Graph filtering for data reduction and reconstruction

ABSTRACT A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction per - formance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulat ed 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 th e 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 tap s. Numerical tests in real image datasets demonstrate the bett er reconstruction performance of the novel method over standard principal component analysis.