Incremental PARAFAC Decomposition for Three-Dimensional Tensors Using Apache Spark

Abstract

Recent studies have focused on the use of tensor analysis for tensor decomposition because this method can identify more latent factor and patterns, compared to the matrix factorization approach. The existing tensor decomposition studies used static dataset in their analyses. However, in practice, data change and increase over time. Therefore, this paper proposes an incremental Parallel Factor Analysis (PARAFAC) tensor decomposition algorithm for three-dimensional tensors. The method of incremental tensor decomposition can reduce recalculation costs associated with the addition of new tensors. The proposed method is called InParTen; it performs distributed incremental PARAFAC tensor decomposition based on the Apache Spark framework. The proposed method decomposes only new tensors and then combines them with existing results without recalculating the complete tensors. In this study, it was assumed that the tensors grow with time as the majority of the dataset is added over a period. In this paper, the performance of InParTen was evaluated by comparing the obtained results for execution time and relative errors against existing tensor decomposition tools. Consequently, it has been observed that the method can reduce the recalculation cost of tensor decomposition.