模式识别课后习题(英文)

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模式识别作业题(2)

模式识别作业题(2)
得证。 3、使用最小最大损失判决规则的错分概率是最小吗?为什么?
答:不是最小的。首先要明确当我们谈到最小最大损失判决规则时,先验概率是未知的, 而先验概率的变化会导致错分概率变化, 故错分概率也是一个变量。 使用最小最大损 失判决规则的目的就是保证在先验概率任意变化导致错分概率变化时, 错分概率的最 坏(即最大)情况在所有判决规则中是最好的(即最小)。 4、 若 λ11 = λ22 =0, λ12 = λ21 ,证明此时最小最大决策面是来自两类的错误率相等。 证明:最小最大决策面满足 ( λ11 - λ22 )+( λ21 - λ11 ) 容易得到
λ11 P(ω1 | x) + λ12 P(ω2 | x) < λ21 P(ω1 | x) + λ22 P(ω2 | x) ( λ21 - λ11 ) P (ω1 | x) >( λ12 - λ22 ) P (ω2 | x) ( λ21 - λ11 ) P (ω1 ) P ( x | ω1 ) >( λ12 - λ22 ) P (ω2 ) P ( x | ω2 ) p( x | ω1 ) (λ 12 − λ 22) P(ω2 ) > 即 p( x | ω2 ) ( λ 21 − λ 11) P (ω1 )
6、设总体分布密度为 N( μ ,1),-∞< μ <+∞,并设 X={ x1 , x2 ,… xN },分别用最大似然 估计和贝叶斯估计计算 μ 。已知 μ 的先验分布 p( μ )~N(0,1)。 解:似然函数为:
∧Байду номын сангаас
L( μ )=lnp(X|u)=
∑ ln p( xi | u) = −
i =1
N
模式识别第三章作业及其解答

模式识别习题集答案解析

模式识别习题集答案解析

模式识别习题集答案解析1、PCA和LDA的区别?PCA是⼀种⽆监督的映射⽅法,LDA是⼀种有监督的映射⽅法。

PCA只是将整组数据映射到最⽅便表⽰这组数据的坐标轴上,映射时没有利⽤任何数据部的分类信息。

因此,虽然做了PCA后,整组数据在表⽰上更加⽅便(降低了维数并将信息损失降到了最低),但在分类上也许会变得更加困难;LDA在增加了分类信息之后,将输⼊映射到了另外⼀个坐标轴上,有了这样⼀个映射,数据之间就变得更易区分了(在低纬上就可以区分,减少了很⼤的运算量),它的⽬标是使得类别的点距离越近越好,类别间的点越远越好。

2、最⼤似然估计和贝叶斯⽅法的区别?p(x|X)是概率密度函数,X是给定的训练样本的集合,在哪种情况下,贝叶斯估计接近最⼤似然估计?最⼤似然估计把待估的参数看做是确定性的量,只是其取值未知。

利⽤已知的样本结果,反推最有可能(最⼤概率)导致这样结果的参数值(模型已知,参数未知)。

贝叶斯估计则是把待估计的参数看成是符合某种先验概率分布的随机变量。

对样本进⾏观测的过程,把先验概率密度转化为后验概率密度,利⽤样本的信息修正了对参数的初始估计值。

当训练样本数量趋于⽆穷的时候,贝叶斯⽅法将接近最⼤似然估计。

如果有⾮常多的训练样本,使得p(x|X)形成⼀个⾮常显著的尖峰,⽽先验概率p(x)⼜是均匀分布,此时两者的本质是相同的。

3、为什么模拟退⽕能够逃脱局部极⼩值?在解空间随机搜索,遇到较优解就接受,遇到较差解就按⼀定的概率决定是否接受,这个概率随时间的变化⽽降低。

实际上模拟退⽕算法也是贪⼼算法,只不过它在这个基础上增加了随机因素。

这个随机因素就是:以⼀定的概率来接受⼀个⽐单前解要差的解。

通过这个随机因素使得算法有可能跳出这个局部最优解。

4、最⼩错误率和最⼩贝叶斯风险之间的关系?基于最⼩风险的贝叶斯决策就是基于最⼩错误率的贝叶斯决策,换⾔之,可以把基于最⼩错误率决策看做是基于最⼩风险决策的⼀个特例,基于最⼩风险决策本质上就是对基于最⼩错误率公式的加权处理。

模式识别习题及答案

模式识别习题及答案

模式识别习题及答案模式识别习题及答案【篇一:模式识别题目及答案】p> t,方差?1?(2,0)-1/2??11/2??1t,第二类均值为,方差,先验概率??(2,2)?122???1??1/21??-1/2p(?1)?p(?2),试求基于最小错误率的贝叶斯决策分界面。

