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In this paper, we present the leader-driven algorithm (LDA) for learning community structure in networks. The algorithm allows one to find overlapping clusters in a network, an important aspect of real networks, especially social networks. The algorithm requires no input parameters and learns the number of clusters naturally from the network. It accomplishes this using leadership centrality in a clever manner. It identifies local minima of leadership centrality as followers which belong only to one cluster, and the remaining nodes are leaders which connect clusters. In this way, the number of clusters can be learned using only the network structure. The LDA is also an extremely fast algorithm, having runtime linear in the network size. Thus, this algorithm can be used to efficiently cluster extremely large networks.

Uncovering the community structure in complex network is a hot research point in recent years. How to identify the community structure accurately in complex network is still an open question under research. There are lots of methods based on topological information, which have some good performances at the expense of longer runtimes. In this paper, we propose a new fuzzy algorithm which follows the line of fuzzy c-means algorithm. A steepest descent framework with projection by optimizing the quality function is presented under the generalized framework. The results of experiments on both real-world networks and synthetic networks show that the proposed method achieves the highest efficiency and is easy for detecting fuzzy community structure in large-scale complex networks.

For a fixed integral commutative cl-monoid M=(L, ≤, *), introducing the notions of M-partitions and M-equivalence relations as the extensions of T-partitions and T-equivalence relations to the integral commutative cl-monoid M=(L, ≤, *), respectively, it is shown that the previous approaches on T-partitions and T-equivalence relations can be unified, and most of the results in these works can be easily stated based on the integral commutative cl-monoid M=(L, ≤, *). Modifying the notion of T-redundancy of finite family of fuzzy sets of a nonempty ordinary set X, it is extended to arbitrary family of L-fuzzy sets on the basis of the integral commutative cl-monoid M, and is shown that the proposed definition has more desirable properties than the previous one. Furthermore, handling the works of Höhle, Klawonn, Gebhardt and Kruse on fuzzy partitions and fuzzy equivalence relations, some of their results are improved, and several new results in this direction are pointed out.

The aim of this paper is to characterize of the measures of entropies without probability or fuzzy measure for compositive fuzzy partitions, taking into account the so-called locality property. We propose a system of functional equations, whose solutions give some forms of entropies without probability or fuzzy measures.

In this paper we present a novel associative classification algorithm for visual concept detection using interest points (color descriptors). Our algorithm relies on fuzzy (soft) partitions to generate a per-descriptor record model which is used for training associative classifiers. In this paper, we use the first 10000 images of the MIR Flickr dataset (with 38 visual concepts — 14 regular annotation topics and 24 pre-annotations) for evaluating our algorithm. Because of its fuzzy nature, our approach also handles polysemy and synonymy (common problems in most crisp (non-fuzzy) image classifiers) very well. As associative classification leverages frequent patterns mined from a given dataset, its performance as adjudged from average area under curve (AUC) values over three-fold cross validation is very good, especially for regular annotation topics and for “scenic” concepts. Our approach has the added advantage that the rules used for classification have clear semantics, and can be comprehended easily, unlike other classifiers, such as SVM, which act as black-boxes. From an empirical perspective (on the MIR Flickr dataset), the performance of our algorithm is much better, than that of either bag-of-words (Linear SVM and SVM RBF Kernel) or Linear SVM based on fuzzy (soft) partitions—both benchmark approaches are based on interest points (color descriptors).