In this study we propose a systematic methodology for constructing a sparse affinity matrix to be used in an advantageous spectral clustering approach. Newton's equations of motion are employed to concentrate the data points around their cluster centers, using an appropriate potential. During this process possibly overlapping clusters are separated, and simultaneously, useful similarity information is gained leading to the enrichment of the affinity matrix. The method was further developed to treat high-dimensional data with application to document clustering. We have tested the method on several benchmark data sets and we witness a superior performance in comparison with the standard approach.
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