解根据后验概率公式p(?ix)?p(x?i)p(?i)p(x),(2’)及正态密度函数p(x?i)?t(x??)?i(x??i)/2] ,i?1,2。

(2’) i?1基于最小错误率的分界面为p(x?1)p(?1)?p(x?2)p(?2),(2’) 两边去对数,并代入密度函数,得(x??1)t?1(x??1)/2?ln?1??(x??2)t?2(x??2)/2?ln?2(1) (2’)1?14/3-2/3??4/32/3??1由已知条件可得?1??2,?1,?2??2/34/3?,(2’)-2/34/31设x?(x1,x2)t,把已知条件代入式(1),经整理得x1x2?4x2?x1?4?0,(5’)二、(15分)设两类样本的类内离散矩阵分别为s1??11/2?, ?1/21?-1/2??1tt,各类样本均值分别为?1?,?2?,试用fisher准(1,0)(3,2)s2-1/21??(2,2)的类别。

则求其决策面方程,并判断样本x?解:s?s1?s2??t20?(2’) ??02?1/20??-2??-1?*?1w?s()?投影方向为12?01/22?1? (6’) ???阈值为y0?w(?1??2)/2??-1-13 (4’)*t2?1?给定样本的投影为y?w*tx??2-1?24?y0,属于第二类(3’) ??1?三、(15分)给定如下的训练样例实例 x0 x1 x2 t(真实输出) 1 1 1 1 1 2 1 2 0 1 3 1 0 1 -1 4 1 1 2 -1用感知器训练法则求感知器的权值,设初始化权值为w0?w1?w2?0;1 第1次迭代2 第2次迭代(4’)(2’)3 第3和4次迭代四、(15分)i. 推导正态分布下的最大似然估计;ii. 根据上步的结论,假设给出如下正态分布下的样本,估计该部分的均值和方差两个参数。

人工智能模式识别技术练习(习题卷1)

人工智能模式识别技术练习(习题卷1)

人工智能模式识别技术练习(习题卷1)第1部分:单项选择题,共45题,每题只有一个正确答案,多选或少选均不得分。

1.[单选题]可视化技术中的平行坐标又称为( )A)散点图B)脸谱图C)树形图D)轮廓图答案:D解析:2.[单选题]描述事物的基本元素,称为( )A)事元B)物元C)关系元D)信息元答案:B解析:3.[单选题]下面不属于层次聚类法的是( )A)类平均法B)最短距离法C)K均值法D)方差平方和法答案:C解析:4.[单选题]核函数方法是一系列先进( )数据处理技术的总称。

A)离散B)连续C)线性D)非线性答案:D解析:5.[单选题]下面哪个网络模型是最典型的反馈网络模型?( )A)BP神经网络B)RBF神经网络C)CPN网络D)Hopfield网络答案:D解析:6.[单选题]粗糙集所处理的数据必须是( )的。

答案:B解析:7.[单选题]模糊聚类分析是通过( )来实现的。

A)模糊相似关系B)模糊等价关系C)模糊对称关系D)模糊传递关系答案:B解析:8.[单选题]模糊系统是建立在( )基础上的。

A)程序语言B)自然语言C)汇编语言D)机器语言答案:B解析:9.[单选题]在模式识别中,被观察的每个对象称为( )A)特征B)因素C)样本D)元素答案:C解析:10.[单选题]群体智能算法提供了无组织学习、自组织学习等进化学习机制,这种体现了群体智能算法的( )A)通用性B)自调节性C)智能性D)自适应性答案:C解析:11.[单选题]下面不属于遗传算法中算法规则的主要算子的是( )A)选择B)交叉C)适应D)变异答案:C解析:12.[单选题]下面不属于蚁群算法优点的是( )。

A)高并行性B)可扩充性C)不易陷入局部最优13.[单选题]只是知道系统的一些信息,而没有完全了解该系统,这种称为( )A)白箱系统B)灰箱系统C)黑箱系统D)红箱系统答案:B解析:14.[单选题]模式分类是一种______方法,模式聚类是一种_______方法。

模式识别课后习题答案

模式识别课后习题答案
• 2.10 随机变量l(x)定义为l(x) = p(x|w1) ,l(x)又称为似然比,试证明 p(x|w2)
– (1) E{ln(x)|w1} = E{ln+1(x)|w2} – (2) E{l(x)|w2} = 1 – (3) E{l(x)|w1} − E2{l(x)|w2} = var{l(x)|w2}(教材中题目有问题) 证∫ 明ln+:1p对(x于|w(12)),dxE={ln∫(x()∫p(|wp(x(1x|}w|w=1)2))∫n)+nl1nd(xx)所p(x以|w∫,1)Ed{xln=(x∫)|w(1p(}p(x(=x|w|Ew1)2{))ln)n+n+11d(xx)又|wE2}{ln+1(x)|w2} = 对于(2),E{l(x)|w2} = l(x)p(x|w2)dx = p(x|w1)dx = 1
对于(3),E{l(x)|w1} − E2{l(x)|w2} = E{l2(x)|w2} − E2{l(x)|w2} = var{l(x)|w2}
• 2.11 xj(j = 1, 2, ..., n)为n个独立随机变量,有E[xj|wi] = ijη,var[xj|wi] = i2j2σ2,计 算在λ11 = λ22 = 0 及λ12 = λ21 = 1的情况下,由贝叶斯决策引起的错误率。(中心极限 定理)
R2
R1
容易得到


p(x|w2)dx = p(x|w1)dx
R1
R2
所以此时最小最大决策面使得P1(e) = P2(e)
• 2.8 对于同一个决策规则判别函数可定义成不同形式,从而有不同的决策面方程,指出 决策区域是不变的。
3
模式识别(第二版)习题解答

