将时间序列转成图像——马尔可夫转移场方法 Matlab实现

clc
clear
close all
 
 
%% 生成数据
% speed = xlsread('3_1_link6_28_5_30min.csv');
speed = xlsread('3_1_link1_1_5_30min.csv');
 
X = speed;
m = length(X);
 
%数据初始化[0,1]
X = (X - min(X))/(max(X) - min(X));
 
%% 构造转移矩阵W
N = length(X);
 
% 分出Q个分位箱（按照个数），从小往大：1、2、3、4
Q = 4;
 
% X_Q把每个元素标记为分为箱1、2、3、4，
X_Q = ones(1,N);
j = 0;
 
% 初始化k
k = ones(1,Q+1);
for i = 2 : Q+1
    
    % 循环计算小于j的数据个数，达到阈值时跳出循环
    while( sum(X < j) < N * (i-1) / Q)
        j = j + 0.0001;
    end
    
    % 记录每一个分位箱的阈值
    k(i) = j;
    
    % 将原先的数据向量变成对应的分位箱次序向量
    X_Q(find(X < k(i) & X > k(i-1))) = i-1;
end
 
%% 计算马尔可夫矩阵
sum_14 = 0;
sum_13 = 0;
sum_24 = 0;
sum_12 = 0;
sum_23 = 0;
sum_34 = 0;
sum_11 = 0;
sum_22 = 0;
sum_33 = 0;
sum_44 = 0;
sum_21 = 0;
sum_32 = 0;
sum_43 = 0;
sum_31 = 0;
sum_42 = 0;
sum_41 = 0;
 
for i = 1:N-1
    switch(X_Q(i) - X_Q(i+1))
        case -3
            sum_14 = sum_14 + 1;
        case -2
            switch(X_Q(i))
                case 1
                    sum_13 = sum_13 + 1;
                case 2
                    sum_24 = sum_24 +1;
            end
        case -1
            switch(X_Q(i))
                case 1
                    sum_12 = sum_12 + 1;
                case 2
                    sum_23 = sum_23 + 1;
                case 3
                    sum_34 = sum_34 + 1;
            end
        case 0
            switch(X_Q(i))
                case 1
                    sum_11 = sum_11 + 1;
                case 2
                    sum_22 = sum_22 + 1;
                case 3
                    sum_33 = sum_33 + 1;
                case 4 
                    sum_44 = sum_44 + 1;
            end
        case 1
            switch(X_Q(i))
                case 2
                    sum_21 = sum_21 + 1;
                case 3
                    sum_32 = sum_32 + 1;
                case 4
                    sum_43 = sum_43 + 1;
            end
        case 2
            switch(X_Q(i))
                case 3
                    sum_31 = sum_31 + 1;
                case 4
                    sum_42 = sum_42 + 1;
            end
        case 3
            sum_41 = sum_41 + 1;
    end
end
 
W = [sum_11 sum_12 sum_13 sum_14;
    sum_21 sum_22 sum_23 sum_24;
    sum_31 sum_32 sum_33 sum_34;
    sum_41 sum_42 sum_43 sum_44];
W = W./repmat(sum(W),[4,1])
 
M = zeros(N,N);
for i = 1: N
    for j = 1:N
        M(i,j) = W(X_Q(i),X_Q(j));
    end
end
 
figure(1)
plot(X)
hold on
for i = 2 : Q
    plot(1:N,ones(1,N)*k(i),'linewidth',1.5);
    hold on;
end
im = figure(2);
imagesc(M)
saveas(im,'MTF_1.bmp');
saveas(figure(1),'MTF_01.bmp');