Mathematical modeling clustering

Catalog

Q Type clustering

R Type clustering

other

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Q Type clustering

Classifying samples is called Q Type cluster analysis , Use distance to measure the similarity between sample points , Two groups Sample points The distance between is usually measured by Euclidean distance , Notice if the dimensions are different , Then it should be standardized . Mahalanobis distance does not need to consider dimension . The distance between two sample classes is also defined

mandist( matrix ) This function is used to find the matrix Column The absolute distance between two vectors

Y=pdist(X) return X Euclidean distance between row and row observations . Return value Y It's a row vector , use squareform(Y) Convert to square matrix , Row vector Y In fact, it is the value of the lower triangular matrix in matrix form .

tril( matrix ) You can intercept the triangular matrix ,nonzeros( matrix ) Remove zero elements from the matrix , Non zero elements are arranged in columns ,unique( matrix ) You can remove repeated non-zero elements ,linkage() Function can find the clustering tree , The parameter should be the row vector of distance ,dendrogram(z,num); Draw a cluster diagram ,num It's the number of nodes , Default maximum 30

  Example ：

w1	1	0
w2	1	1
w3	3	2
w4	4	3
w5	2	4

Yes w To classify

The absolute value distance is used as the classification basis , Theoretical analysis shows the distance ：

  Draw a cluster diagram and a binary tree diagram ：

clc,clear
a = [1,0;1,1;3,2;4,3;2,5];
d = pdist(a,'cityblock');% Calculate the row vector of the direct distance between the sample points 
z = linkage(d);
dendrogram(z);% Draw a cluster diagram 
T = cluster(z,'maxclust',3)% Classify into three categories 
%%  It's fine too ：
z = linkage(a,'single','cityblock');%single Refers to the distance between classes , The latter is the sample point distance 

  Calculation results ：

z =

     1     2     1
     3     4     2
     6     7     3
     5     8     4

intend ：1,2 The sample points are divided into one class , yes h6,3,4 Divide into one class h7,h6、h7 It is divided into h8,h8 And sample points 5 Divide into one class .z The third column contains the connection distance between two rows of objects

T =

     1
     1
     2
     2
     3

T Divided into three categories , Sample points 1,2 It is divided into 1 class ...

R Type clustering

Cluster variables , Then we can find out the main factors that affect the system , There are two commonly used measures of variable similarity ① The correlation coefficient ② Angle cosine , The correlation coefficient is the most used

  Variable clustering methods commonly used are the longest distance method and the shortest distance method

Example ：

give 14 Correlation coefficient between variables , For this 14 Categorize variables

clc,clear
a = readmatrix('data.txt');
a(isnan(a)) = 0;
d = 1-abs(a);               % Perform data transformation , Convert the correlation coefficient into distance 
d = tril(d);                % Propose the lower triangular matrix 
b = nonzeros(d);            % remove 0
b = b';                     % Into a row vector 
z = linkage(b,'complete');  % Cluster according to the longest distance method 
y = cluster(z,'maxclust',2);% Divide the variables into 2 class 
ind1 = find(y==1)           % Display the corresponding variable label of the first type 
ind2 = find(y==2)
h = dendrogram(z);          % Draw a cluster diagram 

other

A = zsore(x) Standardize the data matrix , The way to deal with it is ：

B = corrcoef(A) return A Matrix of correlation coefficients