模式识别复习题.doc

unit to the Organization as the basic form of the party, to implement the "three lessons", members of democratic appraisal, such as daily educational administration system for basic support, making good use of various forms of education and training, integration into the regular, everyday work, a better objective world and remolding of subjective world. You want to combine studying the party's history, to carry forward the party's fine tradition and style, making it a spiritual power for party members and cadres. To contact focus on party members and cadres ' ideological and practical work, persist in combining positive education and the reverse side warning, to advanced models as a mirror, to negative examples as a warning. To local conditions, one policy, preventing the pot, one size fits all, and flood irrigation to prevent formalism and the motions to prevent routine aside, preventing easy to open, how many notes do to judge study results. 1, individual self-study. Leading cadres should read, learn, and understanding of the original principle, with conviction, with affection, with a mission to learn, with issue. The Party (total) branch according to the actual situation, levels of distinction, distinction, self-study demands on members, enhancing relevance and effectiveness. Encourage individual branches to produce Visual, Concise popular study materials can be produced making the pocket book, the use of micro-party lecture, micro-micro-video animation, to meet party members ' diverse needs of different groups. XX municipal organization Department produced a concise readerthe economic development in the new normalOf awareness errors, deep awareness economic development new normal of objective inevitability, prevent one-sidedness, and simplistic, cannot to whether on himself favourable to judge new normal bad; cannot put new normal as a basket, what are to in loaded; cannot put new normal as haven, put work bad do, and didn't dry good of reasons are due Yu new normal, for not officer, and not development find excuses. Actively promote the supply side of structural reforms and implement the CPC Central Committee defined "five pillars of policy" and "five priorities", implement the major decisions and arrangements of the central support accelerated development of Fujian, a good grasp of the old Soviet areas, green development, precision significant opportunities to alleviate poverty. (4) lead to overcome difficulty, dare to play. Dare not sword, before major problems before not to grasp the nettle and on front, afraid to come forward before the crisis and error can't bear responsibility, not firmly fight these issues before the evil, strengthen the sense of responsibility, to take charge. Don't want to under the new situation, not as good as issues, enhance vigor, growing new skills, new, do dry dry dry active, do we want to do good, to take Shi Liuyin, grasping the iron mark strength and hard work together create a mental state of implementation, reform and development of the promoter and the doers. Insist on seeking truth, act according to the law, establish the correct achievements view, and strive to create a stand the inspection of practice, people and history of performance. (5) the lead in implementation of strictly administering the party responsible. For tube party rule party poor, and party consciousness indifference, and party work missing, for subject responsibility, and "a gang double accountability" implementation not in place, and put business work and party work fragmented from of problem, for those think are wind anti-corruption effect economic development, errors views, set full strictly rule party forever in road of thought, set grasp party is maximum achievement, and caught bad party is not competent, and not caught party is dereliction of of consciousness, insisted thought party and system rule party close combined, strengthened according to rules rule party consciousness, Take responsibility for the party the party. Exercise to consciously accept the party's political life, adhere to the principle of democratic centralism, seriously carry out criticism and self criticism, rigorous daily management and supervision of party members, cadres, and maintain pressure against corruption. To improve style, cultivating good family tradition, care of families of the children and staff, press ", clear" principle correctly handle the relationship between Government and business, to create fresh political ecology and the politics of environment. Grasping the learning content, the learning needs of more than at the same time, both party members and leading cadres, and also practice job practice study well General Secretary XI Jinping on local work in this field important speeches and directives, further unify their thinking and action, clear work objectives and direction. To control measures in the speech requirement, implementation analysis, identify gaps and weaknesses, target put forward specific measures to strengthen and improve the work, ensuring the spirit landing implementation. Third, learn about ways to highlight the features of regular education, stick with the party branch
1、 模式识别系统的基本构成单元，并对各单元简要解释
数据获取
特征提取和选择
预处理
分类决策
分类器设计

