A least square semi-supervised local clustering algorithm based on the idea of compressed sensing are proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two stage approaches 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. Several numerical experiments including the synthetic data and real data such as MNIST, AT\&T and YaleB human faces data sets are conducted to demonstrate the performance of our algorithm.
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