DN3MF: deep neural network for non-negative matrix factorization towards low rank approximation

Abstract

Dimension reduction is one of the most sought-after methodologies to deal with high-dimensional ever-expanding complex datasets. Non-negative matrix factorization (NMF) is one such technique for dimension reduction. Here, a multiple deconstruction multiple reconstruction deep learning model (DN3MF) for NMF targeted towards low rank approximation, has been developed. Non-negative input data has been processed using hierarchical learning to generate part-based sparse and meaningful representation. The novel design of DN3MF ensures the non-negativity requirement of the model. The use of Xavier initialization technique solves the exploding or vanishing gradient problem. The objective function of the model has been designed employing regularization, ensuring the best possible approximation of the input matrix. A novel adaptive learning mechanism has been developed to accomplish the objective of the model. The superior performance of the proposed model has been established by comparing the results obtained by the model with that of six other well-established dimension reduction algorithms on three well-known datasets in terms of preservation of the local structure of data in low rank embedding, and in the context of downstream analyses using classification and clustering. The statistical significance of the results has also been established. The outcome clearly demonstrates DN3MF’s superiority over compared dimension reduction approaches in terms of both statistical and intrinsic property preservation standards. The comparative analysis of all seven dimensionality reduction algorithms including DN3MF with respect to the computational complexity and a pictorial depiction of the convergence analysis for both stages of DN3MF have also been presented.