entropy measure
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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 215
Author(s):  
Alejandro Raúl Hernández-Montoya ◽  
Carlos Manuel Rodríguez-Martínez ◽  
Manuel Enríque Rodríguez-Achach ◽  
David Hernández-Enríquez

In this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trader is assigned to each one of these four analyzed markets, DJIA, IPC, Nikkei and DAX. Distribution of differential entropies of the corresponding multi-scale log-returns of the optimal and noise traders are calculated. Kullback-Leiber distances between the different optimal traders returns distributions are also calculated and results discussed. We show that the entropy of returns distribution of optimal traders for each analyzed market indeed reaches minimum values with respect to entropy distribution of noise traders and we measure this distance in σ units for each analyzed market. We also include a discussion on stationarity of the introduced multi-scale log-returns observable. Finally, a practical application of the obtained results related with ranking markets by their entropy measure as calculated here is presented.


Author(s):  
Jerry W. Sangma ◽  
Mekhla Sarkar ◽  
Vipin Pal ◽  
Amit Agrawal ◽  
Yogita

AbstractOver the decade, a number of attempts have been made towards data stream clustering, but most of the works fall under clustering by example approach. There are a number of applications where clustering by variable approach is required which involves clustering of multiple data streams as opposed to clustering data examples in a data stream. Furthermore, a few works have been presented for clustering multiple data streams and these are applicable to numeric data streams only. Hence, this research gap has motivated current research work. In the present work, a hierarchical clustering technique has been proposed to cluster multiple data streams where data are nominal. To address the concept changes in the data streams splitting and merging of the clusters in the hierarchical structure are performed. The decision to split or merge is based on the entropy measure, representing the cluster’s degree of disparity. The performance of the proposed technique has been analysed and compared to Agglomerative Nesting clustering technique on synthetic as well as a real-world dataset in terms of Dunn Index, Modified Hubert $$\varGamma $$ Γ statistic, Cophenetic Correlation Coefficient, and Purity. The proposed technique outperforms Agglomerative Nesting clustering technique for concept evolving data streams. Furthermore, the effect of concept evolution on clustering structure and average entropy has been visualised for detailed analysis and understanding.


2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Tianyi Li ◽  
Ma-Ke Yuan ◽  
Yang Zhou

Abstract Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS3/BCFT2. We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.


2022 ◽  
Vol 11 (1) ◽  
pp. 0-0

Motivated by the structural aspect of the probabilistic entropy, the concept of fuzzy entropy enabled the researchers to investigate the uncertainty due to vague information. Fuzzy entropy measures the ambiguity/vagueness entailed in a fuzzy set. Hesitant fuzzy entropy and hesitant fuzzy linguistic term set based entropy presents a more comprehensive evaluation of vague information. In the vague situations of multiple-criteria decision-making, entropy measure is utilized to compute the objective weights of attributes. The weights obtained due to entropy measures are not reasonable in all the situations. To model such situation, a knowledge measure is very significant, which is a structural dual to entropy. A fuzzy knowledge measure determines the level of precision in a fuzzy set. This article introduces the concept of a knowledge measure for hesitant fuzzy linguistic term sets (HFLTS) and show how it may be derived from HFLTS distance measures. Authors also investigate its application in determining the weights of criteria in multi-criteria decision-making (MCDM).


2021 ◽  
Author(s):  
Muhammad Ali Khan ◽  
Saleem Abdullah ◽  
Abbas Qadir

Abstract In this article, we shall introduce a novel technique for order preference by similarity to ideal solution (TOPSIS)-based methodology to resolve multicriteria group decision-making problems within picture fuzzy environment, where the weights information of both the decision makers (DMs) and criteria are completely unknown. First, we briefly review the definition of picture fuzzy sets (PFS), score function and accuracy function of PFRSs and their basic operational laws. In addition, defined the generalized distance measure for PFRSs based on picture fuzzy rough entropy measure to compute the unknown weights information. Secondly, the picture fuzzy information based decision-making technique for multiple attribute group decision making (MAGDM) is established and all computing steps are simply depicted. In our presented model, it's more accuracy and effective for considering the conflicting attributes. Finally, an illustrative example with robot selection is provided to demonstrate the effectiveness of the proposed picture fuzzy decision support approaches, together with comparison results discussion, proving that its results are feasible and credible.


