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Register a new userCAST: A Correlation-based Adaptive Spectral Clustering Algorithm on Multi-scale Data
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Xiang Li
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity matrix that reflects the proximity of objects. For multi-scale data, distance-based similarity is not effective because objects of a sparse cluster could be far apart while those of a dense cluster have to be sufficiently close. Following [16], we solve the problem of spectral clustering on multi-scale data by integrating the concept of objects reachability similarity with a given distance-based similarity to derive an objects coefficient matrix. We propose the algorithm CAST that applies trace Lasso to regularize the coefficient matrix. We prove that the resulting coefficient matrix has the grouping effect and that it exhibits sparsity. We show that these two characteristics imply very effective spectral clustering. We evaluate CAST and 10 other clustering methods on a wide range of datasets w.r.t. various measures. Experimental results show that CAST provides excellent performance and is highly robust across test cases of multi-scale data.
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Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each players expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
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