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• Aiming for multiphase batch processes with different sampling frequencies, two types of process variables are summarized and the multiphase-based cumulative quality model is developed. It provides useful insights for the quality prediction of industrial batch process. • Aiming for the complex association relationships between multiple process variables and multiple quality indicators, information theory with copula entropy is employed to measure the variable relations for critical variables selection. • A stacking multiway random forest algorithm is proposed to develop the prediction relationship between phase-specific critical process variables and multiple quality indicators. • Experiments on a real-world industrial dataset have demonstrated that the proposed method not only has better accuracy but also has stronger robustness than previous baseline methods. As one of the most important modes of industrial production, the batch process often involves complex and continuous physicochemical reactions, making it challenging to produce identical products between different batch runs even under the same working condition. Optimization and parameter adjustments depend mainly on a good quality prediction model. However, this industrial process has "3M" characteristics of multiple process variables, multiple production phases, and multiple quality indicators, which bring considerable challenges to the accuracy and robustness of the model. This study proposes a multiphase information fusion strategy for data-driven quality prediction of industrial batch processes. Firstly, aiming for real-world industrial datasets with different sampling frequencies, two types of state variables are summarized, and the multiphase-based cumulative quality model is developed. Secondly, information theory with copula entropy is employed to characterize the association relationships between each state variable and the set of multiple quality indicators; thus, phase-specific critical variables are selected by ranking copula entropy. Lastly, a stacking multiway random forest algorithm is proposed to develop the prediction relationship between phase-specific critical variables and multiple quality indicators. Experiments on a real-world industrial dataset have demonstrated that the proposed method has better accuracy and stronger robustness than previous baseline methods. [ABSTRACT FROM AUTHOR]

Social influence analysis has become one of the most important technologies in modern information and service industries. Thus, how to measure social influence of one user on other users in a mobile social network is also becoming increasingly important. It is helpful to identify the influential users in mobile social networks, and also helpful to provide important insights into the design of social platforms and applications. However, social influence modeling is an open and challenging issue, and most evaluation models are focused on online social networks, but fail to characterize indirect influence. In this paper, we present a mechanism to quantitatively measure social influence in mobile social networks. We exploit the graph theory to construct a social relationship graph that establishes a solid foundation for the basic understandings of social influence. We present an evaluation model to measure both direct and indirect influence based on the social relationship graph, by introducing friend entropy and interaction frequency entropy to describe the complexity and uncertainty of social influence. Based on the epidemic model, we design an algorithm to characterize propagation dynamics process of social influence, and to evaluate the performance of our solution by using a customized program on the basis of a real-world SMS/MMS-based communication data set. The real world numerical simulations and analysis show that the proposed influence evaluation strategies can characterize the social influence of mobile social networks effectively and efficiently. [ABSTRACT FROM AUTHOR]

In this paper we study the lattice of all indiscernibility partitions induced from attribute subsets of a knowledge representation system (information table in the finite case). This lattice, that we here call granular partition lattice, is a very well studied order structure in granular computing and data base theory and it provides a complete hierarchical classification of the knowledge obtained from all possible choices of attribute subsets. We show that it has a lattice structure also in the infinite case and we provide several isomorphic characterizations for this lattice. We discuss the potentiality of this order structure from both a micro-granular and a macro-granular perspective. Furthermore, the sub-poset of all the indiscernibility closures needed to determine when an arbitrary partition is an indiscernibility one is studied. Finally, we show the monotonic behaviour of the granular partition lattice with respect to entropy of partitions and attribute dependency in decision tables. [ABSTRACT FROM AUTHOR]

Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on the maximum entropy and large margin principles, but it just uses only one view of the data not all the views of the data. Although Multi-view maximum entropy discrimination considered the multi-view information of the data, it just respects the consensus principle. There are two common principles named consensus and complementarity in multi-view learning. We aim to take the full advantage of the multi-view information of the data for classification, and respect the two common principles consensus and complementarity simultaneously. In this paper, we propose a new method called consensus and complementarity based MED (MED-2C) for multi-view classification, which well utilizes the two principles consensus and complementarity for multi-view learning (MVL). We first transform data from two views into a common subspace and make the transformed data in the new subspace identical to respect the consensus principle. Then we augment the transformed data with their original features to take into account the complementarity principle. Built on the augmented features and meanwhile by relaxing the consensus principle, the objective function of MED-2C is naturally formed whose inner optimization recovers the traditional MED framework. We provide an instantiation of the MED-2C method and derive the corresponding solution. Experimental results on synthetic data and real-world data show the effectiveness of the proposed MED-2C. It not only performs better than three single-view classification methods but also generally outperforms three multi-view classification methods canonical correlation analysis (CCA), ensemble MED (EMED) and the multi-view variant SVM-2K of the classical support vector machine (SVM) algorithm. In addition, MED-2C performs better than or as well as state-of-the-art MVMED on all the data sets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets. First, the proposed method uses the representative values of antecedent fuzzy sets, the representative values of observation fuzzy sets, and the representative values of consequence fuzzy sets of fuzzy rules to get the characteristic points of the fuzzy interpolative result represented by a fuzzy set. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the antecedent fuzzy sets, the piecewise fuzzy entropies between any two characteristic points of the observation fuzzy sets, and the piecewise fuzzy entropies between any two characteristic points of the consequence fuzzy sets of the fuzzy rules, respectively. Then, it calculates the weights of the antecedent fuzzy sets of each fuzzy rule, respectively, and calculates the weight of each fuzzy rule. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the fuzzy interpolative result. Finally, it uses the secant method to calculate the degree of membership of each obtained characteristic point of the fuzzy interpolative result. The experimental results show that the proposed method outperforms the existing methods for dealing with the multivariate regression problems, the Mackey–Glass chaotic time series prediction problem, and the time series prediction problems. [ABSTRACT FROM AUTHOR]

Highlights: [•] Transcripts in algebraic groups. [•] Coupling complexity and properties. [•] Dimensional reduction of conditional multi-information using transcripts. [•] Applications: Dimensional reduction of symbolic transfer entropy and momentary sorting information transfer. [•] Transcript-based information directionality indicators. [Copyright &y& Elsevier]

Abstract: Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. Based on Shannon’s entropy, we study graph entropies which are based on vertex degrees by using so-called information functionals. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. The main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers. Further, conjectures to determine extremal values of graph entropies are given. [Copyright &y& Elsevier]

Abstract: In rough set theory, some information-theoretic measures of uncertainty and granularity have been proposed. A common feature of these measures is that they are only dependent on the partitions and the cardinality of a universe, which means that they are independent of the lower and upper approximations of rough sets. This seems somewhat unreasonable since the basic idea of rough set theory is to describe incomplete or inexact concepts by the lower and upper approximations. In light of this, we develop a new pair of information-theoretic entropy and co-entropy functions associated to partitions and approximations in this paper. Such functions are used to measure the uncertainty and granularity of an approximation space. After introducing the novel notions of entropy and co-entropy, we then examine their properties. In particular, we disclose the relationship of co-entropies between different universes. The theoretical development is accompanied by illustrative numerical examples. [Copyright &y& Elsevier]

Abstract: Information storage is a key component of intrinsic distributed computation. Despite the existence of appropriate measures for it (e.g. excess entropy), its role in interacting with information transfer and modification to give rise to distributed computation is not yet well-established. We explore how to quantify information storage on a local scale in space and time, so as to understand its role in the dynamics of distributed computation. To assist these explorations, we introduce the active information storage, which quantifies the information storage component that is directly in use in the computation of the next state of a process. We present the first profiles of local excess entropy and local active information storage in cellular automata, providing evidence that blinkers and background domains are dominant information storage processes in these systems. This application also demonstrates the manner in which these two measures of information storage are distinct but complementary. It also reveals other information storage phenomena, including the misinformative nature of local storage when information transfer dominates the computation, and demonstrates that the local entropy rate is a useful spatiotemporal filter for information transfer structure. [Copyright &y& Elsevier]

Abstract: The analysis of execution paths (also known as software traces) collected from a given software product can help in a number of areas including software testing, software maintenance and program comprehension. The lack of a scalable matching algorithm operating on detailed execution paths motivates the search for an alternative solution. This paper proposes the use of word entropies for the classification of software traces. Using a well-studied defective software as an example, we investigate the application of both Shannon and extended entropies (Landsberg–Vedral, Rényi and Tsallis) to the classification of traces related to various software defects. Our study shows that using entropy measures for comparisons gives an efficient and scalable method for comparing traces. The three extended entropies, with parameters chosen to emphasize rare events, all perform similarly and are superior to the Shannon entropy. [Copyright &y& Elsevier]

