There exist many approaches to clustering, but the important issue of feature selection, i.e., selecting the data attributes that are relevant for clustering, is rarely addressed. Feature selection for clustering is difficult due to the absence of class labels. We propose two approaches to feature selection in the context of Gaussian mixture-based clustering. In the first one, instead of making hard selections, we estimate feature saliencies. An expectation-maximization (EM) algorithm is derived for this task. The second approach extends Koller and Sahami's mutual-information-based feature relevance criterion to the unsupervised case. Feature selection is then carried out by a backward search scheme. This scheme can be classified as a "wrapper", since it wraps mixture estimation in an outer layer that performs feature selection. Experimental results on synthetic and real data show that both methods have promising performance.
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