Accelerated Search for Non-Negative Greedy Sparse Decomposition via Dimensionality Reduction

TL;DR

This paper introduces the E-NN and U-NN algorithms to significantly accelerate the FNNOMP sparse decomposition method for non-negative signals, especially on large datasets, by reducing search time while maintaining accuracy.

Contribution

The paper proposes the Embedded Nearest Neighbor (E-NN) and Update Nearest Neighbor (U-NN) algorithms to speed up FNNOMP for large datasets, ensuring non-negativity and accuracy.

Findings

Accelerates FNNOMP by a factor of 4 on Raman Spectra data.

Achieves a 22-fold speedup on synthetic datasets.

Maintains accuracy while significantly reducing computational time.

Abstract

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. One fast implementation is the FNNOMP algorithm that updates the non-negative coefficients in an iterative manner. Even though FNNOMP is a good approach when working on libraries of small size, the operational time of the algorithm grows significantly when the size of the library is large. This is mainly due to the selection step of the algorithm that relies on matrix vector multiplications. We here introduce the Embedded Nearest Neighbor (E-NN) algorithm which accelerates the search over large datasets while it is guaranteed to find the most correlated atoms. We then replace the selection step of FNNOMP by E-NN. Furthermore we introduce the Update Nearest Neighbor (U-NN) at the look up table of FNNOMP in order to assure the non-negativity criteria of FNNOMP. The results indicate that the proposed methodology can accelerate FNNOMP with a factor 4 on a real dataset of Raman Spectra and with a factor of 22 on a synthetic dataset.