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# pca()

Read（2051） Label: matrix, pca, dimensionality reduction,

Description:

External library function ; perform PCA on a matrix and return data for dimensionality reduction.

Syntax:

pca(A,n)  Perform PCA (Principal Component Analysis) on matrix A and return data for dimensionality reduction; n is the number of principal components

pca(A,F)  Reduce dimensionality for another matrix having same number of columns

Parameter:

 A A matrix n Number of principal components F The PCA fitting object returned by pca(A,n)

Option:

 @r Enable returning the result of dimensionality reduction on matrix A, which is a matrix of n columns, directly

Return value:

A PCA fitting object or a sequence

Example:

A

1

[[1,2,3,4],[2,3,1,2],[1,1,1,-1],[1,0,-2,-6]]

2

=pca(A1,2) Return data for dimensionality reduction:

A2(1) Averages of columns

A2(2) Variances of principal components ordered descendingly

A2(3) Coefficients of principal components

3

=pca(A1,A2) Execute dimensionality reduction on A1

4

=pca@r(A1,2) Use @r option to reduce A1’s dimensionality directly; result is the same as A3’s

5

[[4,6,2,4],[2,3,1,2],[1,1,1,-1]]

6

=pca(A5,A2) Exectue dimensionality reduction on another matrix having same number of columns as the original matrix