2021 ◽  
Author(s):  
Farnaz Daneshvar Vousoughi

Abstract Two approaches to identify the relation between hydrological time series (rainfall and runoff) and groundwater level (GWL) were used in the Ardabil plain. In this way, Wavelet-entropy measure (WEM) and wavelet transform coherence (WTC) as two approaches of wavelet transform (WT) were used. WEM have been considered as a criterion for the degree of time series fluctuations and WTC present common time-frequency space. In WEM calculation, monthly rainfall, runoff and GWL time series were divided into three different time periods and decomposed to multiple frequent time series and then, the energies of wavelet were calculated for each sub-series. The result showed WEM reduction in rainfall, runoff and GWL. The reduction of WEM presents the natural fluctuations decrease of time series. The reduction of entropy for runoff, rainfall and GWL time series were about 1.58, 1.36 and 29% respectively, it is concluded that fluctuation reduction of hydrological time series has relatively not more effect on the oscillation patterns of GWL signal. In this regard, it could be concluded that the human activities such as water driving from wells can be played main role in the reduction of GWL in Ardabil plain. WTC findings showed that runoff had most coherence (0.9-1) among the hydrological variables with GWL time series in the frequency bands of 4-8 and 8-16 months.


Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 9
Author(s):  
Muhammed Rasheed Irshad ◽  
Radhakumari Maya ◽  
Francesco Buono ◽  
Maria Longobardi

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.


Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 335
Author(s):  
Parul Thakur ◽  
Bartłomiej Kizielewicz ◽  
Neeraj Gandotra ◽  
Andrii Shekhovtsov ◽  
Namita Saini ◽  
...  

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.


2021 ◽  
Vol 22 (23) ◽  
pp. 13066
Author(s):  
Viviana Quevedo-Tumailli ◽  
Bernabe Ortega-Tenezaca ◽  
Humberto González-Díaz

The parasite species of genus Plasmodium causes Malaria, which remains a major global health problem due to parasite resistance to available Antimalarial drugs and increasing treatment costs. Consequently, computational prediction of new Antimalarial compounds with novel targets in the proteome of Plasmodium sp. is a very important goal for the pharmaceutical industry. We can expect that the success of the pre-clinical assay depends on the conditions of assay per se, the chemical structure of the drug, the structure of the target protein to be targeted, as well as on factors governing the expression of this protein in the proteome such as genes (Deoxyribonucleic acid, DNA) sequence and/or chromosomes structure. However, there are no reports of computational models that consider all these factors simultaneously. Some of the difficulties for this kind of analysis are the dispersion of data in different datasets, the high heterogeneity of data, etc. In this work, we analyzed three databases ChEMBL (Chemical database of the European Molecular Biology Laboratory), UniProt (Universal Protein Resource), and NCBI-GDV (National Center for Biotechnology Information - Genome Data Viewer) to achieve this goal. The ChEMBL dataset contains outcomes for 17,758 unique assays of potential Antimalarial compounds including numeric descriptors (variables) for the structure of compounds as well as a huge amount of information about the conditions of assays. The NCBI-GDV and UniProt datasets include the sequence of genes, proteins, and their functions. In addition, we also created two partitions (cassayj= cajand cdataj= cdj) of categorical variables from theChEMBL dataset. These partitions contain variables that encode information about experimental conditions of preclinical assays (caj) or about the nature and quality of data (cdj). These categorical variables include information about 22 parameters of biological activity (ca0), 28 target proteins (ca1), and 9 organisms of assay (ca2), etc. We also created another partition of (cprotj= cpj) including categorical variables with biological information about the target proteins, genes, and chromosomes. These variables cover32 genes (cp0), 10 chromosomes (cp1), gene orientation (cp2), and 31 protein functions (cp3). We used a Perturbation-Theory Machine Learning Information Fusion (IFPTML) algorithm to map all this information (from three databases) into and train a predictive model. Shannon’s entropy measure Shk (numerical variables) was used to quantify the information about the structure of drugs, protein sequences, gene sequences, and chromosomes in the same information scale. Perturbation Theory Operators (PTOs) with the form of Moving Average (MA) operators have been used to quantify perturbations (deviations) in the structural variables with respect to their expected values for different subsets (partitions) of categorical variables. We obtained three IFPTML models using General Discriminant Analysis (GDA), Classification Tree with Univariate Splits (CTUS), and Classification Tree with Linear Combinations (CTLC). The IFPTML-CTLC presented the better performance with Sensitivity Sn(%) = 83.6/85.1, and Specificity Sp(%) = 89.8/89.7 for training/validation sets, respectively. This model could become a useful tool for the optimization of preclinical assays of new Antimalarial compounds vs. different proteins in the proteome of Plasmodium.


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