模式识别英文文献阅读

模式识别英文文献阅读

My Feeling to this CurriculumIn terms of the degree of difficulty of this curriculum,I think it is a little bit higher than the basic requirement to undergraduate students, because most of us have not gained a comprehensive understanding of algorithm and laid a solid foundation of mathematics in our first year. However, after learning some basic knowledge of picture processing, using Matlab as a data processing tool is no longer a formidable task for me. Overall, this course is quite helpful and challenging to undergraduates who have some desire for continuing their study and research in remote sensing after graduation.Through this course, I have gained a better understanding of how to process pictures with more than three wavebands and got to know some classical algorithms in the field of pattern recognition, like K-means,KNN and PCA. Among all of them,what impressed most is K-means.My Experience of Studying K-means algorithmBefore learning this curriculum, I have already had access to this algorithm by participating in the project approval of our university, and the name of our project is …The Cluster Analysis of College students‟ attributes‟. At that time,the principal idea of K-means was used for reference to classify sample students, and the GPA, the family financial situation, the index of happiness and etc. have been regarded as students‟ basic attributes whose degrees of relevance and weights play an important role in clustering.During this course, I have attained a deeper comprehension of the usage of K-means‟idea in processing remote sensing data. To be honest, it is really a difficult task. First of all, unlike common chromatic pictures which have only three wavebands, remote sensing pictures have four or even hundreds of wavebands.That means a single pixel of which enjoys a greater quantity of attributes; therefore, in order to process more informative pictures, our programme should be able to calculate the weighted distance from each pixel to the randomly selected cores of clustering and classify it to the most proximate class in a shorter period of time. As a result of that, I have modified the circulatory part of my programme many times for the sake of its efficiency of operation. Moreover, from the perspectives of the selection of the cores of clustering, the more iterations have been set up ,the more stable the cores are; however, setting up more iterations implies longer operation; therefore, we have to select typical samples as cores of clustering according to the classified result of our first task at the beginning. Unfortunately, I did not get an ideal classification when using the software ENVI to classify.Dissertations ReadingBy making a classification of remote sensing picture given with the concept of K-means, I gradually realized the drawbacks and the limitations of this algorithm. They are having to obtain the number of clusters of data sets in advance and the sensitivity to selecting initial clustering centers. Accordingly, I have read five Englishdissertations which are highly related to the methodology of improving the efficiency and effectiveness of this algorithm, and I benefit greatly from those thoughts.1.Improved k-means clustering algorithm(Journal of Southeast University)In this dissertation, the concept of a silhouette coefficient is introduced to help determine the initial clustering centers.The optimal clustering number K opt of a data set with unknown class information is confirmed by calculating the silhouette coefficient of objects in clusters under different K values. Then the distribution of the data set is obtained through hierarchical clustering and the initial clustering-centers are confirmed. Finally,the clustering is completed by the traditional k-means clustering. In this method, different clusters can be reasonably distinguished and the outliers can be efficiently recognized.Overall,This algorithm conquers the diversity of result clusters and optimizes the quality of clustering.In my opinion, this paper validates the efficiency of the algorithm by testing cases, as when one object cannot be dispatched to a single cluster,we need to distribute the object to several clusters based on different possibilities.However, because of the idea of hierarchy based on, this algorithm will greatly enhance the calculated amount of classification and complexity of calculating.2.Global Optimising K Value for Semi-Supervised K-means Algorithm (Journal of Beijing Jiaotong University)This paper show us a new method which has broken the limits that traditional methods have in selecting samples as the K value. It can direct and plan a great amount of supervision data by using only a small amount of labeled data. Combining the distribution characteristics of data sets and monitoring information in each cluster after clustering, we are able to use the voting rule to guide the cluster labeling in the data sets. By comparing the results of its experiment and traditional methods of classification, we can clearly witness that this method enjoys more efficiency of finding the best data sets for K values and clustering center. Generally, it can enhance the performance of clustering.Taking my own experience as an illustration , in order to shorten the operation, I have used the method of labeling for reference to process the high-optical-spectrum data. If the picture given has a colossal amount of pixels, labeling training data can be a better method to process it in a short time.3.Learning algorithm for RBF Neural Networks based on Improved K- means algorithm (Computer Engineering and Application )This paper a at solving the sensitivity to the initial clustering center of traditional K-means algorithm and introducing an improved learning algorithm based on improved K-means algorithm. The new algorithm optimizes k-means algorithm with subtractive clustering algorithm to eliminate the clustering sensitivity,and constructs RBF neural networks with the optimized k-means algorithm.The simulation results demonstrate the practicability and the effectiveness of the new algorithm. Unfortunately, in spite of the fact that this method can stabilize the clustering center, it enhances the complexity of calculating to a vast degree. Because using subtractiveclustering algorithm to process the data in advance adds difficulty and calculated amount to later clustering.4.Optimizing k-means clustering results with standard software packages (Computational Statistics and Data Analysis)This paper illustrates us another concept of solving the sensitivity to selecting initial clustering centers and proposes a simple procedure that can be invoked to improve the default solution. K-means algorithm, actually, is an iterative algorithm that requires specification of a starting configuration, and many packages use a random start unless the user declares otherwise. For example, Some packages, however, base the default starting option on a preliminary analysis such as hierarchical clustering. This does not allow users to produce different “replicate” solutions, so the temptation is to treat the final solution as a global rather than local optimum. In this regard, an iterative scheme that generally improves on the default solution is suggested.Specifically, to apply this idea to K-means clustering from a fixed starting point we iterate the algorithm, we need to perturb the cluster membership at each iteration but decrease the probability of moving individuals between clusters as the iterations in the meantime. And the above iterative refinement will generally improve the effectiveness of clustering. What I gained from the paper is that the more comprehensive your iterative scheme are, the more typical clustering center can be selected.5.Queuing Theory Supervising K-means Clustering Algorithm and ITS Application in Optimized Design of TTC Network (Journal of Astronautics) This paper proposes an improved K-means clustering algorithm for optimization design of network. it analyzes the call process by queuing theory and calculated the least network group , which was the initial K of K-means clustering. Although this paper is not highly related to what we have learned from pattern recognition, the concept of queuing can be appropriately brought in selecting the initial K. Queuing theory, which can analyze and infer intersection delay formation against non-saturated and oversaturated conditions of communication for information, is widely available in the field of operational research. It can helps K-means calculate the initial K and reduces the computational complexity. However, there are some knotty problems followed. The problem is that the sum (S = INT(λ/μ) + 1) was not generally the best result because of the asymmetrical distributing. Accordingly, adding the idea of the queuing theory to K-means algorithm means that we have to pay more attention to resource consumption to avoid jam of the system programmed by ourselves.Overall, this new concept is quite useful and creative ; however, the field of being referred of which is quite restricted.Hence, we should thick twice before making use of it in big data processing.Advice for this curriculumDue to the high demands for mathematics of this curriculum ,setting aside more time for us to pick up some basic theories of statistics and linear algebra can be beneficial to our for figuring out those algorithm. Moreover, most of us are in great need of the help from assistants.Hopefully,the assistants could instruct us more in their spare time.。

