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

International audienceWe 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 algorithms 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 hardwareefficiency. This paper investigates the shortcomings of the existing range estimation methods while deriving bounds for thevariables of the EVD algorithm. In light of the circumstances, we introduce a range estimation approach based on vector andmatrix norm properties together with a scaling procedure that maintains all the assets of an analytical method. The methodcould derive robust and tight bounds for the variables of EVD algorithm. The bounds derived using the proposed approachremain same for any input matrix and are also independent of the number of iterations or size of the problem. Somebenchmark hyperspectral data sets have been used to evaluate the efficiency of the proposed technique. It was found thatby the proposed range estimation approach, all the variables generated during the computation of Jacobi EVD is boundedwithin ±1