating or unsportsmanlike behavior.4. Learning and Improvement: The chess club is a place for learning and growth. Take advantage of opportunities to improve your skills and knowledge of the game.5. Participation: We encourage all members to participate in club activities and events. Whether it is a tournament, a workshop, or a friendly game, we hope that you will get involved and make the most of your time with us.6. Communication: If you have any questions, concerns, or suggestions, please feel free to communicate with the club organizers. We are here to help and we value your feedback.7. Cleanliness: Please help us keep our club space clean and organized. Dispose of any trash or personal items properly and respect the property of others.8. Enjoyment: Most importantly, have fun! The chess club is a place to relax, socialize, and enjoy the game of chess. We hope that you will make lasting memories and friendships during your time with us.By following these rules and guidelines, we are confident that you will have a positive and enriching experience at our chess club. Thank you for being a part of our international community and we look forward to seeing you at the next club meeting!Warm regards,[Chess Club Organizers]。
FMS加工工艺系统的可靠性评定
3 可靠性评价指标体系
FMS 工艺可靠性指标体系的确定应依据有关
1
L ki -
L -1
ki
CP ( s ) 1 ∑
k i
s =1
( 3)
其中 CP ( s ) 为工序 Prock is 的综合工序能力指数 。
Part k 的综合工序能力指数定义为
工艺可靠性的定义 , 对定义中的各要素分解后进
78
© 1994-2006 China Academic Journal Electronic Publishing House. All rights reserved.
Xext ( t ) = μ( t ) + 3σ( t ) ( 7)
完成加工任务的一步相关系数为
Ri =
k
1
L ki - 1
L -1
ki
s =1
∑r ( s , s + 1)
KR ( t ) = Xmax Xext ( t ) ( 6)
=
1
M
M
l =1
∑S E
k
k ij (
l)
( 12)
其中 , S Ek ij 为工序相对误差指数 。
S Eij ( l ) =
k k
Tij ( l ) - TS ij ( l )
k
TS ij ( l ) ( 13)
k
k k 其中 , TS k ij 是工序 Proc ij 加工的标称值 , Tij 是工序
Rout i
M ki i =1
。 其
k 中 , 对 Part k , 工件选择 Rout k i 的概率为 Pri 。
312 工艺稳定性
工艺的稳定性是指在某段时间内 , 由工艺系 统加工的工件的质量指标保持在一定的范围内 。 工艺的稳定性差同样会降低工艺系统的可靠性水 平 。研 究 FMS 中 工 艺 系 统 的 稳 定 性 需 要 研 究