multidimensional scaling matlab

Multidimensional scaling (MDS) is a technique used for analyzing similarity or dissimilarity data. In MATLAB, there are several functions that can be used for MDS, including cmdscale, mdscale, and cmdscale1.

The cmdscale function performs classical MDS, which is used to represent high-dimensional data in a lower-dimensional space. The mdscale function can be used for both classical MDS and non-classical MDS, which is used for analyzing data that is not Euclidean. The cmdscale1 function is a modified version of cmdscale that allows for missing data.

To use these functions, you will need to provide a distance matrix or similarity matrix as input. The output will be a set of coordinates that represent the data in a lower-dimensional space.

Here is an example of how to use the cmdscale function:

% Generate a random distance matrix
D = rand(5);
D = D + D'; % Make the matrix symmetric

% Perform MDS
[Y, eigvals] = cmdscale(D);

% Plot the results
scatter(Y(:,1), Y(:,2));

This will generate a scatter plot of the data in a two-dimensional space. The cmdscale function also returns the eigenvalues of the distance matrix, which can be used to determine the proportion of variance explained by each dimension.