Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation

TL;DR

This paper introduces RRLPI, a robust method for estimating the Fiedler vector in graphs, effectively handling outliers and noise to improve graph structure learning.

Contribution

The paper proposes a novel robust regularized indexing method for Fiedler vector estimation that accounts for outliers and nonlinear manifold structures.

Findings

RRLPI outperforms existing methods in robustness and accuracy.

Effective in image segmentation and clustering tasks.

Demonstrates computational efficiency on synthetic and real data.

Abstract

The Fiedler vector of a connected graph is the eigenvector associated with the algebraic connectivity of the graph Laplacian and it provides substantial information to learn the latent structure of a graph. In real-world applications, however, the data may be subject to heavy-tailed noise and outliers which results in deteriorations in the structure of the Fiedler vector estimate. We design a Robust Regularized Locality Preserving Indexing (RRLPI) method for Fiedler vector estimation that aims to approximate the nonlinear manifold structure of the Laplace Beltrami operator while minimizing the negative impact of outliers. First, an analysis of the effects of two fundamental outlier types on the eigen-decomposition for block affinity matrices which are essential in cluster analysis is conducted. Then, an error model is formulated and a robust Fiedler vector estimation algorithm is developed. An unsupervised penalty parameter selection algorithm is proposed that leverages the geometric structure of the projection space to perform robust regularized Fiedler estimation. The performance of RRLPI is benchmarked against existing competitors in terms of detection probability, partitioning quality, image segmentation capability, robustness and computation time using a large variety of synthetic and real data experiments.