Data Discovery Using Lossless Compression-Based Sparse Representation

TL;DR

This paper introduces a novel data-driven sparse representation method using orthonormal bases under a lossless compression constraint, leading to unique, optimal, and discriminative features for data discovery in one-dimensional data.

Contribution

It proposes a new sparse representation approach based on lossless compression and MDL principle, enhancing data discovery capabilities.

Findings

Unique and optimal sparse representations achieved

Discriminative features for data discovery obtained

Method applicable to one-dimensional data

Abstract

Sparse representation has been widely used in data compression, signal and image denoising, dimensionality reduction and computer vision. While overcomplete dictionaries are required for sparse representation of multidimensional data, orthogonal bases represent one-dimensional data well. In this paper, we propose a data-driven sparse representation using orthonormal bases under the lossless compression constraint. We show that imposing such constraint under the Minimum Description Length (MDL) principle leads to a unique and optimal sparse representation for one-dimensional data, which results in discriminative features useful for data discovery.