We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees; another finds a "good" clustering, if one exists.
Kernel k-means and spectral clustering have both been used to identify clusters that are non-linearly separable in input space. Despite significant research, these methods have ...
Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonab...
Abstract Many intuitively appealing methods have been suggested for clustering data, however, interpretation of their results has been hindered by the lack of objective criteria...
Data clustering describes a set of frequently employed techniques in exploratory data analysis to extract “natural” group structure in data. Such groupings need to be validated ...
In this letter, we show a direct relation between spectral embedding methods and kernel principal components analysis and how both are special cases of a more general learning p...
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