CONVERGENCE INVESTIGATION OF MULTIFRACTAL ANALYSIS BASED ON Lp-NORM CONSTRAINT

Abstract

In this paper, we propose the multifractal detrending fluctuation analysis based on [Formula: see text]-norm constrain (MF-DFN). We assess the performance of the proposed algorithm by constructing a [Formula: see text]-model based multiplicative cascades time series. We calculate the generalized [Formula: see text] exponent [Formula: see text], [Formula: see text] exponent [Formula: see text], singularity exponent [Formula: see text] and multifractal spectrum [Formula: see text] for multifractal detrended fluctuation analysis (MF-DFA) and MF-DFN, respectively. We notice that under different norm constraints, the distribution of multifractal characteristics is quite different. Appropriate norm constraints can make the multifractal characteristics of time series described more accurately. Based on the analytical solution curve, the distribution of different multifractal numerical curves determines the correct selection of norm constraint value. In this study, using a combination of norms [Formula: see text] and [Formula: see text], the depicted numerical curves almost overlap the theoretical curve, which shows that the proposed MF-DFN is superior to MF-DFA. To eliminate the influence of specific time series, we reset parameters [Formula: see text] and [Formula: see text] in [Formula: see text]-model. Various experimental results also show the effectiveness of the proposed MF-DFN. In addition, we also verify the efficiency of the proposed MF-DFN by using the practical application. The experimental results show that our proposed method plays a significant role in ECG classification.