模式识别练习题(简答和计算)汇总(1)

模式识别练习题(简答和计算)汇总(1)

1、试说明Mahalanobis 距离平方的定义,到某点的Mahalanobis 距离平方为常数的轨迹的几何意义,它与欧氏距离的区别与联系。

答:Mahalanobis 距离的平方定义为:∑---=12)()(),(u x u x u x r T其中x ,u 为两个数据,1-∑是一个正定对称矩阵(一般为协方差矩阵)。

根据定义,距某一点的Mahalanobis 距离相等点的轨迹是超椭球,如果是单位矩阵Σ,则Mahalanobis 距离就是通常的欧氏距离。

2、试说明用监督学习与非监督学习两种方法对道路图像中道路区域的划分的基本做法,以说明这两种学习方法的定义与它们间的区别。

答:监督学习方法用来对数据实现分类,分类规则通过训练获得。

该训练集由带分类号的数据集组成,因此监督学习方法的训练过程是离线的。

非监督学习方法不需要单独的离线训练过程,也没有带分类号(标号)的训练数据集,一般用来对数据集进行分析,如聚类,确定其分布的主分量等。

就道路图像的分割而言,监督学习方法则先在训练用图像中获取道路象素与非道路象素集,进行分类器设计,然后用所设计的分类器对道路图像进行分割。

使用非监督学习方法,则依据道路路面象素与非道路象素之间的聚类分析进行聚类运算,以实现道路图像的分割。

3、已知一组数据的协方差矩阵为⎪⎪⎭⎫⎝⎛12/12/11,试问(1) 协方差矩阵中各元素的含义。

(2) 求该数组的两个主分量。

(3) 主分量分析或称K-L 变换,它的最佳准则是什么? (4) 为什么说经主分量分析后,消除了各分量之间的相关性。

答:协方差矩阵为⎪⎪⎭⎫⎝⎛12/12/11,则(1) 对角元素是各分量的方差,非对角元素是各分量之间的协方差。

(2) 主分量,通过求协方差矩阵的特征值,用⎪⎪⎪⎪⎭⎫ ⎝⎛----121211λλ=0得4/1)1(2=-λ,则 ⎩⎨⎧=2/32/1λ,相应地:2/3=λ,对应特征向量为⎪⎪⎭⎫ ⎝⎛11,21=λ,对应⎪⎪⎭⎫ ⎝⎛-11。

