Tensor representation, constrain (storage) and processing of multidimensional astronomical data over intense computing support

Abstract

The big data problem in Astronomy is a well now know issue, but in majority of the cases is constrains to volume of this data. Our propose take care of another aspect of the problem: the dimensionality problem, in the scope of multidimensional data especially Astronomical data cubes. We use tensor decompositions for two goals, first using tucker we achieve super compression rates that allowed to saving until 91% disks space and network traffic and second using a CANDECOMP/PARAFAC or Canonical Decomposition (CP) we build a system to find the multi-linear manifold in this astronomical cubes. Because this is a problem of BigData, for ours library we test three implementations: One approach over an intense use of GPU supported by PyTorch and using the traditional approach of HPC using MPI. Our proposed start from a simple but powerful idea, if we are dealing with multidimensional data (astronomical cubes), Why are we limited to use bi-dimensional techniques?. For example we use PCA for dimensionality reductions in spectral cubes instead of multidimensional approach that preserve the multi linear manifold inside this multidimensional data, we propose to pass from a linear algebra approach to a multi-linear algebra approach using tensor theory.