Estimating Periodicities in Symbolic Sequences Using Sparse Modeling

Abstract

Abstract-In this work, we propose a method for estimating statistical periodicities in symbolic sequences. Different from other common approaches used for the estimation of periodicities of sequences of arbitrary, finite, symbol sets, that often map the symbolic sequence to a numerical representation, we here exploit a likelihood-based formulation in a sparse modeling framework to represent the periodic behavior of the sequence. The resulting criterion includes a restriction on the cardinality of the solution; two approximate solutions are suggested, one greedy and one using an iterative convex relaxation strategy to ease the cardinality restriction. The performance of the proposed methods are illustrated using both simulated and real DNA data, showing a notable performance gain as compared to other common estimators.

Ramanujan subspace pursuit for signal periodic decomposition

“…There exist many periodic patterns, such as periodicities, repetitions and regularities, in the Biomolecular sequence [1]- [4], speech [5], music [6], and machine vibration signal [7]. To identify these periodic patterns is a long-standing problem in many application domains.…”