Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation
This work addresses robustness in graph-based learning for applications like clustering and image segmentation, but it is incremental as it builds on existing methods with specific enhancements.
The paper tackled the problem of Fiedler vector estimation in graphs under heavy-tailed noise and outliers by developing a Robust Regularized Locality Preserving Indexing (RRLPI) method, which improved detection probability, partitioning quality, and robustness in synthetic and real data experiments.
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.