模式識別聚類算法和線性判別算法

1、Pattern Classificationheight weight C-means clustering algorithm Hierarchical clusteringHierarchical clusteringLinear decision Pattern Classification1.1 C-means clustering algorithmThe flow chart of C-means clustering algorithm 1.2 Hierarchical clusteringThe flow chart of Hierarchical clustering 1.3

2、 Function M = mean (A)：Find the average number or mean of the array Returns the average value of the elements in the different dimension along the array. If A is a vector, mean (A) returns the average value of the elements in the A. If A is a matrix, mean (A) is regarded as a vector, each column in

3、the matrix as a vector, the return of a row vector containing the average value of all elements of each column. If A is an array of multiple, mean (A) will be the first in the array of non single dimensional values as a vector, the average value of the return of each vector.M = mean (A, dim) Returns

4、 the average value of the elements in the dimension specified by the scalar dim along the A. For a matrix, mean (A, 2) is the column vector containing the average value of each row.C-means clustering： 1.4 Source Program and Simulation Result Simulation Result of C-means clustering Simulation Result

5、of C-means clustering Hierarchical clustering 1.4 Source Program and Simulation Result Simulation Result of Hierarchical clusteringSimulation Result of Hierarchical clustering1.5 Effect of initial value of different clustering on clustering results2.1 Linear decision Program first calls to randQ to

6、distinguish between training samples and testing samples, obtained through the related parameters and design the minimum Euclidean distance classifier, and used to detect all the test samples, finally, get every mistake rate .2.1 Linear decision Design a linear classifier with the minimum Euclidean

7、distance criterion: Discriminant function ： Source Program of RandQ Source Program of Linear decision Simulation Result of Linear decision Simulation Result of Linear decision err_vg（將汽車誤判為背景時的錯判率）；err_gv(將背景誤判為汽車時的錯判率)；err_VG（將汽車誤判為背景時的錯判率）；err_GV(將背景誤判為汽車時的錯判率)；Program description: Pdist function

8、is used to calculate the distance between each other, and then the linkage function is used to establish the hierarchical structure tree. By comparing the classification results, the least error algorithm is selected for the class of inner square distance. The final call cluster function, the struct

9、ure of the tree to cluster, determine the final category.2.2 Hierarchical clustering2.2 Hierarchical clustering 1.pdist Y=pdist(X,metric) Description: use the metric method to calculate the distance between objects in the X data matrix. X: a m * n matrix, which is composed of M objects of the data s

10、et, the size of each object is n. Metric values are as follows: Euclidean:歐氏距離（默認）; seuclidean:標準化歐氏距離; Mahalanobis:馬氏距離 cityblock:布洛克距離; Minkowski:明可夫斯基距離；the Function of Hierarchical clustering： 2.linkage Z=linkage(Y,method) Input value Description: Y for the return of the pdist function M* (M-1)

11、/2 elements of the row vector, using the method parameter specified algorithm to calculate the system clustering tree. Method: can be valued as follows : single：最短距離法（默認）； complete：最長距離法； average：未加權(quán)平均距離法； weighted： 加權(quán)平均法； centroid：質(zhì)心距離法； median：加權(quán)質(zhì)心距離法； ward：內(nèi)平方距離法（最小方差算法）2.2 Hierarchical clusterin

12、gthe Function of Hierarchical clustering：3.cluster T=cluster(Z,) Description: according to the output of linkage function Z to create classification. In order to express the matrix Z, we can use more intuitive clustering number to display, the method is dendrogram (z), produced by the clustering num

13、ber is a n type tree, the bottom said sample, then a level to clustering, and eventually become the top. The vertical axis represents the height of column distance. In addition, you can set the number of clusters of the lowest number of samples, the default is 30, you can modify the dendrogram (Z, n

14、) parameter n to achieve, 1nM. Dendrogram (Z, 0) is the case of the table n=M, showing all the leaf nodes.2.2 Hierarchical clusteringthe Function of Hierarchical clustering：load feature_table;W=feature_table;Dist=pdist(W); 計算兩兩對象之間的距離Tree=linkage(Dist,ward); 建立層次化的結(jié)構(gòu)樹（類內(nèi)平方距離最小誤差）class=cluster(Tree,3

15、); 聚類class_1=find(class=1); 第一類class_2=find(class=2); 第二類class_3=find(class=3); 第三類n1=size(class_1);n2=size(class_2);n3=size(class_3); Source Program of Hierarchical clusteringBy clustering:Background error probability (sample as the background, misjudged other) err_bg = 0.0420;Auto error probabilit

16、y (sample for the car, misjudged other) err_car = 0.0400;Pedestrian error probability (sample for pedestrians, misjudged other) err_hm=0.002; Simulation Result of Hierarchical clustering Simulation Result of Hierarchical clusteringWhere the array class_1, class_2, class_3 store the data each other c

17、orresponding to the sample in the total sample set the index value. From which we can get the correct classification of the samples, which are divided into different categories.Summary: hierarchical clustering algorithm is no label learning, so there is no learning training process, directly according to the sample data in the feature space clustering, so the selection of suitable samples distribution characteristics of clustering algorithm is