Tail-Net: Extracting Lowest Singular Triplets for Big Data Applications

TL;DR

Tail-Net is a novel neural network-based method designed to efficiently extract the lowest singular triplets from large datasets, addressing memory and computational challenges in big data applications.

Contribution

This paper introduces Tail-Net, an extension of Range-Net, for memory-efficient extraction of lowest singular factors in big data, enabling practical analysis of large-scale datasets.

Findings

Tail-Net accurately identifies lowest singular triplets in synthetic and real datasets.

It outperforms traditional SVD in terms of memory usage and computational efficiency.

Numerical experiments validate Tail-Net's effectiveness and scalability.

Abstract

SVD serves as an exploratory tool in identifying the dominant features in the form of top rank-r singular factors corresponding to the largest singular values. For Big Data applications it is well known that Singular Value Decomposition (SVD) is restrictive due to main memory requirements. However, a number of applications such as community detection, clustering, or bottleneck identification in large scale graph data-sets rely upon identifying the lowest singular values and the singular corresponding vectors. For example, the lowest singular values of a graph Laplacian reveal the number of isolated clusters (zero singular values) or bottlenecks (lowest non-zero singular values) for undirected, acyclic graphs. A naive approach here would be to perform a full SVD however, this quickly becomes infeasible for practical big data applications due to the enormous memory requirements. Furthermore, for such applications only a few lowest singular factors are desired making a full decomposition computationally exorbitant. In this work, we trivially extend the previously proposed Range-Net to \textbf{Tail-Net} for a memory and compute efficient extraction of lowest singular factors of a given big dataset and a specified rank-r. We present a number of numerical experiments on both synthetic and practical data-sets for verification and bench-marking using conventional SVD as the baseline.