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

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 proposed by Lai and Mckenzie (SIAM J Math Data Sci 2:368-395, 2020). However, under a weaker assumption and with less computational complexity, our algorithms are 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. 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 algorithms.