A Fuzzy Entropy-Based Thematic Classification Method Aimed at Improving the Reliability of Thematic Maps in GIS Environments

Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, eval uation of the reliability of the resulting thematic map. We propose a novel fuzzy-based thematic classification method applied to construct thematic maps in Geographical Information Systems. An initial fuzzy partition of the domain of the features of the spatial dataset is constructed using triangular fuzzy numbers; our method finds an optimal fuzzy partition evaluating the fuzziness of the fuzzy sets by using a fuzzy entropy measure. An assessment of the reliability of the final thematic map is performed according to the fuzziness of the fuzzy sets. We implement our method on a GIS framework, testing it on various vector and image spatial datasets. The results of these tests confirm that our thematic classification method provide thematic maps with a higher reliability with respect to that obtained through fuzzy partitions constructed by expert users

Median evidential c-means algorithm and its application to community detection

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods

On fuzzy-qualitative descriptions and entropy

This paper models the assessments of a group of experts when evaluating different magnitudes, features or objects by using linguistic descriptions. A new general representation of linguistic descriptions is provided by unifying ordinal and fuzzy perspectives. Fuzzy qualitative labels are proposed as a generalization of the concept of qualitative labels over a well-ordered set. A lattice structure is established in the set of fuzzy-qualitative labels to enable the introduction of fuzzy-qualitative descriptions as L-fuzzy sets. A theorem is given that characterizes finite fuzzy partitions using fuzzy-qualitative labels, the cores and supports of which are qualitative labels. This theorem leads to a mathematical justification for commonly-used fuzzy partitions of real intervals via trapezoidal fuzzy sets. The information of a fuzzy-qualitative label is defined using a measure of specificity, in order to introduce the entropy of fuzzy-qualitative descriptions. (C) 2016 Elsevier Inc. All rights reserved.Peer ReviewedPostprint (author's final draft

Evidential relational clustering using medoids

In real clustering applications, proximity data, in which only pairwise similarities or dissimilarities are known, is more general than object data, in which each pattern is described explicitly by a list of attributes. Medoid-based clustering algorithms, which assume the prototypes of classes are objects, are of great value for partitioning relational data sets. In this paper a new prototype-based clustering method, named Evidential C-Medoids (ECMdd), which is an extension of Fuzzy C-Medoids (FCMdd) on the theoretical framework of belief functions is proposed. In ECMdd, medoids are utilized as the prototypes to represent the detected classes, including specific classes and imprecise classes. Specific classes are for the data which are distinctly far from the prototypes of other classes, while imprecise classes accept the objects that may be close to the prototypes of more than one class. This soft decision mechanism could make the clustering results more cautious and reduce the misclassification rates. Experiments in synthetic and real data sets are used to illustrate the performance of ECMdd. The results show that ECMdd could capture well the uncertainty in the internal data structure. Moreover, it is more robust to the initializations compared with FCMdd.Comment: in The 18th International Conference on Information Fusion, July 2015, Washington, DC, USA , Jul 2015, Washington, United State

Evidential Communities for Complex Networks

Community detection is of great importance for understand-ing graph structure in social networks. The communities in real-world networks are often overlapped, i.e. some nodes may be a member of multiple clusters. How to uncover the overlapping communities/clusters in a complex network is a general problem in data mining of network data sets. In this paper, a novel algorithm to identify overlapping communi-ties in complex networks by a combination of an evidential modularity function, a spectral mapping method and evidential c-means clustering is devised. Experimental results indicate that this detection approach can take advantage of the theory of belief functions, and preforms good both at detecting community structure and determining the appropri-ate number of clusters. Moreover, the credal partition obtained by the proposed method could give us a deeper insight into the graph structure

On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step process is applied : 1) transformation of the original distribution into a standard uniform distribution by means of the probability integral transform. Since the original distribution is generally unknown, the cumulative distribution function is approximated by computing the q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy partition in the transformed attribute space using a fixed number of equally distributed triangular membership functions. Despite the aforementioned transformation, the definition of every fuzzy set in the original space can be recovered by applying the inverse cumulative distribution function (also known as quantile function). The experimental results reveal that the proposed methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT) induction algorithm to maintain classification accuracy with up to 6 million fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData Congress). arXiv admin note: text overlap with arXiv:1902.0935

A similarity-based community detection method with multiple prototype representation

Communities are of great importance for understanding graph structures in social networks. Some existing community detection algorithms use a single prototype to represent each group. In real applications, this may not adequately model the different types of communities and hence limits the clustering performance on social networks. To address this problem, a Similarity-based Multi-Prototype (SMP) community detection approach is proposed in this paper. In SMP, vertices in each community carry various weights to describe their degree of representativeness. This mechanism enables each community to be represented by more than one node. The centrality of nodes is used to calculate prototype weights, while similarity is utilized to guide us to partitioning the graph. Experimental results on computer generated and real-world networks clearly show that SMP performs well for detecting communities. Moreover, the method could provide richer information for the inner structure of the detected communities with the help of prototype weights compared with the existing community detection models