In this paper, we propose a one-dimensional (1D) multifractal sign retention detrending fluctuation analysis algorithm (MF-S-DFA). The proposed method is based on conventional multifractal detrending fluctuation analysis (MF-DFA). As negative values may exist in the calculation in the original MF-DFA model, sign retention is considered to improve performance. We evaluate the two methods based on time series constructed by p-model multiplication cascades. The results indicate that the generalized Hurst exponent H(q), the scale exponent τ(q) and the singular spectrum f(α) estimated by MF-S-DFA behave almost consistently with the theoretical values. Moreover, we also employ distance functions such as DH and Dτ. The results prove that MF-S-DFA achieves more accurate estimation. In addition, we present various numerical experiments by transforming parameters such as nmax, q and p. The results imply that MF-S-DFA obtains more excellent performance than that of conventional MF-DFA in all cases. Finally, we also verify the high feasibility of MF-S-DFA in ECG signal classification. Through classification of normal and abnormal ECG signals, we further corroborate that MF-S-DFA is more effective than conventional MF-DFA.
In this paper, we propose an improved algorithm based on the original two-dimensional (2D) multifractal detrended fluctuation analysis (2D MF-DFA) that involves increasing the number of cumulative summations in the computational steps of 2D MF-DFA. The proposed method aims to modify the distribution of the generalized Hurst exponent to ensure that skin lesion image features are extracted based on enhanced multifractal features. We calculate the generalized Hurst exponent using 0, 1, or 2 cumulative summation processes. A support vector machine (SVM) is adopted to examine the classification performance under these three conditions. Computation shows that the process involving two cumulative summations achieves an accuracy, sensitivity, and specificity of [Formula: see text], [Formula: see text], and [Formula: see text], respectively, which indicates that its performance is much better than with 0 and 1 cumulative summations.
In this paper, we propose a two-dimensional multifractal sign retention detrending fluctuation analysis algorithm (2D MF-S-DFA), which takes the sign of the residual matrix into account when calculating the detrending fluctuation function in traditional 2D MF-DFA. We evaluate these two methods based on images constructed from [Formula: see text]-model multiplicative cascades. The results indicate that the numerical solution of the images extracted by 2D MF-S-DFA is closer to the theoretical solution of the multiplicative cascade images. In addition, we also compare the performance of the two methods after transforming the important parameters of the multiplicative cascade images. The results show that the relative errors and overall distance between the generalized Hurst exponent [Formula: see text] and the scale exponent [Formula: see text] extracted by 2D MF-S-DFA and the image feature values are smaller than those of 2D MF-DFA. We can conclude that the sign retention algorithm outperforms the traditional 2D MF-DFA.
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