Graph filtering for data reduction and reconstruction

TL;DR

This paper introduces a graph filtering method that leverages data similarity on a graph to enhance data reduction and reconstruction, outperforming traditional PCA in image datasets.

Contribution

It presents a novel graph filtering framework for data reduction and reconstruction, optimizing filters via mean-square error in the spectral domain.

Findings

Better reconstruction performance than PCA

Effective use of graph spectral domain

Numerical validation on real image datasets

Abstract

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connectivity in a graph via the adjacency matrix. The unknown reducing and reconstruction filters are determined by optimizing a mean-square error cost that entails the data, as well as their graph adjacency matrix. Working in the graph spectral domain enables the derivation of simple gradient descent recursions used to update the matrix filter taps. Numerical tests in real image datasets demonstrate the better reconstruction performance of the novel method over standard principal component analysis.