Efficient Distribution Mining and Classification

We define and solve the problem of “distribution classification”, and, in general, “distribution mining”. Given n distributions (i.e., clouds) of multi-dimensional points, we want to classify them into k classes, to find patterns, rules and out-lier clouds. For example, consider the 2-d case of sales of items, where, for each item sold, we record the unit price and quantity; then, each customer is represented as a distribution/cloud of 2-d points (one for each item he bought). We want to group similar users together, e.g., for market segmentation, anomaly/fraud detection. We propose D-Mine to achieve this goal. Our main contribution is Theorem 3.1, which shows how to use wavelets to speed up the cloud-similarity computations. Extensive experiments on both synthetic and real multidimensional data sets show that our method achieves up to 400 faster wall-clock time over the naive implementation, with comparable (and occasionally better) classification quality.