After PCA, ALS method, use coefficients to reproduce decomposition

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Joshua Diamond 2022-7-19

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回答： Balavignesh 2023-10-4

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I have a matrix A with 100 rows (trials) and 64 columns (variables). This matrix contains NaN values.

I am using the syntax:

[coeff,score] = pca(A,'algorithm','als');

This produces coeff, which is 64 x 64, and score, which is 100 x 64.

I then have a second matrix, B, which is 100 x 64. B also contains NaNs.

Usually, I could do:

score_b = B * coeff

However, this just produces a matrix full of NaNs. It doesn't work because of the NaN values in B. How do I recreate the effect of doing PCA, ALS algorithm, on B?

For instance, I can do as follows, but it doesn't seem as elegant.

[~,score] = pca([A;B],'algorithm','als')
score_b = score(101:200,:)

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Answer 1

Balavignesh 2023-10-4

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Hi Joshua,

As per my understanding, you would like to find 'score_b' for a matrix 'B' by using 'PCA' score of matrix 'A', which has 'NaN' values.

However, applying the 'PCA' to matrix 'A' resulted in a 'score' and 'coeff' which are 'NaN'.

I would suggest you apply 'PCA' to some legitimate dataset to get valid results.

Here is an example code that could help you understand this:

% This is an example dataset. Input your own dataset
load hald.mat
ingredients
ingredients = 13×4
     7    26     6    60
     1    29    15    52
    11    56     8    20
    11    31     8    47
     7    52     6    33
    11    55     9    22
     3    71    17     6
     1    31    22    44
     2    54    18    22
    21    47     4    26
[coeff , score] = pca(ingredients,'Algorithm','als')
coeff = 4×4
   -0.0678   -0.6460    0.5673    0.5062
   -0.6785   -0.0200   -0.5440    0.4933
    0.0290    0.7553    0.4036    0.5156
    0.7309   -0.1085   -0.4684    0.4844
score = 13×4
   36.8218   -6.8709   -4.5909    0.3967
   29.6073    4.6109   -2.2476   -0.3958
  -12.9818   -4.2049    0.9022   -1.1261
   23.7147   -6.6341    1.8547   -0.3786
   -0.5532   -4.4617   -6.0874    0.1424
  -10.8125   -3.6466    0.9130   -0.1350
  -32.5882    8.9798   -1.6063    0.0818
   22.6064   10.7259    3.2365    0.3243
   -9.2626    8.9854   -0.0169   -0.5437
   -3.2840  -14.1573    7.0465    0.3405