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Entropy
Published in Nicholas Stergiou, Nonlinear Analysis for Human Movement Variability, 2018
Lempel and Ziv (1976) also developed an algorithm to calculate entropy in finite-sized time series to provide an entropy rate estimate. Originally developed as an algorithm for data compression (e.g., zip files), this algorithm relies on counting patterns and their rate of occurrence within a data sequence. It must be noted though that the use of Lempel–Ziv’s algorithm alone cannot be interpreted as complexity from a deterministic component. Surrogate analysis must be used along with the Lempel–Ziv entropy (Nagarajan 2002). Lempel–Ziv entropy (also known as Lempel–Ziv complexity) has been shown to be sensitive to the health of a fetus (Ferrario et al. 2006b). Much like other entropy algorithms, Lempel–Ziv complexity has also been applied to heart rate dynamics (Heffernan et al. 2007), EEG recordings (Zhang and Roy 1999), as well as various other signals. Importantly, caution should be taken with application and interpretation of Lempel–Ziv complexity as has been suggested by several authors (Aboy et al. 2006; Hu et al. 2006).
Chaos or Randomness? Effect of Vagus Nerve Stimulation During Sleep on Heart-Rate Variability
Published in IETE Journal of Research, 2022
Karthi Balasubramanian, Nithin Nagaraj, Sandipan Pati
Lempel Ziv complexity [10] is derived from the original Lempel Ziv lossless compression algorithm [11]. It identifies the history of the sequence that can be used to uniquely express (compress) the original sequence. The minimum size of the dictionary used to quantify this minimum exhaustive history is taken as the Lempel Ziv complexity value. LZC also requires a symbolic sequence as input. For this work, we have chosen 4 bins.
Silicon Carbide Surface Quality Prediction Based on Artificial Intelligence Methods on Multi-sensor Fusion Detection Test Platform
Published in Machining Science and Technology, 2019
Yawei Zhang, Beizhi Li, Jianguo Yang, Xiao Liu, Jinqiang Zhou
Most surface quality predictive models are empirical and generally based on experiments. In addition, it is practically very difficult to control all factors as required to obtain reproducible results (Sayuti et al., 2012). Maher et al. (2014) applied the adaptive neuro-fuzzy inference system (ANFIS) to predict the surface roughness in computer numerical control (CNC) end milling, spindle speed, feed rate and depth of cut were predictive variables. The ANFIS model was validated experimentally; detection of dynamical changes of nonlinear time series is an important issue in engineering (Cao et al., 2004). Lempel Ziv complexity (LZC) analysis is proposed by Lempel and Ziv, and its derivatives is applied to characterize the randomness of measurement signals. LZC evaluates the randomness of finite data-series by measuring the number of distinct sub-strings, and analyze their rate of occurrence along a given sequence. The signals collected from the grinding process can be evaluated with LZC in this paper. On the basis of features of LZC above, the integrated grinding process can be analyzed with LZC. Extreme learning machine (ELM) can be interpreted as a single hidden-layer neural network where the bias and the weights for the neuron in the inner layer are randomly generated. It was rigorously demonstrated that ELMs can approximate any non-linear piecewise functions simply by training the coefficients in the output layer under rather general conditions (Huang et al., 2006). For this reason, the training operation for the ELMs can be carried out by one-pass least-square algorithm. As nonlinearity is common in industrial processes, nonlinear principal component analysis (PCA) has become an attractive research topic over the past two decades. Kernel PCA (KPCA) belongs to classic nonlinear PCA methods (Schölkopf et al., 1998). Because of its simplicity and effectiveness, KPCA gains most attention in the research field of nonlinear PCA. Due to the randomness of ELM, ELM can be optimized by improved genetic algorithm to form modified extreme learning machine (MELM) (Aybar-Ruiz et al., 2016), to achieve a desired surface finish, a good predictive model is required for stable grinding. Surface roughness predictive models available in literature is very limited, and the advantages of KPCA and MELM should be taken together for.