lsa.m

用于文本语义分析的潜在语义分析算法LSA(Latent Semantic Analysis)

function [dr,wr]=lsa(X,k)
% LSA  Latent Semantic Analysis of document-word co-occurrence matrix X
% Input:
%       k --- number of topics
% Output:
%       dr --- Spearman Rank Correlation of documents
%       wr --- Spearman Rank Correlation of words

% About Spearman Rank Correlation:
%   Spearman Rank Correlation is an effective measure of two matrices/arrays.
%   Firstly you are supposed to get the Spearman Rank matrices/arrays of the
%   original matrices/arrays( This is done by spearmanrankcollums.m &
%   spearmanrankrows.m ). Then use the following equation to compute the
%   distance(correlation) of them:
%           r=1-6*sum(d.^2)/(n*(n^2-1))
%     (d = array1 - array2, for matrix array1/2 is replaced with the
%     collum/row components, n = length(array1)=length(array2))
%   r belongs to [-1,1], the bigger r is, the more relative the two arrays
%   are.
% See details in spearmanrankcollums.m spearmanrankrows.m
% spearmanrcollums.m spearmanrrows.m

% Reference: "Tang Ketan,LSA"

% By Tang Ketan, [e-mail]
% 2007/10/25

[m,n]=size(X);
[U,S,V]=svd(X);   % svd decomposition

% let all the diagnal elements of S to be zeros except the first k elements
for i=k+1:min(size(S))
    S(i,i)=0;
end

Y=U*S*V';  % regenerate the data

d = spearmanrankcollums(Y);   % generate Spearman Rank matrix of Y, i.e. words array
w = spearmanrankrows(Y);      % generate Spearman Rank matrix of Y, i.e. documents array

dr = spearmanrcollums(d)
wr = spearmanrrows(w)