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SOM是一种无监督学习的神经网络，先贴上最近写的一个利用SOM对图片进行压缩并恢复的简单应用，留个大坑：1.有空再来总结SOM的概念，学习过程，优化算法。2.把代码再用python和C++重新实现一遍作为编程练习。。。
训练过程大致如下：
将图片分解并形成输入向量X = {Xi}， 竞争层只设了一层，即竞争层即是输出层。 对每个Xi，计算其与所有竞争结点的距离，并找到最小距离，最小距离对应的结点竞争获胜，获得修改权值的权利，（这里还定义的获胜结点的邻居，及获胜结点及其邻居获得修改权值的权利）。
图片压缩传输过程：
训练完成获得的权值矩阵作为码本，对于一张新的图片，我们计算图片中各个patch与竞争层结点的距离，最小距离对应的结点的权值向量即可近似认为是图片的patch的表示。然而在传输图片时并不直接传输权值向量，而是传输权值向量的索引，这样就达到了压缩图片进行传输的目的。
在另一端：
假设保存了该权值向量（码本），对于接收到的索引，逐一从码本中找出索引对应的权值向量，并将其按照对应位置组成图片，即完成了图片的恢复。
算法的质量评估：
通常用PSNR（峰值信噪比）描述，一般好的应该在30以上吧，由于这里仅用了最简单的实现算法，PSNR仅有21. 图片的质量并不是非常好。
main.m
clear,clc;
%------------------------------------------------------------
% represent the image by vectors
%------------------------------------------------------------
foo = pwd;
path = fullfile(foo,‘Image‘);
cd(path);
im = imread(‘LENA.BMP‘); % LENA.BMP for the training
cd(foo);
im = double(im);
% (256*256)/(4*4)
% 将（256*256） 分成（4*4）的图像块
n = 4;
m = 4;
block_n = n*ones(1,256/n); % block_n = [4,4....4] 64个4
block_m = m*ones(1,256/m);
im_block = mat2cell (im,block_n,block_m);
%im_block = reshape(im_block,1,4096);
X = ones(16,4096);
for i =1:4096
tmp = cell2mat(im_block(i));
%X(:,i) = reshape(tmp,16,1);
for a = 1:4
for b = 1:4
X(:,i) = tmp(a,b);
end
end
end
[L,K] = size(X);
%------------------------------------------------------------
% code book design
%------------------------------------------------------------
N = 512;
d = ones(1,N);
a = 0.3;
dq = ones(1,4096);
q = ones(1,4096);
t = 1;
W = randint(16,512,[0,255]); % j=1:512 N=512 L=16 random values for W for initialization
pW = ones(16,512); % W(k-1)
iter = 10; % iteration
while iter > 0 %(norm((pW-W),2) > exp(-10))
while (t<=K) % start to train the SOM
for j = 1:N
d(j) = dist(X(:,t),W(:,j));
end
[D,IX] = min(d);
%disp(sprintf(‘%d‘,IX(1)));
dq(t) = D; % find the min{dj} and label q
q(t) = IX;
pW = W; % record current W
W = Update(W,q(t),X(:,t),t,a); % update the W through index
%W = Update2(W,q(t),X(:,t),t,a,d); % update the W through distances
t = t+1;
end
iter = iter - 1;
a = a * 0.95;
end
if pW == W % norm((pW-W),2) 求矩阵的2范数
disp(‘Training Done!!!‘);
else
disp(‘dimensions run out!!!‘);
end
%------------------------------------------------------------
% testing
%------------------------------------------------------------
foo = pwd;
path = fullfile(foo,‘Image‘);
cd(path);
im_1 = imread(‘CR.BMP‘);
im_2 = imread(‘HS4.BMP‘);
im_3 = imread(‘LENA.BMP‘);
cd(foo);
im_1 = double(im_1);
% im_2 = double(im_2);
% im_3 = double(im_3);
test(im_1,W);
% test(im_2,W);
% test(im_3,W);
dist.m
function [d] = dist(x,y) % compute the dist between two vectors m = size(x,1); n = size(y,1); if m ~= n disp(‘different dimensions!!!‘); end s = 0; for i =1:n s = s + (x(i)-y(i))^2; end d = sqrt(s);
Update.m
function [W] = Update(W,q,X,t,a)
% update the values in W
[m,n] = size(W);
Nq = 60; % distance of Neighbor
for j = q-Nq:q+Nq
if j <= 0 || j > 512
continue
end
for i = 1:m
W(i,j) = W(i,j) + a * (X(i)-W(i,j));
end
end
test.m
function [res] = test(im,W)
% test for the image data compression based on SOM network
% (256*256)/(4*4)
% 将（256*256） 分成（4*4）的图像块
n = 4;
m = 4;
block_n = n*ones(1,256/n); % block_n = [4,4....4] 64个4
block_m = m*ones(1,256/m);
im_block = mat2cell (im,block_n,block_m);
%im_block = reshape(im_block,1,4096);
X = ones(16,4096);
for i =1:4096
tmp = cell2mat(im_block(i));
%X(:,i) = reshape(tmp,16,1);
for a = 1:4
for b = 1:4
X(:,i) = tmp(a,b);
end
end
end
[L,K] = size(X);
dq = ones(1,4096);
q = ones(1,4096);
t = 1;
N = 512;
while (t<=K)
for j = 1:N
d(j) = dist(X(:,t),W(:,j));
end
[D,IX] = min(d);
dq(t) = D; % find the min{dj} and label q
q(t) = IX;
t = t+1;
end
%----------------------------------------------------------------
% recover the image
%----------------------------------------------------------------
Y = zeros(L,K);
i =1;
while (i<=K)
tmp = q(i);
for j = 1:16
Y(j,i) = W(j,tmp);
end
i = i+1;
end
res = ones(256,256);
block_n = 4*ones(1,256/4); % block_n = [4,4....4] 64个4
block_m = 4*ones(1,256/4);
res = mat2cell(res,block_n,block_m);
for i =1:K
%temp = reshape(Y(:,i),4,4);
for a = 1:4
for b = 1:4
temp(a,b) = Y(4*(a-1)+b,i);
end
end
res(i) = mat2cell(temp);
end;
res = cell2mat(res);
%Y = imresize(Y,[256,256]);
figure:imshow(res,[0,255]);
tmp = 0;
for m = 1 : 256
for n = 1 : 256
tmp = tmp + (im(m,n) - res(m,n))^2;
end;
end;
MSE = tmp/(256*256);
a = 255*255/MSE;
PSNR = 10*log10(a);
disp(sprintf(‘%f‘,PSNR));
Self-Organizing Feature Map Neural Networks (SOM)
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原文地址：http://www.cnblogs.com/kkangwing/p/5023367.html
