An Overflow Free Fixed-point Eigenvalue Decomposition Algorithm: Case Study of Dimensionality Reduction in Hyperspectral Images

TL;DR

This paper presents a robust fixed-point eigenvalue decomposition algorithm with a novel range estimation method that ensures accuracy and hardware efficiency, demonstrated through hyperspectral image data sets.

Contribution

It introduces a new range estimation approach for fixed-point EVD that provides tight, input-independent bounds, improving reliability and efficiency in hardware implementations.

Findings

Variables during Jacobi EVD are bounded within ±1.

The method is effective across different input matrices and problem sizes.

Benchmark tests on hyperspectral data validate the approach.

Abstract

We consider the problem of enabling robust range estimation of eigenvalue decomposition (EVD) algorithm for a reliable fixed-point design. The simplicity of fixed-point circuitry has always been so tempting to implement EVD algo- rithms in fixed-point arithmetic. Working towards an effective fixed-point design, integer bit-width allocation is a significant step which has a crucial impact on accuracy and hardware efficiency. This paper investigates the shortcomings of the existing range estimation methods while deriving bounds for the variables of the EVD algorithm. In light of the circumstances, we introduce a range estimation approach based on vector and matrix norm properties together with a scaling procedure that maintains all the assets of an analytical method. The method could derive robust and tight bounds for the variables of EVD algorithm. The bounds derived using the proposed approach remain same for any input matrix and are also independent of the number of iterations or size of the problem. Some benchmark hyperspectral data sets have been used to evaluate the efficiency of the proposed technique. It was found that by the proposed range estimation approach, all the variables generated during the computation of Jacobi EVD is bounded within $\pm1$.