Can PCA be applied to achieve any data dimension that we want?

Recently, I was trying to reproduce an algorithm in other's paper. In it, the author exploited PCA to reduce the dimensionality of a matrix to which is shown below as Fig.1. I was not familiar with the PCA. After reading the MATLAB documentation of PCA, I was wondering whether this reduction in matrix dimensionality was possible.

If it is true, how should I realize it in MATLAB?

The matrix represents the coupling from transmit antennas to receive antennas. Each row () represents the coupling from all J transmit antennas to the corresponding receive antenna.

Answer 1

[Walter Roberson]

pca() can be applied to any 2D matrix (including matrixes that include NaN)

pca() does not have an inherent limitations on the size of the 2D matrix you pass in, other than the normal MATLAB size limits.

However, as part of the work, MATLAB may need to construct a covariance matrix, which for an input of n rows and p columns, would be a p x p matrix. If you have many more columns in your matrix than you have rows, then that could be trying to construct a matrix that you do not have room for in memory.

[奥 刘]

Thanks for the reply! I was wodering whether it is possible to exploited PCA to reduce the dimensionality of a matrix to and if it can be down, how should I peroform it?

[Walter Roberson]

https://stats.stackexchange.com/questions/192722/dimension-reduction-using-pca-in-matlab

[奥 刘]

@Walter Roberson Thanks! I will read it carefully!