模式识别课后习题(英文)

模式识别课后习题(英文)

模式识别课后习题(英文)Pattern Recognition Theory and Its ApplicationPROBLEMS2.5 (1) 对C 类情况推广最小错误率贝叶斯决策规则;(2)指出此时使最小错误率最小等价于后验概率最大,即 (|)(|)i j P x P x ωω> 对一切1j i ω≠∈成立时,x 。

2.5 (1)Generalize the minimum error Bayes decision rule in case of class C;(2) Show that the minimum error rate is equivalent to themaximum posterior probability, namely (|)(|)i j P x P x ωω> where j i ≠ and 1ω∈x .2.6 对两类问题,证明最小风险贝叶斯决策规则可表示为若11222222111121()(),((|)()()|)p x p x p x p ωλλωωλωλωω?-∈?-?则¤ 。

2.6 In the two-category case, show that the minimum risk Bayes decisionrule may be expressed as 12x ωω?∈?? if 122222112111()()((|)(|))()p p p x p x λλωλλωωω--£ .2.7 若11220λλ==,1221λλ=,证明此时最小最大决策面是来自两类的错误率相等。

2.7 Consider minimax criterion for 11220λλ==and 1221λλ=.Prove that in this case 12()()p error p error =.2.22 似然比决策准则为若1221(|)()(|)()()p x p x p p l x ωωωω=¤ 则 12x ωω?∈??付对数似然比为[]()ln ()h x l x =-,当(|)i P x ω是均值向量为i μ 和协方差矩阵为i∑的正态分布时:(1)试推导出()h x ,并指出其决策规则;(2)当12==∑∑∑时,推导()h x 及其决策规则;(3)分析(1),(2)两种情况下的决策面类型。

模式识别习题及答案

模式识别习题及答案

第一章 绪论1.什么是模式?具体事物所具有的信息。

模式所指的不是事物本身,而是我们从事物中获得的___信息__。

2.模式识别的定义?让计算机来判断事物。

3.模式识别系统主要由哪些部分组成?数据获取—预处理—特征提取与选择—分类器设计/ 分类决策。

第二章 贝叶斯决策理论1.最小错误率贝叶斯决策过程? 答:已知先验概率,类条件概率。

利用贝叶斯公式得到后验概率。

根据后验概率大小进行决策分析。

2.最小错误率贝叶斯分类器设计过程?答:根据训练数据求出先验概率类条件概率分布 利用贝叶斯公式得到后验概率如果输入待测样本X ,计算X 的后验概率根据后验概率大小进行分类决策分析。

3.最小错误率贝叶斯决策规则有哪几种常用的表示形式? 答:4.贝叶斯决策为什么称为最小错误率贝叶斯决策?答:最小错误率Bayes 决策使得每个观测值下的条件错误率最小因而保证了(平均)错误率 最小。

Bayes 决策是最优决策:即,能使决策错误率最小。

5.贝叶斯决策是由先验概率和(类条件概率)概率,推导(后验概率)概率,然后利用这个概率进行决策。

6.利用乘法法则和全概率公式证明贝叶斯公式答:∑====mj Aj p Aj B p B p A p A B p B p B A p AB p 1)()|()()()|()()|()(所以推出贝叶斯公式7.朴素贝叶斯方法的条件独立假设是(P(x| ωi) =P(x1, x2, …, xn | ωi)⎩⎨⎧∈>=<211221_,)(/)(_)|()|()(w w x w p w p w x p w x p x l 则如果∑==21)()|()()|()|(j j j i i i w P w x P w P w x P x w P 2,1),(=i w P i 2,1),|(=i w x p i ∑==21)()|()()|()|(j j j i i i w P w x P w P w x P x w P ∑===Mj j j i i i i i A P A B P A P A B P B P A P A B P B A P 1)()|()()|()()()|()|(= P(x1| ωi) P(x2| ωi)… P(xn| ωi))8.怎样利用朴素贝叶斯方法获得各个属性的类条件概率分布?答:假设各属性独立,P(x| ωi) =P(x1, x2, …, xn | ωi) = P(x1| ωi) P(x2| ωi)… P(xn| ωi) 后验概率:P(ωi|x) = P(ωi) P(x1| ωi) P(x2| ωi)… P(xn| ωi)类别清晰的直接分类算,如果是数据连续的,假设属性服从正态分布,算出每个类的均值方差,最后得到类条件概率分布。

模式识别复习要点和参考习题

模式识别复习要点和参考习题

复习要点绪论1、举出日常生活或技术、学术领域中应用模式识别理论解决问题的实例。

答:我的本科毕设内容和以后的研究方向为重症监护病人的状态监测与预诊断,其中的第一步就是进行ICU病人的死亡率预测,与模式识别理论密切相关。

主要的任务是分析数据库的8000名ICU病人,统计分析死亡与非死亡的生理特征,用于分析预测新进ICU病人的病情状态。

按照模式识别的方法步骤,首先从数据库中采集数据,包括病人的固有信息,生理信息,事件信息等并分为死亡组和非死亡组,然后分别进行数据的预处理,剔除不正常数据,对数据进行插值并取中值进行第一次特征提取,然后利用非监督学习的方法即聚类分析进行第二次特征提取,得到训练样本集和测试样本集。

