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Using the ensemble learning method to mine valuable information from a sea of financial data accumulated on the market of financial securities is very important for studying data processing. On the basis of financial data from A-share companies listed on Shanghai Stock Market, this article takes the perspective of unbalanced classification of ST stocks to carry out a study of the construction of a financial warning model for the listed companies. In our experiment, HDRF (HDRandom Forest, Hellinger Distance based Random Forest), ensemble classification models of Bagging, AdaBoost, and Rotation Forest, which take Hellinger distance decision tree (HDDT) as the base classifier, and the ensemble classification model which takes the C4.5 decision tree as the base classifier, are compared in respect of both the area under the ROC curve and the F-measure. As shown in the experimental results, the HDRF and the HDDT based classifier, as an ensemble method, are effective for financial data of listed companies.

We study the nonparametric maximum likelihood estimator (NPMLE) for estimating Gaussian location mixture densities in d-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Gaussian mixture without any prior information on the number of mixture components. NPMLEs can naturally be used to yield empirical Bayes estimates of the oracle Bayes estimator in the Gaussian denoising problem. We prove bounds for the accuracy of the empirical Bayes estimate as an approximation to the oracle Bayes estimator. Here our results imply that the empirical Bayes estimator performs at nearly the optimal level (up to logarithmic factors) for denoising in clustering situations without any prior knowledge of the number of clusters.

As the popularity of the Internet is increasing, the number of threats is also increasing at a rapid pace. DoS attack is one such threat. DoS attacks deplete the network bandwidth, thereby, preventing the genuine users from accessing the resources. These types of attacks exhaust the computing resources of its victim without advanced warning. The goal of our research is to detect DoS/DDoS attacks effectively using the Hellinger distance technique. We have tested the performance of our approach using real network traces. Our proposed model achieved approx 91.41% Accuracy in DoS detection.We have also analyzed and compared our own dataset with standard NSLKDD dataset and UNSW_NB15 Dataset and it is observed that our proposed model has better accuracy than that of NSLKDD dataset and UNSW_NB15 Dataset which shows an accuracy of 85.29% and 81.42% respectively.

Intuitionistic fuzzy sets (IFSs), as a representative variant of fuzzy sets, has substantial advantages in managing and modeling uncertain information, so it has been widely studied and applied. Nevertheless, how to perfectly measure the similarities or differences between IFSs is still an open question. The distance metric offers an elegant and desirable solution to such a question. Hence, in this paper, we propose a new distance measure, named DIFS, inspired by the Hellinger distance in probability distribution space. First, we provide the formal definition of the new distance measure of IFSs, and analyze the outstanding properties and axioms satisfied by DIFS, which means it can measure the difference between IFSs well. Besides, on the basis of DIFS, we further present a normalized distance measure of IFSs, denoted DIFS˜. Moreover, numerical examples verify that DIFS˜ can obtain more reasonable and superior results. Finally, we further develop a new decision-making method on top of DIFS˜ and evaluate its performance in two applications.

The essential factors of information-aware systems are heterogeneous multi-sensory devices. Because of the ambiguity and contradicting nature of multi-sensor data, a data-fusion method based on the cloud model and improved evidence theory is proposed. To complete the conversion from quantitative to qualitative data, the cloud model is employed to construct the basic probability assignment (BPA) function of the evidence corresponding to each data source. To address the issue that traditional evidence theory produces results that do not correspond to the facts when fusing conflicting evidence, the three measures of the Jousselme distance, cosine similarity, and the Jaccard coefficient are combined to measure the similarity of the evidence. The Hellinger distance of the interval is used to calculate the credibility of the evidence. The similarity and credibility are combined to improve the evidence, and the fusion is performed according to Dempster’s rule to finally obtain the results. The numerical example results show that the proposed improved evidence theory method has better convergence and focus, and the confidence in the correct proposition is up to 100%. Applying the proposed multi-sensor data-fusion method to early indoor fire detection, the method improves the accuracy by 0.9–6.4% and reduces the false alarm rate by 0.7–10.2% compared with traditional and other improved evidence theories, proving its validity and feasibility, which provides a certain reference value for multi-sensor information fusion.

Deployed machine learning systems are necessarily learned from historical data and are often applied to current data. When the world changes, the learned models can lose fidelity. Such changes to the statistical properties of data over time are known as concept drift. Similarly, models are often learned in one context, but need to be applied in another. This is called concept shift. Quantifying the magnitude of drift or shift, especially in the context of covariate drift or shift, or unsupervised learning, requires use of measures of distance between distributions. In this paper, we survey such distance measures with respect to their suitability for estimating drift and shift magnitude between samples of numeric data.

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

Picture fuzzy sets (PFSs) are a versatile generalization of fuzzy sets and intuitionistic fuzzy sets (IFSs), providing a robust framework for modeling imprecise, uncertain, and inconsistent information across various fields. As an advanced extension of PFSs, interval-valued picture fuzzy sets (IvPFSs) offer superior capabilities for handling incomplete and indeterminate information in various practical applications. Distance measures have always been an important topic in fuzzy sets and their variants. Some existing distance measures for PFSs have shown limitations and may yield counterintuitive results under certain conditions. Furthermore, there are currently few studies on distance measures for IvPFSs. To solve these problems, in this paper we devised a series of novel distance measures between PFSs and IvPFSs inspired by the Hellinger distance. Specifically, all the distance measures were divided into two parts: One considered the positive membership degree, neutral membership degree and negative membership degree, and the other added the refusal membership degree. Moreover, the proposed distance measures met some important properties, including boundedness, non-degeneracy, symmetry, and consistency, but also showed superiority compared to the existing measures, as confirmed through numerical comparisons. Finally, the proposed distance measures were validated in pattern recognition and medical diagnosis applications, indicating that the proposed distance measures can deliver credible, reasonable results, particularly in similar cases.

Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence. However, in 2003, Eve studied seven means from a geometrical point of view, which are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal. In this paper, we have obtained new inequalities among non-negative differences arising from these seven means. Correlations with generalized triangular discrimination and some new generating measures with their exponential representations are also presented.

As an important method for uncertainty modeling, Dempster–Shafer (DS) evidence theory has been widely used in practical applications. However, the results turned out to be almost counter-intuitive when fusing the different sources of highly conflicting evidence with Dempster’s combination rule. In previous researches, most of them were mainly dependent on the conflict measurement method between the evidence represented by the evidence distance. However, it is inaccurate to characterize the evidence conflict only through the evidence distance. To address this issue, we comprehensively consider the impacts of the evidence distance and evidence angle on conflicts in this paper, and propose a new method based on the mutual support degree between the evidence to characterize the evidence conflict. First, the Hellinger distance measurement method is proposed to measure the distance between the evidence, and the sine value of the Pignistic vector angle is used to characterize the angle between the evidence. The evidence distance indicates the dissimilarity between the evidence, and the evidence angle represents the inconsistency between the evidence. Next, two methods are combined to get a new method for measuring the mutual support degree between the evidence. Afterward, the weight of each evidence is determined by using the mutual support degree between the evidence. Then, the weights of each evidence are utilized to modify the original evidence to achieve the weighted average evidence. Finally, Dempster’s combination rule is used for fusion. Some numerical examples are given to illustrate the effectiveness and reasonability for the proposed method.