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FuzzyEn_H_Update_Mean.m
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FuzzyEn_H_Update_Mean.m
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function H_Grad = FuzzyEn_H_Update_Mean(Y,W,H,m,p,r) %#codegen
%% Update of H matrix using a fuzzy entropy distance measure
%
% Inputs:
% Y: Data matrix [X by N]
% W: Decomposition matrix [X by K]
% H: Decomposition matrix [K by N]
% m: Length of sequences to be compared
% p: Gradient of the exponential boundary
% r: Vector of widths of exponential boundary for each row of Y
%
% Output:
% H_Grad: Matrix of gradients of each element of W [X by K]
%
% codegen FuzzyEn_H_Update_Mean -args {coder.typeof(double(0),[100 100000],1),coder.typeof(double(0),[100 100],1),coder.typeof(double(0),[100 100000],1),0,0,coder.typeof(double(0),[1 100000],1)} -report -o FuzzyEn_H_Update_Mean_mex
% Calculate the dimensions
[X,N] = size(Y);
[~,K] = size(W);
% calculate the current value of the approximation of Y
WH = W*H;
% Initialize variables
Phi = zeros(X,1); % Phi(m) for each row of Y & WH
Phi1 = zeros(X,1); % Phi(m+1) for each row of Y & WH
gradPhi_H = zeros(K,N); % Gradient of Phi(m) for each element of H
gradPhi1_H = zeros(K,N); % Gradient of Phi(m+1) for each element of H
H_Grad = zeros(K,N); % Overall gradient of each element of H
c = 0;
% Update H
for n=1:N % Iterate through each column of H
for k=1:K % Iterate through each row of H
gradPhi_tmp = 0; % Initialize temporary variables for current elements gradient
gradPhi1_tmp = 0;
for x = 1:X % Iterate through each row of Y & W
dPhi_x = 0; % Initialize variables for gradient of current row
dPhi1_x = 0;
for i=1:N-m % Iterate through all sequences in current row of Y
% Select m and m+1 elements of current row of Y starting from i
y_m = Y(x,i:i+m-1);
y_m = y_m - mean(y_m);
y_m1 = Y(x,i:i+m);
y_m1 = y_m1 - mean(y_m1);
% Check if first iteration
if n==1 && k==1
% If so iterate through all j in the first row
for j=1:N-m
% Select m and m+1 elements of current row of WH starting from j
wh_m = WH(x,j:j+m-1);
wh_m = wh_m - mean(wh_m);
wh_m1 = WH(x,j:j+m);
wh_m1 = wh_m1 - mean(wh_m1);
% Calculate the current distances and similarity of vectors
d_m = norm(y_m-wh_m,Inf);
d_m1 = norm(y_m1-wh_m1,Inf);
D_m = exp(-d_m^p/r(x));
D_m1 = exp(-d_m1^p/r(x));
% On the first iteration calculate the average degree of similarity of all the vectors
Phi(x) = Phi(x) + D_m;
Phi1(x) = Phi1(x) + D_m1;
z = n-j+1; % Find the position of the current element in the vectors
if j>=max(1,n-m+1) && j<=min(n,N-m) % Check whether the current element is in the current vector of length m
c(1) = find(abs(y_m-wh_m) == d_m,1,'first');
% Check whether the current element contributes to the maximum distance
if (c == z)
% If so calculate the values of the gradient of the similarity
dPhi_x = dPhi_x + D_m*(p/r(x))*d_m^(p-1)*((m-1)/m)*sign(y_m(c)-wh_m(c))*W(x,k);
else
dPhi_x = dPhi_x + D_m*(p/r(x))*d_m^(p-1)*(1/m)*sign(y_m(c)-wh_m(c))*W(x,k);
end
if j>=max(1,n-m) && j<=min(n,N-m) % Check whether the current element is in the current vector of length m+1
c(1) = find(abs(y_m1-wh_m1) == d_m1,1);
% Check whether the current element contributes to the maximum distance
if (c == z)
% If so calculate the values of the gradient of the similarity
dPhi1_x = dPhi1_x + D_m1*(p/r(x))*d_m1^(p-1)*(m/(m+1))*sign(y_m1(c)-wh_m1(c))*W(x,k);
else
dPhi1_x = dPhi1_x + D_m1*(p/r(x))*d_m1^(p-1)*(1/(m+1))*sign(y_m1(c)-wh_m1(c))*W(x,k);
end
end
end
end
else
% If not the first iteration select only the j (n-m) either side of n
for j=max(1,n-m):min(n,N-m)
z = n-j+1; % Find the position of the current element in the vectors
if j>=max(1,n-m+1) % Check whether the current element is in the current vector of length m
% Select m elements of current row of WH starting from j
wh_m = WH(x,j:j+m-1);
wh_m = wh_m - mean(wh_m);
% Calculate the current distance and similarity of vectors
d_m = norm(y_m-wh_m,Inf);
D_m = exp(-d_m^p/r(x));
c(1) = find(abs(y_m-wh_m) == d_m,1);
% Check whether the current element contributes to the maximum distance
if (c == z)
% Calculate the values of the gradient of the similarity
dPhi_x = dPhi_x + D_m*(p/r(x))*d_m^(p-1)*((m-1)/m)*sign(y_m(c)-wh_m(c))*W(x,k);
else
dPhi_x = dPhi_x + D_m*(p/r(x))*d_m^(p-1)*(1/m)*sign(y_m(c)-wh_m(c))*W(x,k);
end
end
% Select m+1 elements of current row of WH starting from j
wh_m1 = WH(x,j:j+m);
wh_m1 = wh_m1 - mean(wh_m1);
% Calculate the current distances and similarity of vectors
d_m1 = norm(y_m1-wh_m1,Inf);
D_m1 = exp(-d_m1^p/r(x));
c(1) = find(abs(y_m1-wh_m1) == d_m1,1);
% Check whether the current element contributes to the maximum distance
if (c == z)
% Calculate the values of the gradient of the similarity
dPhi1_x = dPhi1_x + D_m1*(p/r(x))*d_m1^(p-1)*(m/(m+1))*sign(y_m1(c)-wh_m1(c))*W(x,k);
else
dPhi1_x = dPhi1_x + D_m1*(p/r(x))*d_m1^(p-1)*(1/(m+1))*sign(y_m1(c)-wh_m1(c))*W(x,k);
end
end
end
end
if Phi(x)~=0
% Calculate the gradient for the current element across the rows of WH for m and m+1
gradPhi_tmp = gradPhi_tmp + dPhi_x/Phi(x);
end
if Phi1(x)~=0
gradPhi1_tmp = gradPhi1_tmp + dPhi1_x/Phi1(x);
end
end
% Store the gradients for the current element for m and m+1
gradPhi_H(k,n) = gradPhi_tmp;
gradPhi1_H(k,n) = gradPhi1_tmp;
% Calculate the overal gradient of the element of
H_Grad(k,n) = gradPhi1_H(k,n) - gradPhi_H(k,n);
end
end