分别利用判别分析,人工神经网络,支持向量机的方法进行训练,测试,得到分类器,实验效果比传统ICU 中采用的评价预测系统好一些。

由于两组数据具有较大重叠,特征提取,即提取模式特征就变得尤为重要。

语音识别,图像识别,车牌识别,文字识别,人脸识别,通信中的信号识别;① 文字识别汉字已有数千年的历史,也是世界上使用人数最多的文字,对于中华民族灿烂文化的形成和发展有着不可磨灭的功勋。

所以在信息技术及计算机技术日益普及的今天,如何将文字方便、快速地输入到计算机中已成为影响人机接口效率的一个重要瓶颈,也关系到计算机能否真正在我过得到普及的应用。

目前,汉字输入主要分为人工键盘输入和机器自动识别输入两种。

其中人工键入速度慢而且劳动强度大;自动输入又分为汉字识别输入及语音识别输入。

从识别技术的难度来说,手写体识别的难度高于印刷体识别,而在手写体识别中,脱机手写体的难度又远远超过了联机手写体识别。

到目前为止,除了脱机手写体数字的识别已有实际应用外,汉字等文字的脱机手写体识别还处在实验室阶段。

②语音识别语音识别技术技术所涉及的领域包括:信号处理、模式识别、概率论和信息论、发声机理和听觉机理、人工智能等等。

近年来,在生物识别技术领域中,声纹识别技术以其独特的方便性、经济性和准确性等优势受到世人瞩目,并日益成为人们日常生活和工作中重要且普及的安验证方式。

模式识别 清华版 课后题解

模式识别 清华版 课后题解
2
1
1
i 1
2
2
N
( xi ) C
2
i 1
18
•课后题
3.1 设总体分布密度为N ( ,1) ,
并设 { x 1, x 2 , ... x N } , 分别用最大似然估计和贝叶斯估计计算已知 的先验分布: ( ) ~ N (0,1) p
5
知识要点


4. 线性判别函数的理解及应 用,能用不同的方法处理多 类分类问题,重点掌握 Fisher线性判别的主要过程 及步骤。 5. 特征选择及特征提取的含 义、区别与联系,类别可分 离性判据满足的要求,K-L 降维过程等。
6
知识要点

6. 无监督学习与聚类的含义, 主要包括两类学习方法,理 解投影法的过程,重点掌握 动态聚类方法中的K-Means 算法。
3.1 设总体分布密度为N ( ,1) ,
并设 { x 1, x 2 , ... x N } , p 分别用最大似然估计和贝叶斯估计计算已知 的先验分布: ( ) ~ N (0,1)
1
最大似然估计
解: •对数似然函数
L ( ) ln p ( )
11
例题讲解
2.4 分别写出在以下两种情况
(1) P (x |ω 1 )= P (x |ω 2 ) (2) P (ω 1 )= P (ω 2 )
下的最小错误率贝叶斯决策规则。
12
例题讲解
贝叶斯决策规则:
如 果 P ( i | x ) m a x P (
j 1, 2
j
| x ), 则 x i
模式识别 Pattern Recognition

模式识别英文版

模式识别英文版

Figure 3.2 (a) Globular (b) filamentary datasets for comparison of clustering methods.
The vertical icicle plot represents the hierarchical clustering tree and must be inspected bottom-up. Figure 3.3 b shows the clustering schedule graph. These usually correspond to a plateau before a high jump in the distance measure.
average of the distances of all possible pairs of patterns, as if they formed a single cluster:
d (ωi ,ω j ) = 1 ∑,ωx)− y C(ni + n j ,2) x, y∈(ωi j
(3-3c)
Multidimensional scaling is another method of representing data in a smaller number of dimensions preserving as much as
possible the similarity structure of the data. The following quadratic error measure known as stress is iteratively minimized:
Figure 3.1 Cross data with Euclidian clustering