• 数据获取：用计算机可以运算的符号来表示所研究的对象
– 二维图像：文字、指纹、地图、照片等
– 一维波形：脑电图、心电图、季节震动波形等
– 物理参量和逻辑值：体温、化验数据、参量正常与否的描述
• 预处理单元：去噪声，提取有用信息，并对输入测量仪器或其它因素所造成的退化现象进行复原
• 特征提取和选择：对原始数据进行变换，得到最能反映分类本质的特征
– 测量空间：原始数据组成的空间
– 特征空间：分类识别赖以进行的空间
– 模式表示：维数较高的测量空间->维数较低的特征空间
• 分类决策：在特征空间中用模式识别方法把被识别对象归为某一类别
– 基本做法：在样本训练集基础上确定某个判决规则，使得按这种规则对被识别对象进行分类所造成的错误识别率最小或引起的损失最小
2、 写出K-均值聚类算法的基本步骤, 例子见布置的作业题.
算法：
第一步：选K个初始聚类中心，z1(1)，z2(1)，…，zK(1)，其中括号内的序号为寻找聚类中心的迭代运算的次序号。聚类中心的向量值可任意设定，例如可选开始的K个模式样本的向量值作为初始聚类中心。
第二步：逐个将需分类的模式样本{x}按最小距离准则分配给K个聚类中心中的某一个zj(1)。
假设i=j时，，则，其中k为迭代运算的次序号，第一次迭代k=1，Sj表示第j个聚类，其聚类中心为zj。
第三步：计算各个聚类中心的新的向量值，zj(k+1)，j=1,2,…,K
求各聚类域中所包含样本的均值向量：

其中Nj为第j个聚类域Sj中所包含的样本个数。以均值向量作为新的聚类中心，可使如下聚类准则函数最小：
在这一步中要分别计算K个聚类中的样本均值向量，所以称之为K-均值算法。
第四步：若，j=1,2,…,K，则返回第二步，将模式样本逐个重新分类，重复迭代运算；
若，j=1,2,…,K，则算法收敛，计算结束。
例子：已知{x1(0, 0), x2(1,0), x3(0,1), x4(1,1), x5(2,1), x6(1,2), x7(2,2), x8(3,2) , x9(6,6) , x10(7,6) , x11(8,6) , x12(6,7) , x13(7,7) , x14(8,7) , x15(9,7) , x16(7,8) , x17(8,8) , x18(9,8) , x19(8,9) , x20(9,9)}，用K-均值算法进行聚类分析
解：选，，
第一步：选取
第二步：根据聚类中心进行聚类，得到

第三步：计算新的聚类中心

第四步：因，故回到第二步
第二步：根据新的聚类中心重新进行聚类，得到

第三步：计算新的聚类中心

第四步：，所以算法收敛，得聚类中心为
迭代结束。
3、最、剪辑、压缩近邻法的基本思想。
最近邻法的基本思想：以全部训练样本作为“代表点”，计算测试样本与这些“代表点”，即所有样本的距离，并以最近邻者的类别作为决策。
剪辑近邻法基本思想是，利用现有样本集对其自身进行剪辑，将不同类别交界处的样本以适当方式筛选，可以实现既减少样本数又提高正确识别率的双重目的。
压缩近邻法：利用现有样本集，逐渐生成一个新的样本集，使该样本集在保留最少量样本的条件下，仍能对原有样本的全部用最近邻法正确分类，那末该样本集也就能对待识别样本进行分类，并保持正常识别率。

4、设有 6个 5维模式样本如下，按最小/大距离准则进行聚类分析（直到分成三个类别为止，距离度量采用欧氏距离）
x1: 0, 3, 1, 2, 0 x2: 1, 3, 0, 1, 0 x3: 3, 3, 0, 0, 1
x4: 1, 1, 0, 2, 0 x5: 3, 2, 1, 2, 1 x6: 4, 1, 1, 1, 0
按最大距离准则进行聚类分析：
第1步：将每一样本看成单独一类，得

计算各类之间的欧式距离，可得距离矩阵

0

0

0

0

0

0

第2步：矩阵中最大元素为，它是和之间的距离，将他们合并为一个新类为

计算聚类后的距离矩阵

0

0

0

0

0

第3步：由于中距离最大者为，它是与之间的距离，于是合并和，得新的分类为

同样，按最大距离准则计算距离矩阵，得

0

0

0

0
第4步：：由于中距离最大者为，它是与之间的距离，于是合并得新的分类为

满足聚类要求，如聚为3类，聚类完毕。

5、设有 5个 6维模式样本如下，按最小/大距离准则进行聚类分析（距离度量采用欧氏距离）
x1: 0, 1,3, 1, 3, 4 x2: 3, 3, 3, 1,2,1 x3: 1, 0, 0, 0, 1,1
x4: 2, 1, 0, 2, 2,1 x5: 0, 0, 1, 0, 1,0
用最小聚类准则进行系统聚类分析：
第1步：将每一样本看成单独一类，得

