Dimensionality reduction on matrices with missing entries

Hi guys,

I wanted to do dimensionality reduction on many matrices so that they all have the same dimensions.

So, I have matrices of the dimensions: 50x220, 50x190, 50x300, 50x235, 50x149, etc. At the end I want to reduce second dimension to 10 so I would have matrices 50x10, 50x10, 50x10, 50x10 and so on for each of them. The problem is that in my case I have matrices with missing values and I use the general pca function for raw data.

So I have matrices something like that:

X(1).matrix = [1 2 3 ...
               3 4 5 ...
               3 4 4 ...
               6 NaN 7 ...
               ...........
               NaN NaN NaN]
           
X(2).matrix = [3 4 5 ... 
               5 6 7 ...
               4 4 4 ...
               NaN 3 3 ...
               NaN 4 4 ...
               ...........
               NaN NaN 7]
X(3).matrix = [3 3 3
               2 1 3
               ...........
               NaN 1 2]
         
           

After applying function pca I just get some coeff. But I dont know how to actually get to the dimensionality reduction (i.e. matrices having dimensions 50x10 dimensions). Thanks in advance for your time and help!

Answer 1

[KSSV]

[coeff,score,latent] = pca(mymatrix)

here latent gives you variance of the principal components in decreasing order. You can pick the first n (10) number of columns.

For more information read: http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf

[Spresi]

Thanks for the answer!

So, I pick the first 10 columns of score matrix right?

Or do I pick the first 10 rows of the score matrix?