Improved Lempel-Ziv Algorithm Based on Complexity Measurement of Short Time Series

Abstract

The Lempel-Ziv algorithm is not fully suitable for measuring the complexity of short series. When the Lempel-Ziv algorithm is applied, the assumption that the sequence must be long enough is always ignored: the series length is usually too large, and the equi-probability assumption also is not considered in some papers. Based on these facts, the universal algorithm of trial and error is presented when the conditions of different sequence lengths and different symbol probabilities are comprehensively considered. The facts that the overvaluation would occur in measuring normalized complexity of short sequences with the original Lempel-Ziv algorithm and obtained results through improved LempelZiv algorithm more in accord with the reality are testified by virtue of tests of ultra-short series, Logistic equation of different state, observed traffic flow.