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

Distance-based clustering is widely used to group mixed numeric and categorical data (mixed-type data), where a predefined metric is used to quantify dissimilarity or distance between data points for clustering data. However, many existing metrics for mixed-type data convert continuous attributes to categorical attributes, or vice versa, and treat variables collectively as a single type, or calculate a distance between each variable separately and combine them. We propose a flexible kernel metric learning approach that balances numeric and categorical data types while determining which variables are relevant to dissimilarities within a dataset. The distance using kernel product similarity (DKPS) function uses kernel functions to measure similarity, with a maximum similarity cross-validated (MSCV) bandwidth selection technique that automatically scales and selects variables relevant to the underlying dissimilarities between data points. We prove that the DKPS function is a metric and show that the DKPS metric is a shrinkage method between maximum dissimilarity between all data points to uniform dissimilarity across data points. We demonstrate that when using the DKPS metric in various distance-based clustering algorithms, we improve clustering accuracy for simulated and real-world mixed-type datasets. In the context of clustering, we show that the DKPS metric with MSCV bandwidths is able to smooth out irrelevant variables and balance variables important to dissimilarity within mixed-type datasets.