  Referring back to the original text in the course of hierarchical learning is
a common human trait that ensures the right direction of learning. The models
developed based on the concept of Non-negative Matrix Factorization (NMF), in
this paper are inspired by this idea. They aim to deal with high-dimensional
data by discovering its low rank approximation by determining a unique pair of
factor matrices. The model, named Input Guided Multiple Deconstruction Single
Reconstruction neural network for Non-negative Matrix Factorization
(IG-MDSR-NMF), ensures the non-negativity constraints of both factors. Whereas
Input Guided Multiple Deconstruction Single Reconstruction neural network for
Relaxed Non-negative Matrix Factorization (IG-MDSR-RNMF) introduces a novel
idea of factorization with only the basis matrix adhering to the non-negativity
criteria. This relaxed version helps the model to learn more enriched low
dimensional embedding of the original data matrix. The competency of preserving
the local structure of data in its low rank embedding produced by both the
models has been appropriately verified. The superiority of low dimensional
embedding over that of the original data justifying the need for dimension
reduction has been established. The primacy of both the models has also been
validated by comparing their performances separately with that of nine other
established dimension reduction algorithms on five popular datasets. Moreover,
computational complexity of the models and convergence analysis have also been
presented testifying to the supremacy of the models.
