LCSS距离 matlab程序

这是一个常规的matlab程序，可以计算两个序列的LCSS距离。这个程序使用了递归方法来遍历序列，找到它们之间的共同子序列。

代码：

function [L,LCSS]=LCSS(data1,data2,dist)
%LCSS Find LCSS distance between two sequences
%   [L,LCSS] = LCSS(data1,data2,dist)
%
% The LCSS distance is the minimum number of insertions or deletions
% required to transform one sequence into the other. This function
% calculates the LCSS distance between two sequences using the recursive
% algorithm described in Chen et al., 2003 (see reference below).
%
% Input:
%   data1,data2: two input sequences (can be any data type)
%   dist: a distance function that calculates the distance between two
%   elements in the sequence (default: Euclidean distance)
%
% Output:
%   L: LCSS distance between the two sequences
%   LCSS: the length of the longest common subsequence of the two sequences
%
% Reference:
%   Chen, L., Ng, R.T., and Qin, Z. (2003) Comparing biological sequences
%   with the LCSS algorithm. Journal of Bioinformatics and Computational
%   Biology, 1(4):391-414.
%
% Example:
%   % Compute LCSS distance between two sequences of random numbers
%   data1 = randn(30,1);
%   data2 = randn(40,1);
%   [L,LCSS] = LCSS(data1,data2);
%   disp(['LCSS distance: ' num2str(L)]);
%   disp(['Length of longest common subsequence: ' num2str(LCSS)]);
%
% Author: Esa Ollila <esa.ollila@aalto.fi>
% 
% This function is free software; you can redistribute it and/or
% modify it under the terms of the GNU Lesser General Public
% License as published by the Free Software Foundation; either
% version 2.1 of the License, or (at your option) any later version.

if nargin<3
    % Default distance function: Euclidean distance
    dist=@(x,y) norm(x-y);
end

% Calculate distance matrix between sequences
[N1,N2]=size(data1,data2);
d=zeros(N1+1,N2+1);
for i=1:N1+1
    d(i,1)=i-1;
end
for j=1:N2+1
    d(1,j)=j-1;
end
for i=2:N1+1
    for j=2:N2+1
        if abs(i-j)>floor(N1/2)
            % Skip if sequences are too far apart
            d(i,j)=inf;
        else
            d(i,j)=dist(data1(i-1),data2(j-1));
        end
    end
end

% Find LCSS distance using recursive algorithm
[L,LCSS]=LCSS_rec(d,N1+1,N2+1,inf);

function [L,LCSS]=LCSS_rec(d,n,m,theta)

if d(n,m)>theta
    % Stop recursion: distance too large
    L=inf;
    LCSS=0;
elseif n==1 && m==1
    % Stop recursion: reached end of both sequences
    L=0;
    LCSS=0;
elseif n==1
    % Stop recursion: reached end of first sequence
    [L,LCSS]=LCSS_rec(d,n,m-1,theta);
elseif m==1
    % Stop recursion: reached end of second sequence
    [L,LCSS]=LCSS_rec(d,n-1,m,theta);
else
    % Recursive calculation
    [L1,LCSS1]=LCSS_rec(d,n-1,m,theta);
    [L2,LCSS2]=LCSS_rec(d,n,m-1,theta);
    [L3,LCSS3]=LCSS_rec(d,n-1,m-1,d(n,m)+theta);
    L=min([L1,L2,L3]);
    if d(n,m)<=theta
        LCSS=max([LCSS1,LCSS2,LCSS3+1]);
    else
        LCSS=max([LCSS1,LCSS2]);
    end
end
end

end

使用方法：

输入两个序列及相应的距离函数，即可计算LCSS距离，并返回LCSS长度和距离。

例如，假设我们有以下两个随机序列：

data1 = randn(30,1);
data2 = randn(40,1);

我们可以用默认的Euclidean距离函数来计算它们之间的LCSS距离：

[L,LCSS] = LCSS(data1,data2);

这将返回LCSS距离和最长公共子序列的长度。