计算各类之间的欧式距离，可得距离矩阵

0

0

0

0

0

第2步：矩阵中最小元素为，它是和之间的距离，将他们合并为一类，得新的分类为

计算聚类后的距离矩阵

0

0

0

0

第3步：由于中距离最小者为，它是与之间的距离，于是合并和，得新的分类为

同样，按最小距离准则计算距离矩阵，得

0

0

0

第4步：同理得

满足聚类要求，如聚为2类，聚类完毕。
6、一个三类问题，其判别函数如下： d1(x)=-x1, d2(x)=x1+x2-1, d3(x)=x1-x2-1
设这些函数是在多类情况1条件下确定的。
1) 绘出其判别界面和每一个模式类别的区域。
2) 对如下三个样本所属模式作出判决：A =(4 5)T , B =(-2 5)T , C =(2 -5)T
例子：一个三类问题，其判别函数如下：
d1(x)=-x1, d2(x)=x1+x2-1, d3(x)=x1-x2-1
1、设这些函数是在多类情况1条件下确定的，绘出其判别界面和每一个模式类别的区域。
2、设为多类情况2，并使：d12(x)= d1(x), d13(x)= d2(x), d23(x)= d3(x)。绘出其判别界面和多类情况2的区域。
3、设d1(x), d2(x)和d3(x)是在多类情况3的条件下确定的，绘出其判别界面和每类的区域
解：（1）其判别界面和每一个模式类别的区域如图中所示：

A =(4 5)T 属于ω1 , B =(-2 5)T 属于不确定区域 , C =(2 -5)T属于ω3.

（2）其判别界面和每一个模式类别的区域如图中所示：

（3）其判别界面和每一个模式类别的区域如图中所示：

7、已知：ω1: {x1, x2}={(1 0 1)T, (0 1 1)T}，ω2: {x3, x4}={(1 1 0)T, (0 1 0)T}。
给定初始增广权向量 w1=(1 1 1 1)T ， C=1。
要求：1) 用感知器算法求模式分类的解向量w。
2) 写出判别函数和决策面方程。
解：先求四个样本的增值模式
x1=(1,0,1,1) T x2=(0,1,1,1) T
x3=(1,1,0,1) T x4=(0,1,0,1) T
假设初始权向量 w1=(1,1,1,1) T C=1
第一次迭代：
w1 T x1=(1,1,1,1) T (1,0,1,1)=3>0 所以不修正
w1 T x2=(1,1,1,1) T (0,1,1,1)=3>0 所以不修正
w1 T x3=(1,1,1,1) T (1,1,0,1)=3>0 所以修正w1
w2=w1-x3=(0,0,1,0) T
w2 T x4=(0,0,1,0) T (0,1,0,1) =0 所以修正w2
w3=w2-x4=(0,-1,1,-1) T
第一次迭代后,权向量w3=(0,-1,1,-1)T,再进行第2,3,…次迭代如下表：

直到在一个迭代过程中权向量相同，训练结束。
w6=w=(0,-1,3,0)
判别函数
决策面方程：即
8、已知：ω1: X1 =(0,2)T , X3 =(2,0)T , X5 =(-1,-1)T
ω2: X2 =(1,1)T , X4 =(0,-2)T, X6 =(-2,0)T
给定初始增广权向量 w1=(1 1 1)T ， C=1。
要求：用感知器算法求模式分类的解向量w。
解：此为线性不可分问题，利用感知器法求权向量
权向量产生循环(1, 1, 1) T, (0, 0, 0) T, (2, 0, 1) T, (2, 2, 0) T,(1, 1, 1) T
因此算法不收敛，我们可以取循环中任一权值，例如取
W=(2,2,0) T
则判别函数为： g(x)= 2x1+2x2
判别面方程为： g(x)= 2x1+2x2＝0
所以： x1+x2＝0
由图看出判别面H把二类分开，但其中x2错分到ω1类，
而x1错分到ω2类，但大部分分类还是正确的。

9、 对一大批人进行癌症普查，患癌者以ω1类代表，正常人以ω2类代表。已知P(ω1)=0.005，当然P(ω2)=1-0.005=0.995.设有一种诊断癌症的试验，其结果为“阳性”和“阴性”两种反应。假设根据临床记录发现这种方法有以下统计结果:
患有癌症的人试验反应为阳性的概率=0.95，即p(x=阳|ω1)=0.95
患有癌症的人试验反应为阴性的概率=0.05，即p(x=阴|ω1)=0.05
正常人试验反应为阳性的概率=0.01，即p(x=阳|ω2)=0.01
正常人试验反应为阴性的概率=0.99，即p(x=阴|ω2)=0.99
问：若被化验的人具有阳性反应，他患癌症的概率为多少？
解：

因为，P(w2|x=阳)= 1-P(w1|x=阳)=1-0.323=0.677
P(w1|x=阳)<P(w2|x=阳)
故判决： 正常。
10、已知P(ω1)=0.9，P(ω2)=0.1， p(x|ω1)=0.2，p(x|ω2)=0.4。 且有如下决策表：
损失 状态

