A Computationally Efficient Data-Dependent Projection for Dimensionality Reduction

Abstract

Principal component analysis (PCA) is a commonly used statistical technique for unsupervised dimensionality reduction, with a drawback of high-computational cost. Random projection (RP) is a matrix-based dimensionality reduction (DR) technique, which projects data by using a projection matrix i.e., constructed with random vectors. Random projection projects the high-dimensional data into low-dimensional feature space with the help of a projection matrix, which is constructed independent of input data. RP uses randomly generated matrices for projection purpose, even though it is computationally more advantageous than PCA, it has been giving unstable results, due to its randomness and data-independence property. Here in this work, we propose a via-medium solution which captures the structure-preserving feature of PCA and the pair-wise distance preserving feature from RP, and also takes less computational cost compared to PCA. Extensive experiments on low and high-dimensional data sets illustrate the efficiency and effectiveness of our proposed method.