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# A Clustering Algorithm Merging MCMC and EM Methods Using SQL Queries

*Proceedings of the 3rd International Workshop on Big Data, Streams and Heterogeneous Source Mining: Algorithms, Systems, Programming Models and Applications*, PMLR 36:61-76, 2014.

#### Abstract

CClustering is an important problem in Statistics and Machine Learning that is usually solved using Likelihood Maximization Methods, of which the Expectation-Maximization Algorithm (EM) is the most common. In this work we present an SQL implementation of an algorithm merging Markov Chain Monte Carlo methods with the EM algorithm to find qualitatively better solutions for the clustering problem. Even though SQL is not optimized for complex calculations, as it is constrained to work on tables and columns, it is unparalleled in handling all aspects of storage management, security of the information, fault management, etc. Our algorithm makes use of these characteristics to produce portable solutions that are comparable to the results obtained by other algorithms and are more efficient since the calculations are all performed inside the DBMS. To simplify the calculation we use very simple scalar UDFs, of a type that is available in most DBMS. The solution has linear time complexity on the size of the data set and it has a linear speedup with the number of servers in the cluster. This was achieved using sufficient statistics and a simplified model that assigns the data-points to different clusters during the E-step in an incremental manner and the introduction of a Sampling step in order to explore the solution space in a more efficient manner. Preliminary experiments show very good agreement with standard solutions.