Discretization is the transformation of continuous data into discrete bins. It is an important and general pre-processing technique, and a critical element of many data mining and data management tasks. The general goal is to obtain data that retains as much information in the continuous original as possible. In general, but in particular for exploratory tasks, a key open question is how to discretize multivariate data such that significant associations and patterns are preserved. That is exactly the problem we study in this paper. We propose IPD, an information-theoretic method for unsupervised discretization that focuses on preserving multivariate interactions. To this end, when discretizing a dimension, we consider the distribution of the data over all other dimensions. In particular, our method examines consecutive multivariate regions and combines them if (a) their multivariate data distributions are statistically similar, and (b) this merge reduces the MDL encoding cost. To assess the similarities, we propose \( ID \), a novel interaction distance that does not require assuming a distribution and permits computation in closed form. We give an efficient algorithm for finding the optimal bin merge, as well as a fast well-performing heuristic. Empirical evaluation through pattern-based compression, outlier mining, and classification shows that by preserving interactions we consistently outperform the state of the art in both quality and speed.
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We thank the anomymous reviewers for their insightful comments. Hoang-Vu Nguyen is supported by the German Research Foundation (DFG) within GRK 1194. Emmanuel Müller is supported by the YIG program of KIT as part of the German Excellence Initiative. Jilles Vreeken is supported by the Cluster of Excellence “Multimodal Computing and Interaction” within the Excellence Initiative of the German Federal Government. Emmanuel Müller and Jilles Vreeken are supported by Post-Doctoral Fellowships of the Research Foundation—Flanders (fwo).
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