Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation

The Fiedler vector is the eigenvector associated with the algebraic connectivity of the graph Laplacian. It is central to graph analysis as 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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE open journal of signal processing 2024, Vol.5, p.867-885
Main Authors: Tastan, Aylin, Muma, Michael, Zoubir, Abdelhak M.
Format: Article
Language:English
Subjects:
Algorithms
Birds
Data analysis
Dimension reduction
eigen-decomposition
Eigenvalues and eigenfunctions
Eigenvectors
Error analysis
Error detection
Estimation
Fiedler vector
Graph theory
Image quality
Image segmentation
Impact analysis
Indexing
Laplace equations
locality preserving indexing
Operators (mathematics)
Outliers (statistics)
Regularization
Robustness
Vectors
Vectors (mathematics)
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Fiedler vector is the eigenvector associated with the algebraic connectivity of the graph Laplacian. It is central to graph analysis as 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 deteriorate the structure of the Fiedler vector estimate and lead to a breakdown of popular methods. Thus, we propose a Robust Regularized Locality Preserving Indexing (RRLPI) Fiedler vector estimation method that approximates the nonlinear manifold structure of the Laplace Beltrami operator while minimizing the impact of outliers. To achieve this aim, an analysis of the effects of two fundamental outlier types on the eigen-decomposition of block affinity matrices is conducted. Then, an error model is formulated based on which the RRLPI method is developed. It includes an unsupervised regularization parameter selection algorithm that leverages the geometric structure of the projection space. The performance is benchmarked against existing methods in terms of detection probability, partitioning quality, image segmentation capability, robustness and computation time using a large variety of synthetic and real data experiments.
ISSN:2644-1322
2644-1322
DOI:10.1109/OJSP.2024.3400683