Depth estimation in Markov models of time-series data via spectral analysis

摘要: Symbol sequences are generated from observed time series data to construct probabilistic finite state automata (PFSA) models that capture the evolution of dynamical system under consideration. One key challenges here is estimate relevant history or depth (i.e., size temporal memory) symbol sequences; in this context, spectral decomposition one-step transition matrix has been recently proposed for estimation. This paper compares performance estimation by analysis with other commonly used metrics (e.g., log-likelihood, entropy rate and signal reconstruction) symbolic dynamic systems. For experimental validation concept, time-series fatigue damage a polycrystalline alloy, collected on laboratory apparatus, have discretized generate sequences. The depths, estimated method, then compared those obtained metrics, results found be close agreement. Furthermore, unsupervised clustering data, number test specimens fatigue-test experiments, demonstrates efficacy method as well accuracy via PFSA model construction.