A Compressed Sensing Based Least Squares Approach to Semi-supervised Local Cluster Extraction

TL;DR

This paper introduces a semi-supervised local clustering algorithm based on compressed sensing that efficiently extracts individual clusters from graphs, outperforming previous methods in weaker assumptions and computational complexity.

Contribution

The paper presents a novel compressed sensing-based least squares approach for semi-supervised local clustering with improved assumptions and lower computational cost.

Findings

Successfully extracts clusters from synthetic and real datasets.

Outperforms existing methods in accuracy and efficiency.

Effective on diverse data types like images and social networks.

Abstract

A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one in \cite{LaiMckenzie2020}. However, under a weaker assumption and with less computational complexity than the one in \cite{LaiMckenzie2020}, the algorithm is shown to be able to find a desired cluster with high probability. The ``one cluster at a time" feature of our method distinguishes it from other global clustering methods. Several numerical experiments are conducted on the synthetic data such as stochastic block model and real data such as MNIST, political blogs network, AT\&T and YaleB human faces data sets to demonstrate the effectiveness and efficiency of our algorithm.