Dynamic CUR, an alternative to variable selection in CUR decomposition.

Abstract

[EN]CUR decomposition is one of the matrix decomposition techniques proposed in the literature for the selection of rows and/or columns of a data matrix. Dynamic CUR is proposed as an alternative to the selection criteria of the CUR decomposition based on probabilistic criteria. This alternative tries to fit the most adequate theoretical probability distribution to the empirical distribution of the leverages obtained from the start and based on it, automatically determines not only the individuals and/or variables that need to be selected, but also their numbers. In this way, Dynamic CUR sets itself apart from CUR in the information selection criteria, dynamizing the calculation of the approximation error starting from an optimal initial selection of parameters based on the most adequate probability distribution. Lastly, with the purpose of facilitating the use of this new method in any practical context, the Dynamic CUR algorithm has been developed in C#.NET and R languages.