  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.
