Unsupervised clustering of multidimensional distributions using earth mover distance
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '11
Multidimensional distributions are often used in data mining to describe and summarize different features of large datasets. It is natural to look for distinct classes in such datasets by clustering the data. A common approach entails the use of methods like k-means clustering. However, the k-means method inherently relies on the Euclidean metric in the embedded space and does not account for additional topology underlying the distribution. In this paper, we propose using Earth Mover Distance
... th Mover Distance (EMD) to compare multidimensional distributions. For a n-bin histogram, the EMD is based on a solution to the transportation problem with time complexity O(n 3 log n). To mitigate the high computational cost of EMD, we propose an approximation that reduces the cost to linear time. Other notions of distances such as the information theoretic Kullback-Leibler divergence and statistical χ 2 distance, account only for the correspondence between bins with the same index, and do not use information across bins, and are sensitive to bin size. A cross-bin distance measure like EMD is not affected by binning differences and meaningfully matches the perceptual notion of "nearness". Our technique is simple, efficient and practical for clustering distributions. We demonstrate the use of EMD on a practical application of clustering over 400,000 anonymous mobility usage patterns which are defined as distributions over a manifold. EMD allows us to represent inherent relationships in this space. We show that EMD allows us to successfully cluster even sparse signatures and we compare the results with other clustering methods. Given the large size of our dataset a fast approximation is crucial for this application.