A new clustering approach based on mode identification is developed by applying new optimiza- tion techniques to a nonparametric density estimator. A cluster is formed by those sample points that ascend to the same local maximum (mode) of the density function. The path from a point to its associated mode is efficiently solved by an EM-style algorithm, namely, the Modal EM (MEM). This method is then extended for hierarchical clustering by recursively locating modes of kernel density estimators with increasing bandwidths. Without model fitting, the mode-based clustering yields a density description for every cluster, a major advantage of mixture-model-based clustering. Moreover, it ensures that every cluster corresponds to a bump of the density. The issue of diagnos- ing clustering results is also investigated. Specifically, a pairwise separability measure for clusters is defined using the ridgeline between the density bumps of two clusters. The ridgeline is solved for by the Ridgeline EM (REM) algorithm, an extension of MEM. Based upon this new measure, a cluster merging procedure is created to enforce strong separation. Experiments on simulated and real data demonstrate that the mode-based clustering approach tends to combine the strengths of linkage and mixture-model-based clustering. In addition, the approach is robust in high dimensions and when clusters deviate substantially from Gaussian distributions. Both of these cases pose diffi- culty for parametric mixture modeling. A C package on the new algorithms is developed for public access at http://www.stat.psu.edu/∼jiali/hmac.
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