Clustering is the process of putting observations into groups based on their distance, or dissimilarity, from one another. Measuring distance for continuous variables often requires scaling or monotonic transformation. Determining dissimilarity when observations have both continuous and categorical measurements can be difficult because each type of measurement must be approached differently. We introduce a new clustering method that uses one of three new distance metrics. In a dataset with p variables, we create p trees, one with each variable as the response. Distance is measured by determining on which leaf an observation falls in each tree. Two observations are similar if they tend to fall on the same leaf and dissimilar if they are usually on different leaves. The distance metrics are not affected by scaling or transformations of the variables and easily determine distances in datasets with both continuous and categorical variables. This method is tested on several well-known datasets, both with and without added noise variables, and performs very well in the presence of noise due in part to automatic variable selection. The new distance metrics outperform several existing clustering methods in a large number of scenarios.
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