Classification of glucose records from patients at diabetes risk using a combined permutation entropy algorithm

A Federated Learning-Inspired Evolutionary Algorithm: Application to Glucose Prediction

In this paper, we propose an innovative Federated Learning-inspired evolutionary framework. Its main novelty is that this is the first time that an Evolutionary Algorithm is employed on its own to directly perform Federated Learning activity. A further novelty resides in the fact that, differently from the other Federated Learning frameworks in the literature, ours can efficiently deal at the same time with two relevant issues in Machine Learning, i.e., data privacy and interpretability of the solutions. Our framework consists of a master/slave approach in which each slave contains local data, protecting sensible private data, and exploits an evolutionary algorithm to generate prediction models. The master shares through the slaves the locally learned models that emerge on each slave. Sharing these local models results in global models. Being that data privacy and interpretability are very significant in the medical domain, the algorithm is tested to forecast future glucose values for diabetic patients by exploiting a Grammatical Evolution algorithm. The effectiveness of this knowledge-sharing process is assessed experimentally by comparing the proposed framework with another where no exchange of local models occurs. The results show that the performance of the proposed approach is better and demonstrate the validity of its sharing process for the emergence of local models for personal diabetes management, usable as efficient global models. When further subjects not involved in the learning process are considered, the models discovered by our framework show higher generalization capability than those achieved without knowledge sharing: the improvement provided by knowledge sharing is equal to about 3.03% for precision, 1.56% for recall, 3.17% for F1, and 1.56% for accuracy. Moreover, statistical analysis reveals the statistical superiority of model exchange with respect to the case of no exchange taking place.

Video-based eye tracking performance for computer-assisted diagnostic support of diabetic neuropathy

Diabetes is currently one of the major public health threats. The essential components for effective treatment of diabetes include early diagnosis and regular monitoring. However, health-care providers are often short of human resources to closely monitor populations at risk. In this work, a video-based eye-tracking method is proposed as a low-cost alternative for detection of diabetic neuropathy. The method is based on the tracking of the eye-trajectories recorded on videos while the subject follows a target on a screen, forcing saccadic movements. Upon extraction of the eye trajectories, representation of the obtained time-series is made with the help of heteroscedastic ARX (H-ARX) models, which capture the dynamics and latency on the subject's response, while features based on the H-ARX model's predictive ability are subsequently used for classification. The methodology is evaluated on a population constituted by 11 control and 20 insulin-treated diabetic individuals suffering from diverse diabetic complications including neuropathy and retinopathy. Results show significant differences on latency and eye movement precision between the populations of control subjects and diabetics, while simultaneously demonstrating that both groups can be classified with an accuracy of 95%. Although this study is limited by the small sample size, the results align with other findings in the literature and encourage further research.

Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities

Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE results' dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasets-whereas the standard PE method only did in four-and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement.

Multi-Feature Fusion Method Based on EEG Signal and its Application in Stroke Classification

Electroencephalogram (EEG) analysis has been widely used in the diagnosis of stroke diseases for its low cost and noninvasive characteristics. In order to classify the EEG signals of stroke patients with cerebral infarction and cerebral hemorrhage, this paper proposes a novel EEG stroke signal classification method. This method has two highlights. The first is that a multi-feature fusion method is given by combining wavelet packet energy, fuzzy entropy and hierarchical theory. The second highlight is that a suitable classification model based on ensemble classifier is constructed for perfectly classification stroke signals. Entropy is an accessible way to measure information and uncertainty of time series. Many entropy-based methods have been developed these years. By comparing with the performances of permutation entropy, sample entropy, approximate entropy in measuring the characteristic of stroke patient's EEG signals, it can be found that fuzzy entropy has best performance in characterization stroke EEG signal. By combining hierarchical theory, wavelet packet energy and fuzzy entropy, a multi-feature fusion method is proposed. The method first calculates wavelet packet energy of EEG stroke signal, then extracts hierarchical fuzzy entropy feature by combining hierarchical theory and fuzzy entropy. The experimental results show that, compared with the fuzzy entropy feature, the classification accuracy based on the fusion feature of wavelet packet energy and hierarchical fuzzy entropy is much higher than benchmark methods. It means that the proposed multi-feature fusion method based on stroke EEG signal is an efficient measure in classifying ischemic and hemorrhagic stroke. Support vector machine (SVM), decision tree and random forest are further used as the stroke signal classification models for classifying ischemic stroke and hemorrhagic stroke. Experimental results show that, based on the proposed multi-feature fusion method, the ensemble method of random forest can get the best classification performance in accuracy among three models.

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear IRn mapping into IR, where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ, only general recommendations such as N>>m!, τ=1, or m=3,…,7. This paper deals specifically with the study of the practical implications of N>>m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N>>m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.