模式识别课后习题答案

模式识别课后习题答案

• 2.4 分别写出在以下两种情况 1. P (x|w1 ) = P (x|w2 ) 2. P (w1 ) = P (w2 ) 下的最小错误率贝叶斯决策规则。 解: 当P (x|w1 ) = P (x|w2 )时,如果P (w1 ) > P (w2 ),则x ∈ w1 ,否则x ∈ w2 。 当P (w1 ) = P (w2 )时,如果P (x|w1 ) > P (x|w2 ),则x ∈ w1 ,否则x ∈ w2 。 • 2.5 1. 对c类情况推广最小错误率率贝叶斯决策规则; 2. 指出此时使错误率最小等价于后验概率最大,即P (wi |x) > P (wj |x) 对一切j ̸= i 成立时,x ∈ wi 。 2
模式识别(第二版)习题解答
解:对于c类情况,最小错误率贝叶斯决策规则为: 如果 P (wi |x) = max P (wj |x),则x ∈ wi 。利用贝叶斯定理可以将其写成先验概率和
j =1,...,c
类条件概率相联系的形式,即 如果 p(x|wi )P (wi ) = max p(x|wj )P (wj ),则x ∈ wi 。
• 2.16 证明M ahalanobis距离r符合距离定义三定理,即 – (1) r(a, b) = r(b, a) – (2) 当且仅当a = b时,r(a, b) = 0 – (3) r(a, c) ≤ r(a, b) + r(b, c) 证明: (1) r(a, b) = (a − b)T Σ−1 (a − b) = (b − a)T Σ−1 (b − a) = r(b, a) (2) Σ为半正定矩阵所以r(a, b) = (a − b)T Σ−1 (a − b) ≥ 0,只有当a = b时,才有r(a, b) = 0。 (3) Σ−1 可对角化,Σ−1 = P ΛP T • 2.17 若将Σ−1 矩阵写为:Σ−1 h1d h2d ,证明M ahalanobis距离平方为 . . . hdd

模式识别习题及答案

模式识别习题及答案

模式识别习题及答案案场各岗位服务流程销售大厅服务岗:1、销售大厅服务岗岗位职责:1)为来访客户提供全程的休息区域及饮品;2)保持销售区域台面整洁;3)及时补足销售大厅物资,如糖果或杂志等;4)收集客户意见、建议及现场问题点;2、销售大厅服务岗工作及服务流程阶段工作及服务流程班前阶段1)自检仪容仪表以饱满的精神面貌进入工作区域2)检查使用工具及销售大厅物资情况,异常情况及时登记并报告上级。

班中工作程序服务流程行为规范迎接指引递阅资料上饮品(糕点)添加茶水工作要求1)眼神关注客人,当客人距3米距离时,应主动跨出自己的位置迎宾,然后侯客迎询问客户送客户注意事项15度鞠躬微笑问候:“您好!欢迎光临!”2)在客人前方1-2米距离领位,指引请客人向休息区,在客人入座后问客人对座位是否满意:“您好!请问坐这儿可以吗?”得到同意后为客人拉椅入座“好的,请入座!”3)若客人无置业顾问陪同,可询问:请问您有专属的置业顾问吗?,为客人取阅项目资料,并礼貌的告知请客人稍等,置业顾问会很快过来介绍,同时请置业顾问关注该客人;4)问候的起始语应为“先生-小姐-女士早上好,这里是XX销售中心,这边请”5)问候时间段为8:30-11:30 早上好11:30-14:30 中午好 14:30-18:00下午好6)关注客人物品,如物品较多,则主动询问是否需要帮助(如拾到物品须两名人员在场方能打开,提示客人注意贵重物品);7)在满座位的情况下,须先向客人致歉,在请其到沙盘区进行观摩稍作等待;阶段工作及服务流程班中工作程序工作要求注意事项饮料(糕点服务)1)在所有饮料(糕点)服务中必须使用托盘;2)所有饮料服务均已“对不起,打扰一下,请问您需要什么饮品”为起始;3)服务方向:从客人的右面服务;4)当客人的饮料杯中只剩三分之一时,必须询问客人是否需要再添一杯,在二次服务中特别注意瓶口绝对不可以与客人使用的杯子接触;5)在客人再次需要饮料时必须更换杯子;下班程序1)检查使用的工具及销售案场物资情况,异常情况及时记录并报告上级领导;2)填写物资领用申请表并整理客户意见;3)参加班后总结会;4)积极配合销售人员的接待工作,如果下班时间已经到,必须待客人离开后下班;1.3.3.3吧台服务岗1.3.3.3.1吧台服务岗岗位职责1)为来访的客人提供全程的休息及饮品服务;2)保持吧台区域的整洁;3)饮品使用的器皿必须消毒;4)及时补充吧台物资;5)收集客户意见、建议及问题点;1.3.3.3.2吧台服务岗工作及流程阶段工作及服务流程班前阶段1)自检仪容仪表以饱满的精神面貌进入工作区域2)检查使用工具及销售大厅物资情况,异常情况及时登记并报告上级。

