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Distance-based clustering and classification are widely used in variousfields to group mixed numeric and categorical data. In many algorithms, apredefined distance measurement is used to cluster data points based on theirdissimilarity. While there exist numerous distance-based measures for data withpure numerical attributes and several ordered and unordered categoricalmetrics, an efficient and accurate distance for mixed-type data that utilizesthe continuous and discrete properties simulatenously is an open problem. Manymetrics convert numerical attributes to categorical ones or vice versa. Theyhandle the data points as a single attribute type or calculate a distancebetween each attribute separately and add them up. We propose a metric calledKDSUM that uses mixed kernels to measure dissimilarity, with cross-validatedoptimal bandwidth selection. We demonstrate that KDSUM is a shrinkage methodfrom existing mixed-type metrics to a uniform dissimilarity metric, andimproves clustering accuracy when utilized in existing distance-basedclustering algorithms on simulated and real-world datasets containingcontinuous-only, categorical-only, and mixed-type data.

Mixed-type Distance Shrinkage and Selection for Clustering via Kernel Metric Learning