I'm trying to use multidimensional scaling in Matlab. The goal is to convert a similarity matrix to scatter plot (in order to use k-means).
I've got the following test set:
London Stockholm Lisboa Madrid Paris Amsterdam Berlin Prague Rome Dublin
0 569 667 530 141 140 357 396 570 190
569 0 1212 1043 617 446 325 423 787 648
667 1212 0 201 596 768 923 882 714 714
530 1043 201 0 431 608 740 690 516 622
141 617 596 431 0 177 340 337 436 320
140 446 768 608 177 0 218 272 519 302
357 325 923 740 340 218 0 114 472 514
396 423 882 690 337 272 114 0 364 573
569 787 714 516 436 519 472 364 0 755
190 648 714 622 320 302 514 573 755 0
I got this dataset from the book Modern Multidimensional Scaling (Borg & Groenen, 2005). Tested it in SPSS using the PROXSCAL MDS method and I get the same result as stated in the book.
But I need to use MDS in Matlab in order to speed up the process. The tutorial on the site: http://www.mathworks.nl/help/stats/multidimensional-scaling.html#briu08r-4 looks the same as what I'm using above. When I change the data set as what is displayed above and run the code I get the following error: "Not a valid dissimilarity or distance matrix.".
I'm not sure what I'm doing wrong, and if classical MDS is the right choice. I also miss the possibility to say that I want the result in three dimensions (this will be needed in a later stage).
Your matrix is not symetric, check the indices (9,1) and (1,9). To quickly find asymetric indices use [x,y]=find(~(D'==D))