Robust PCA for data matrix

HI, could anyone explain to me by performing a robust PCA on a large matrix to eliminate the outliers? Please

Answer 1

[Aditya]

Performing Robust Principal Component Analysis (RPCA) is a technique used to decompose a data matrix into a low-rank component and a sparse component, effectively separating the underlying structure of the data from the outliers. This is particularly useful when dealing with large datasets where outliers can significantly affect the results of standard PCA.Steps to Perform RPCA

Here’s a step-by-step guide to performing RPCA using the inexact_alm_rpca algorithm, which is one of the most popular methods for RPCA. This algorithm can be implemented using the RPCA package in MATLAB.

Using MATLAB

In MATLAB, you can use the inexact_alm_rpca function from the RPCA package. If you don't have this package, you can download it from GitHub.

Step 1: Add the RPCA Package to Your MATLAB Path

Download the RPCA package and add it to your MATLAB path:

addpath('path_to_rpca_package');

Step 2: Perform RPCA

% Assume DATASET is your large matrix
DATASET = [
    10.0, 6.0;
    11.0, 4.0;
    8.0, 5.0;
    3.0, 3.0;
    2.0, 2.8;
    1.0, 1.0
];

% Perform RPCA
[L, S] = inexact_alm_rpca(DATASET);

disp('Low-rank component:');
disp(L);
disp('Sparse component (outliers):');
disp(S);