Improved Dimensionality Reduction of various Datasets using Novel Multiplicative Factoring Principal Component Analysis (MPCA)

TL;DR

This paper introduces Multiplicative Factoring PCA (MPCA), an improved dimensionality reduction method that reduces the influence of outliers by applying multiplicative penalties, demonstrating superior performance on multiple datasets.

Contribution

The paper proposes MPCA, a novel PCA enhancement using multiplicative penalties with distance and similarity metrics to better handle outliers in various datasets.

Findings

MPCA outperforms traditional PCA and recent methods on multiple datasets.

MPCA effectively reduces outlier influence in dimensionality reduction.

Experimental results show improved low-rank projections with MPCA.

Abstract

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of various datasets. In this paper, we present an improvement to the traditional PCA approach called Multiplicative factoring Principal Component Analysis (MPCA). The advantage of MPCA over the traditional PCA is that a penalty is imposed on the occurrence space through a multiplier to make negligible the effect of outliers in seeking out projections. Here we apply two multiplier approaches, total distance and cosine similarity metrics. These two approaches can learn the relationship that exists between each of the data points and the principal projections in the feature space. As a result of this, improved low-rank projections are gotten through multiplying the data iteratively to make negligible the effect of corrupt data in the training set. Experiments were carried out on YaleB, MNIST, AR, and Isolet datasets and the results were compared to results gotten from some popular dimensionality reduction methods such as traditional PCA, RPCA-OM, and also some recently published methods such as IFPCA-1 and IFPCA-2.