Abstract: There are mainly two methodologies dealing with uncertainty measurement issue in rough set theory: pure rough set approach and information theory approach. Pure rough set approach is based on the concepts of accuracy, roughness and approximation accuracy proposed by Pawlak. Information theory approach is based on Shannon’s entropy or its variants. Several authors have extended the information theory approach into incomplete information systems. However, there are few studies on extending the pure rough set approach to incomplete information systems. This paper focuses on constructing uncertainty measures in incomplete information systems by pure rough set approach. Three types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy, roughness and approximation accuracy are investigated. Theoretical analysis indicates that two of the three types can be used to evaluate the uncertainty in incomplete information systems. Experiments on incomplete real-life data sets have been conducted to test the two selected types (the first type and the third type) of uncertainty measures. Results show that the two types of uncertainty measures are effective. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an axiomatic definition of the similarity measure of intuitionistic fuzzy sets (IFS) that differs from the definition of Li . The relationship between the similarity measure and the entropy of IFS is investigated in detail. Six theorems on how the similarity measure could be transformed into the entropy for IFS and vice versa are proposed based on their axiomatic definitions. Some formulas have been proposed to calculate the similarity measure and the entropy of IFS. Finally, sufficient conditions to transform the similarity measures to the entropy for IFS and vice versa are given. [Copyright &y& Elsevier]

Abstract: This survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures. Setting the scene with a review of classical measures for determining the structural information content of graphs, we discuss graph entropy measures which play an important role in a variety of problem areas, including biology, chemistry, and sociology. In addition, we examine relationships between selected entropy measures, illustrating differences quantitatively with concrete examples. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the definition of the conditional Rényi entropy for continuous random variables and show that the so-called chain rule holds. Then, we use this rule to obtain another relation for getting the rate of Rényi entropy. Using this relation and properties of the Rényi entropy we obtain the Rényi entropy rate for stationary Gaussian processes. Finally, we show that the bound for the Rényi entropy rate is simply the Shannon entropy rate and that the Rényi entropy rate reduces to the Shannon entropy rate as . [Copyright &y& Elsevier]

Abstract: Image registration consists in finding the transformation that brings one image into the best possible spatial correspondence with another image. In this paper, we present a new framework for image registration based on compression. The basic idea underlying our approach is the conjecture that two images are correctly registered when we can maximally compress one image given the information in the other. The contribution of this paper is twofold. First, we show that image registration can be formulated as a compression problem. Second, we demonstrate the good performance of the similarity metric, introduced by Li et al., in image registration. Two different approaches for the computation of this similarity metric are described: the Kolmogorov version, computed using standard real-world compressors, and the Shannon version, calculated from an estimation of the entropy rate of the images. [Copyright &y& Elsevier]

Abstract: In this paper, we define the conditional Rényi entropy and show that the so-called chain rule holds for the Rényi entropy. Then, we introduce a relation for the rate of Rényi entropy and use it to derive the rate of the Rényi entropy for an irreducible-aperiodic Markov chain. We also show that the bound for the Rényi entropy rate is simply the Shannon entropy rate. [Copyright &y& Elsevier]

Abstract: In this paper, we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory. Firstly, we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems. Secondly, in inconsistent covering decision systems, the limitary conditional entropy of the covering is proposed and attribute reductions are defined. And finally, by the significance of the covering, some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems. We prove that their computational complexity are polynomial. Numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets. In addition, in traditional rough set theory, MIBARK-algorithm [G.Y. Wang, H. Hu, D. Yang, Decision table reduction based on conditional information entropy, Chinese J. Comput., 25 (2002) 1–8] cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems. Here, we solve this problem in inconsistent covering decision systems. [Copyright &y& Elsevier]

The possibility that memory is related to the collective rotational energy levels of the molecules is considered. Treating the molecule as a quantum rotator, the probability of the ‘hidden-crossing’ transitions between rotational states, induced by the external periodic electric field, is analyzed. It is found that this probability depends on frequency only. i.e. the external signal causes the information transfer rather than the energy. Using the data of the typical sources of electric signals in brain cells and the criterium of maximization of the information entropy, the relevant number of water molecules (rotators) per cell is estimated. The results appear to be close to the actual number of water molecules per cortical neuron. [ABSTRACT FROM AUTHOR]