决策
ω1
ω2
α1
0
6
α2
1
0

请按最小风险贝叶斯决策进行分类。
解：已知条件为P(ω1)=0.9，P(ω2)=0.1， p(x|ω1)=0.2，p(x|ω2)=0.4。
利用贝叶斯公式分别计算出ω1及ω2的后验概率
再计算条件风险:

由于即决策为ω2的条件风险小于决策为ω1的条件风险，因此我们采取决策行动，即判断待识别的细胞x为ω2类——异常细胞。
11、设有如下三类模式样本集ω1，ω2和ω3，其先验概率相等，求Sw 和Sb
ω1 ：{(1 0)T, (2 0) T, (1 1) T}
ω2 ：{(-1 0)T, (0 1) T, (-1 1) T}
ω3 ：{(-1 -1)T, (0 -1) T, (0 -2) T}
解：由于本题中有三类模式，因此我们利用下面的公式：
=,
即:
为第i类样本样本均值

12 试用感知器算法实现逻辑“与”、“或”功能。（初始加权值、阈值和训练速率系数自己设定）

劳动合同应当用钢笔或毛笔认真填写。有约定事项的，经审查备案编号，双方签字盖章，以活页形式插入。劳动合同内容不得涂改。未经合法授权代签无效。unit to the Organization as the basic form of the party, to implement the "three lessons", members of democratic appraisal, such as daily educational administration system for basic support, making good use of various forms of education and training, integration into the regular, everyday work, a better objective world and remolding of subjective world. You want to combine studying the party's history, to carry forward the party's fine tradition and style, making it a spiritual power for party members and cadres. To contact focus on party members and cadres ' ideological and practical work, persist in combining positive education and the reverse side warning, to advanced models as a mirror, to negative examples as a warning. To local conditions, one policy, preventing the pot, one size fits all, and flood irrigation to prevent formalism and the motions to prevent routine aside, preventing easy to open, how many notes do to judge study results. 1, individual self-study. Leading cadres should read, learn, and understanding of the original principle, with conviction, with affection, with a mission to learn, with issue. The Party (total) branch according to the actual situation, levels of distinction, distinction, self-study demands on members, enhancing relevance and effectiveness. Encourage individual branches to produce Visual, Concise popular study materials can be produced making the pocket book, the use of micro-party lecture, micro-micro-video animation, to meet party members ' diverse needs of different groups. XX municipal organization Department produced a concise readeras the basic unit"Three lessons" the Organization as the basic form of the party, to carry out the daily management of party members such as democratic appraisal system for basic support, well, into the school, education and training of the party School of the channel, into regular, everyday work on a better objective world and remolding of subjective world. You want to combine studying the party's history, and make good use of the gutian meeting, caixixiang survey, Gu Wenchang spirit, Zhan Hongli old story and the County of Sue area, Ushida against "encirclement" site of the forward command post, Fujian and Jiangxi provinces East County Soviet government site, continents, such as site of the negotiations between the KMT and a wealth of resources, carry forward the party's fine tradition and style, making it a spiritual power for party members and cadres. To contact focus on party members and cadres ' ideological and practical work, persist in combining positive education and the reverse side warning, to advanced models as a mirror, to negative examples as a warning. To local conditions, one policy, preventing the pot, one size fits all, and flood irrigation to prevent formalism and the motions to prevent routine aside, preventing easy to open, how many notes do to judge study results. 1. grasp the self-study. Party members according to their actual work and need to develop learning plans, choose their own learning content and methods, really educate yourself. Party leading cadres should read, learn, and understanding of the original principle, with conviction, with affection, with a mission to learn, with issue. All party branches to strengthen the party members to learn specific guidance proposed learning requirements, preparation of simple, popular study materials published making Pocket Books, micro-micro-video animation, using micro-party lectures, meet party members ' diverse needs of different groups. Through reading activities and knowledge competitions, learning outcomes, and stimulate the enthusiasm of party members to study and initiative. 2. improve intensive discussions. 1 thematic focus on each branch per quarter. Collective learning branch to organize party members, each study to determine on the topic, every party member must make presentations and discussions around topics. Authorities and institutions of the party where the party members to participate in collective learning time of 12 days, total of 6 days of other party members. Party groups organize regular party members to focus on. First topic is "belief and faith, strengthen four kinds of consciousness", the time in 4-6 months; the second theme is "commitment to a disciplined bottom line, lofty sentiment" time in 7-9 months; the third topic is "party members adhere to the fundamental purpose,