摘要
This paper exposes some intrlnsic chsracterlstlca of the spectral clustering method by using the tools from the mstrlx perturbation theory. We construct s welght mstrix of s graph and study Its elgenvalues and elgenvectors. It shows that the number of clusters Is equal to the number of elgenvslues that are larger than 1, and the number of polnts In each of the clusters can be spproxlmsted by the associated elgenvslue. It also shows that the elgenvector of the weight rnatrlx can be used dlrectly to perform clusterlng; that Is, the dlrectlonsl angle between the two-row vectors of the mstrlx derlved from the elgenvectors Is s sultable distance measure for clustsrlng. As s result, an unsupervised spectral clusterlng slgorlthm based on welght mstrlx （USCAWM） Is developed. The experlmental results on s number of srtlficisl and real-world data sets show the correctness of the theoretical analysis.
This paper exposes some intrlnsic chsracterlstlca of the spectral clustering method by using the tools from the mstrlx perturbation theory. We construct s welght mstrix of s graph and study Its elgenvalues and elgenvectors. It shows that the number of clusters Is equal to the number of elgenvslues that are larger than 1, and the number of polnts In each of the clusters can be spproxlmsted by the associated elgenvslue. It also shows that the elgenvector of the weight rnatrlx can be used dlrectly to perform clusterlng; that Is, the dlrectlonsl angle between the two-row vectors of the mstrlx derlved from the elgenvectors Is s sultable distance measure for clustsrlng. As s result, an unsupervised spectral clusterlng slgorlthm based on welght mstrlx （USCAWM） Is developed. The experlmental results on s number of srtlficisl and real-world data sets show the correctness of the theoretical analysis.
基金
Supported by the National Natural Science Foundation of China (Grant No. 60375003)
the Aeronatical Science Foundation of China (Grant No. 03I53059)