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4 1 0 5
following three partitions: ⑴ 1 = x1 , x2 , 2 = x3 , x4 ⑵ 1 = x1 , x4 , 2 = x2 , x3 ⑶ 1 = x1 , x2 , x3 , 2 = x4 Show that by the sum-of-square error J c criterion, the third partition is favored, whereas by the S criterion the first two partitions are favored.
4.4 Consider a two-dimensional linear discriminant(判别) function
g x x1 2 x2 2
⑴ Transform the discriminant function into the form of g x wT x 0 , and describe the geometric figure(几何图形) of g x 0 ; ⑵ Map the discriminant function to obtain the generalized( 广 义 ) homogeneous(齐次) linear discriminant function g x aT y . ⑶ Show that the X-space is actually a subspace of the Y-space, and the partition of the X-space by aT y 0 is the same as the partition of the X-space by wT x 0 0 in the original space. Describe it by a figure. 8.1 Given three partitions 1,2,3 as shown in the figure below.
Pattern Recognition Theory and Its Application PROBLEMS
2.5 (1) 对 C 类情况推广最小错误率贝叶斯决策规则; (2)指出此时使最小错误率最小等价于后验概率最大,即
P (i | x ) P ( j | x )
2.5
对一切 j i成立时,x 1 。
P ( x | i ) ~ N ( i , i ) .
(1) (2)
Deduce h( x) and find the decisi1 2
.Find the decision rule;
(3)Analyze the decision surface types in question(1) and question(2).
2
x12 0, 0,1
2 x2 0,1, 0 2 x3 0,1,1 2 x4 1,1,1 T
x1 2 1, 0, 0
1 x3 1, 0,1
T
T
T
T
x1 4 1,1, 0
T
T
Respectively reduce the feature space dimension to d 2 and d 1 , then describe the positions of the samples in the feature space. 10.5 Let x1 , x2 , x3 and x4 , and consider the 5 4 1 0
付对数似然比为 h( x ) ln l ( x ) , 当 P ( x | i ) 是均值向量为 i 和协方差矩阵为 的正态分布时: (1)试推导出 h( x ) ,并指出其决策规则;

i
(2)当

1 2
时,推导 h( x ) 及其决策规则;
(3)分析(1) , (2)两种情况下的决策面类型。 2.22
1 x3 1, 0,1
T
T
T
T
x1 4 1,1, 0
T
T
Calculate the transform to obtain the biggest
1 by J 2 =tr S Sb .
J2
expressed
9.1 Given two sample sets
1
1 x1 0, 0, 0 T
= x1 , x2 , …,xN
drawn from a is known.
multivariate normal distribution p x ~ N ,
where
ˆ of . Calculate the maximum likelihood estimate
2 1 2
T
, 2 1, 0 ,
T
I , p( ) p( ) 。Find the minus-log-likelihood ratio decision rule。
2.24 在 2.23 中,若
1 1 1 1 2 2 ,写出负对数似然比规 , , 1 2 1 1 2 1 1 1 2 2
Consider minimax criterion for 11 22 0 and 12 21 .
Prove that in this case p1 (error ) p2 (error ) .
2.22 似然比决策准则为 若 l ( x)
1 p ( x | 1 ) p (2 ) 则 x ¤ p ( x | 2 ) p (1 ) 2
Likelihood ratio decision rules can be expressed as if l ( x)
p ( x | 1 ) p (2 ) . ¤ p ( x | 2 ) p (1 )
x 1 2
minus-log-likelihood ratio can be expressed as h( x) ln l ( x) ,where
follows the uniform
ˆ distribution f P 1 , 0 P 1 . Calculate the Bayesian estimation P
under the condition of exercise 3.3. 3.14 Consider the sample set
3.3
Consider the sample set = x1 , x2 ,…,xN drawn from a binomial
distribution f x, P P xQ 1 x , x 0,1 , 0 P 1 , Q 1 P . Calculate the
习题 2.24 的情况下,若考虑损失函数 11 22 0 , 12 21 ,画出似然比阈与错
误率之间的关系。 (1) 求出 pi (error ) 0.05 时完成 Neyman-Pearson 决策时总的错误率;
(2) 求出最小最大决策的阈值和总的错误率。
2.25 under the condition of exercise 3.3,let 11 22 0 , 12 21 . (1) Consider the Neyman-Pearson criterion , what is the error rate for pi (error ) 0.05 ; (2) Calculate the threshold of the minimax decision and overall error rate. 3.1 Consider the sample set = x1 , x2 ,…,xN with the distribution is
则。
2.24
Let 1 2
1 1 1 1 2 2 . , 1 , 2 1 1 1 1 2 2
Find the minus-log-likelihood ratio decision rule under the condition of exercise 3.3. 2.25
2.6 若 对两类问题,证明最小风险贝叶斯决策规则可表示为
p ( x | 1 ) (12 22 ) p(2 ) ¤ , 则x 1 p ( x | 2 ) (21 11 ) p(1 ) 2

2.6
In the two-category case, show that the minimum risk Bayes decision
(1) Generalize the minimum error Bayes decision rule in case of
class C; (2) Show that the minimum error rate is equivalent to the maximum posterior probability, namely P (i | x) P ( j | x) where j i and x 1 .
3.2
Consider the sample set = x1 , x2 ,…,xN drawn from a multivariate
N , 2 . Respectively calculate the maximum
normal population
ˆ, ˆ 2 of , 2 . likelihood estimate
1 2
rule may be expressed as x
2.7 2.7
if
p ( x | 1 ) (12 22 ) p(2 ) £ p ( x | 2 ) (21 11 ) p(1 )
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