# Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation

arXiv: https://arxiv.org/abs/2107.12070 · HTML: https://mlsanity.com/paper/2107.12070/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 86 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 14 of 14)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [GAP: Generalizable Approximate Graph Partitioning Framework](https://mlsanity.com/paper/1903.00614/) (2019)
- [A General Optimization Technique for High Quality Community Detection in Complex Networks](https://mlsanity.com/paper/1308.3508/) (2013)
- [An ensemble-based system for automatic screening of diabetic retinopathy](https://mlsanity.com/paper/1410.8576/) (2014)
- [Toward Unobtrusive In-home Gait Analysis Based on Radar Micro-Doppler Signatures](https://mlsanity.com/paper/1809.06653/) (2018)
- [Fiedler Regularization: Learning Neural Networks with Graph Sparsity](https://mlsanity.com/paper/2003.00992/) (2020)
- [A Linearly Convergent Algorithm for Distributed Principal Component Analysis](https://mlsanity.com/paper/2101.01300/) (2021)
- [Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs](https://mlsanity.com/paper/1802.07648/) (2018)
- [Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian](https://mlsanity.com/paper/1810.10695/) (2018)
- [Self-Weighted Robust LDA for Multiclass Classification with Edge Classes](https://mlsanity.com/paper/2009.12362/) (2020)
- [Compound Rank-k Projections for Bilinear Analysis](https://mlsanity.com/paper/1411.6231/) (2014)
- [Spectral Clustering Revisited: Information Hidden in the Fiedler Vector](https://mlsanity.com/paper/2003.09969/) (2020)
- [Distributed Estimation and Control of Algebraic Connectivity over Random Graphs](https://mlsanity.com/paper/1309.3200/) (2013)

## Built on by (most cited first, 1 of 1)

- [Fast and Robust Sparsity-Aware Block Diagonal Representation](https://mlsanity.com/paper/2312.01137/) (2023)

## Abstract (arXiv)

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.