Large Scale Tensor Decompositions: Algorithmic Developments and Applications

Tensor decompositions are increasingly gaining popularity in data science applications. Albeit extremely powerful tools, scalability to truly large datasets for such decomposition algorithms is still a challenging problem. In this paper, we provide an overview of recent algorithmic developments towards the direction of scaling tensor decompositions to big data. We present an exact Map/Reduce based algorithm, as well as an approximate, fully parallelizable algorithm that is sparsity promoting. In both cases, careful design and implementation is key, so that we achieve scalability and efficiency. We showcase the effectiveness of our methods, by providing a variety of real world applications whose volume previously rendered their analysis very hard, if not impossiblewhere our algorithms were able to discover interesting patterns and anomalies.

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