An Overflow Free Fixed-point Eigenvalue Decomposition Algorithm: Case Study of Dimensionality Reduction in Hyperspectral Images
Résumé
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 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 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 ±1.
Mots clés
satisfiability-
modulo-theory
fixed-point arithmetic
overflow
interval arithmetic
integer bit-width alloca- tion
formal methods
range analysis
satisfiability- modulo-theory
Affine arithmetic
eigenvalue decomposition
Index Terms— Affine arithmetic
eigenvalue decomposition
formal methods
integer bit-width alloca-
tion
interval arithmetic
overflow
range analysis
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