Title: An Overflow Free Fixed-point Eigenvalue Decomposition Algorithm: Case Study of Dimensionality Reduction in Hyperspectral Images,
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 $\pm1$.