Multiscale and Multiresolution methods for Sparse representation of Large datasets.

Abstract

In this paper, we have presented a strategy for studying a large observational dataset at different resolutions to obtain a sparse representation in a computationally efficient manner. Such representations are crucial for many applications from modeling and inference to visualization. Resolution here stems from the variation of the correlation strength among the different observation instances. The motivation behind the approach is to make a large dataset as small as possible by removing all the redundant information so that, the original data can be reconstructed with minimal losses of information.Our past work borrowed ideas from multilevel simulations to extract a sparse representaiton. Here, we introduce the use of multi-resolution kernels. We have tested our approach on a carefully designed suite of analytical functions along with gravity and altimetry time series datasets from a section of the Greenland Icesheet. In addition to providing a good strategy for data compression, the proposed approach also finds application in efficient sampling procedures and error filtering in the datasets. The results, presented in the article clearly establish the promising nature of the approach along with prospects of its application in different fields of data analytics in the scientific computing and related domains.