Fast Entropy Clustering of sparse high dimensional binary data

We introduce Sparse Entropy Clustering (SEC) which uses minimum entropy criterion to split high dimensional binary vectors into groups. The idea is based on the analogy between clustering and data compression: every group is reflected by a single encoder which provides its optimal compression. Following the Minimum Description Length Principle the clustering criterion function includes the cost of encoding the elements within clusters as well as the cost of clusters identification. Proposed model is adopted to the sparse structure of data - instead of encoding all coordinates, only non-zero ones are remembered which significantly reduces the computational cost of data processing. Our theoretical and experimental analysis proves that SEC works well with imbalance data, minimizes the average entropy within clusters and is able to select the correct number of clusters.