A Review of Feature Selection Methods Based on Mutual Information

In this work we present a review of the state of the art of information theoretic feature selection methods. The concepts of feature relevance, redundance and complementarity (synergy) are clearly defined, as well as Markov blanket. The problem of optimal feature selection is defined. A unifying theoretical framework is described, which can retrofit successful heuristic criteria, indicating the approximations made by each method. A number of open problems in the field are presented

Axiomatic Origins of Mathematical Entropy: Grading Ordered Sets

Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence is derived based on "common sense' assumptions about comparing grading functions. Shannon's entropy formulas emerge from the respective relative divergence ones, entropy based methods are extended to more general cases and some new applications

The Noncommutative Constraints on the Standard Model \`a la Connes

Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.Comment: 12 pages LaTeX, 4 figure

Elite Capture Through Information Distortion: Uniformly Distributed Signal

Common wisdom as well as well-grounded analytical arguments suggest that stronger punishment of deviant behavior meted out by a principal typically prompts the agents to better conform with his objectives. Addressing the specific issue of donor-beneficiary relationships in the context of participatory development programs, we nevertheless show that greater tolerance on the part of donors may, under certain conditions, favor rather than hurt the interests of the poor. Also, greater uncertainty surrounding the donor's knowledge regarding the poor's preference may have the same paradoxical effect. Critical features of our framework are: (i) communities are heterogeneous and dominated by the local elite in dealing with external agencies, (ii) the elite choose the project proposed to the donor strategically, knowing that the latter has a certain amount of tolerance toward elite capture and an imperfect knowledge of the poor's priorities.community-driven development, aid effectiveness, elite capture, corruption, preference targeting.

Temporal fuzzy association rule mining with 2-tuple linguistic representation

This paper reports on an approach that contributes towards the problem of discovering fuzzy association rules that exhibit a temporal pattern. The novel application of the 2-tuple linguistic representation identifies fuzzy association rules in a temporal context, whilst maintaining the interpretability of linguistic terms. Iterative Rule Learning (IRL) with a Genetic Algorithm (GA) simultaneously induces rules and tunes the membership functions. The discovered rules were compared with those from a traditional method of discovering fuzzy association rules and results demonstrate how the traditional method can loose information because rules occur at the intersection of membership function boundaries. New information can be mined from the proposed approach by improving upon rules discovered with the traditional method and by discovering new rules

Feature Selection for multi-labeled variables via Dependency Maximization

Feature selection and reducing the dimensionality of data is an essential step in data analysis. In this work, we propose a new criterion for feature selection that is formulated as conditional information between features given the labeled variable. Instead of using the standard mutual information measure based on Kullback-Leibler divergence, we use our proposed criterion to filter out redundant features for the purpose of multiclass classification. This approach results in an efficient and fast non-parametric implementation of feature selection as it can be directly estimated using a geometric measure of dependency, the global Friedman-Rafsky (FR) multivariate run test statistic constructed by a global minimal spanning tree (MST). We demonstrate the advantages of our proposed feature selection approach through simulation. In addition the proposed feature selection method is applied to the MNIST data set.Comment: 5 pages, 3 Figures, 1 Tabl

Nonextensive statistics, entropic gravity and gravitational force in a non-integer dimensional space

Based on the connection between Tsallis nonextensive statistics and fractional dimensional space, in this work we have introduced, with the aid of Verlinde's formalism, the Newton constant in a fractal space as a function of the nonextensive constant. With this result we have constructed a curve that shows the direct relation between Tsallis nonextensive parameter and the dimension of this fractal space. We have demonstrated precisely that there are ambiguities between the results due to Verlinde's approach and the ones due to fractional calculus formalism. We have shown precisely that these ambiguities appear only for spaces with dimensions different from three. Hence, we believe that this is a result in favor of our three dimensional world.Comment: 13 pages. Revised version, figures added and new titl

Rescaling the state in Flanders: new problem or old solution?

The rescaling of state emphasizes the rise of the regional and the city-regional scale in particular, as a new unit for policy making. The new governing strategy is referred to as regional governance, were both governmental and / or nongovernmental entities work together for the purpose of joint policy making or service delivery. This paper focuses on the operationalization of regional governance and links those findings to the actual debates surrounding the institutional organization of Flanders. A quantitative analysis of regional arrangements in Flanders and in the area of Mid-West Flanders, helps to clarify the nature of the rescaling of the state: the rescaling is the result of bottom – up and top – down initiatives and covers as well joined government arrangements as collaborative governance arrangements integrating public and private organizations. Further, we notice different roles of the Flemish government, as she is present at the regional level both as a meta-governor, actor and financier. By showing the nature and the content of regional governance, this paper helps to clarify the political debate that is going on now in Flanders. A debate dominated by classical institutional discussions and related to the issue of institutional fuzziness, efficiency and accountability. It is argued however that the political discussion and the organization of the public sector in Flanders should be renewed and should be inspired by this relatively new phenomenon. The rescaling of the regional state should be understood by using concepts, theories and instruments inspired by the literature on networks and collaborative governance

Uncertainty measures for probabilistic hesitant fuzzy sets in multiple criteria decision making

This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In the sequel, we develop a new axiomatic framework of entropy measures for probabilistic hesitant fuzzy elements (PHFEs) by considering two facets of uncertainty associated with PHFEs which are known as fuzziness and nonspecificity. Respect to each kind of uncertainty, a number of formulae are derived to permit flexible selection of PHFE entropy measures. Moreover, based on the proposed PHFE entropy measures, we introduce some entropy-based distance measures which are used in the portion of comparative analysis.Comment: International Journal of Intelligent System

Fuzzy Information Measures with Multiple Parameters

Information theory deals with the study of problems concerning any system. This includes information processing, information storage, information retrieval and decision making. Information theory studies all theoretical problems connected with the transmission of information over communication channels. This includes the study of uncertainty (information) measures and various practical and economical methods of coding information for transmission. In this chapter, the introduction of a new generalised measure of fuzzy information involving two real parameters is given. The proposed measure satisfies all the necessary properties of being a measure. Some additional properties of the proposed measure have also been studied. Further, the monotonic nature of generalised fuzzy information measure with respect to the parameters is studied and validity of the same is checked by constructing the computed tables and plots on taking different fuzzy sets and different values of the parameters. Also, a new generalised fuzzy information measure involving three parameters has been introduced