Compressive Sensing for Cut Improvement and Local Clustering

Lai, Ming-Jun; McKenzie, Daniel

doi:10.1137/19m1265971

Cited by 4 publications

(17 citation statements)

References 27 publications

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“…The local clustering problem hasn't been studied exhaustively, and many aspects of the local clustering problem still remain open. Some recent related work are [18], [45], [46], [42], and [26]. Especially the work in [26], which is one of the recent works with the same setting as ours.…”

Section: Introductionmentioning

confidence: 94%

“…Some recent related work are [18], [45], [46], [42], and [26]. Especially the work in [26], which is one of the recent works with the same setting as ours. However, as we will see in the numerical experiments section, our approach outperforms them in terms of both the accuracy and efficiency.…”

Section: Introductionmentioning

confidence: 94%

“…It is worthwhile to note that the information theoretical bound for exact cluster recovery in SBM are given in [1] and [2]. It was also shown in [26] that a general SBM with certain choice of parameters can be clustered by using a compressed sensing approach. Our model requires a weaker assumption than the one in [26], indeed, we remove the assumption on the eigenvalues of graph Laplacian L in [26].…”

Section: Graph Model Assumptionmentioning

confidence: 99%

“…The main contribution of this paper is that it proposes the local cluster extraction algorithms LeastSquareClustering and IterLeastSquareClustering which improves the results in [26]. The subsequent sections in this paper are structured as follows.…”

Section: Introductionmentioning

confidence: 99%

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mentioning

confidence: 99%

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

Lai¹,

Shen²

2022

Preprint

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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 [26]. However, under a weaker assumption and with less computational complexity than the one in [26], 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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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 94%

Section: Graph Model Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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

Lai¹,

Shen²

2022

Preprint

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

Lai

Shen

2023

J Sci Comput

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Graph Sparsification by Universal Greedy Algorithms

Lai¹,

Xie²,

Xu³

2023

JCM

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Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, and numerical solution of symmetric positive definite linear systems. In this paper, inspired by the well-known sparse signal recovery algorithm called orthogonal matching pursuit (OMP), we introduce a deterministic, greedy edge selection algorithm, which is called the universal greedy approach (UGA) for the graph sparsification problem. For a general spectral sparsification problem, e.g., the positive subset selection problem from a set of m vectors in R n , we propose a nonnegative UGA algorithm which needs O(mn 2 + n 3 /ǫ 2 ) time to find a 1+ǫ/β 1−ǫ/β -spectral sparsifier with positive coefficients with sparsity at most ⌈ n ǫ 2 ⌉, where β is the ratio between the smallest length and largest length of the vectors. The convergence of the nonnegative UGA algorithm is established. For the graph sparsification problem, another UGA algorithm is proposed which can output a 1+O(ǫ) 1−O(ǫ) -spectral sparsifier with ⌈ n ǫ 2 ⌉ edges in O(m+n 2 /ǫ 2 ) time from a graph with m edges and n vertices under some mild assumptions. This is a linear time algorithm in terms of the number of edges that the community of graph sparsification is looking for. The best result in the literature to the knowledge of the authors is the existence of a deterministic algorithm which is almost linear, i.e. O(m 1+o(1) ) for some o(1) = O( (log log(m)) 2/3 log 1/3 (m)). Finally, extensive experimental results, including applications to graph clustering and least squares regression, show the effectiveness of proposed approaches.

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Compressive Sensing for Cut Improvement and Local Clustering

Cited by 4 publications

References 27 publications

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

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

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

Graph Sparsification by Universal Greedy Algorithms

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