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Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy estimation methods are required to characterize the chaotic dynamic of the system. Our concept of Neural Network Entropy (NNetEn) is based on the classification of special datasets in relation to the entropy of the time series recorded in the reservoir of the neural network. NNetEn estimates the chaotic dynamics of time series in an original way and does not take into account probability distribution functions. We propose two new classification metrics: R2 Efficiency and Pearson Efficiency. The efficiency of NNetEn is verified on separation of two chaotic time series of sine mapping using dispersion analysis. For two close dynamic time series (r = 1.1918 and r = 1.2243), the F-ratio has reached the value of 124 and reflects high efficiency of the introduced method in classification problems. The electroenceph-alography signal classification for healthy persons and patients with Alzheimer disease illustrates the practical application of the NNetEn features. Our computations demonstrate the synergistic effect of increasing classification accuracy when applying traditional entropy measures and the NNetEn concept conjointly. An implementation of the algorithms in Python is presented., Comment: 26 pages, 18 figures, 2 tables

Heart disease morbidity and mortality rates are increasing, which has a negative impact on public health and the global economy. Early detection of heart disease reduces the incidence of heart mortality and morbidity. Recent research has utilized quantum computing methods to predict heart disease with more than 5 qubits and are computationally intensive. Despite the higher number of qubits, earlier work reports a lower accuracy in predicting heart disease, have not considered the outlier effects, and requires more computation time and memory for heart disease prediction. To overcome these limitations, we propose hybrid random forest quantum neural network (HQRF) using a few qubits (two to four) and considered the effects of outlier in the dataset. Two open-source datasets, Cleveland and Statlog, are used in this study to apply quantum networks. The proposed algorithm has been applied on two open-source datasets and utilized two different types of testing strategies such as 10-fold cross validation and 70-30 train/test ratio. We compared the performance of our proposed methodology with our earlier algorithm called hybrid quantum neural network (HQNN) proposed in the literature for heart disease prediction. HQNN and HQRF outperform in 10-fold cross validation and 70/30 train/test split ratio, respectively. The results show that HQNN requires a large training dataset while HQRF is more appropriate for both large and small training dataset. According to the experimental results, the proposed HQRF is not sensitive to the outlier data compared to HQNN. Compared to earlier works, the proposed HQRF achieved a maximum area under the curve (AUC) of 96.43% and 97.78% in predicting heart diseases using Cleveland and Statlog datasets, respectively with HQNN. The proposed HQRF is highly efficient in detecting heart disease at an early stage and will speed up clinical diagnosis.

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N=19625 elements that must be filled with the given data. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal to Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise., Comment: 24 pages, 24 figures, 2 tables. Nonlinear Dyn (2023)

Measuring the predictability and complexity of time series using entropy is essential tool de-signing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the res-ervoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice., Comment: 15 pages, 14 figures, 1 table

In the age of neural networks and Internet of Things (IoT), the search for new neural network architectures capable of operating on devices with limited computing power and small memory size is becoming an urgent agenda. Designing suitable algorithms for IoT applications is an important task. The paper proposes a feed forward LogNNet neural network, which uses a semi-linear Henon type discrete chaotic map to classify MNIST-10 dataset. The model is composed of reservoir part and trainable classifier. The aim of the reservoir part is transforming the inputs to maximize the classification accuracy using a special matrix filing method and a time series generated by the chaotic map. The parameters of the chaotic map are optimized using particle swarm optimization with random immigrants. As a result, the proposed LogNNet/Henon classifier has higher accuracy and the same RAM usage, compared to the original version of LogNNet, and offers promising opportunities for implementation in IoT devices. In addition, a direct relation between the value of entropy and accuracy of the classification is demonstrated., Comment: 9 pages, 7 figures