Clustering is one of the most important task in pattern recognition. For most of partitional clustering algorithms, a partition that represents as much as possible the structure of the data is generated. In this paper, we adress the problem of finding the optimal number of clusters from data. This can be done by introducing an index which evaluates the validity of the generated fuzzy c-partitio...

In order to partition nodes into the nearest MIs (Multicast Islands) in overlay multicast network (OMN), a MI partitioning model is designed. The model uses RTT (Round Trip Time) of links and the network-accessing frequencies of nodes as properties to partition nodes to the nearest MIs, whose centre are called MSNs (Multicast Service Nodes). Also, the similarity degree between nodes and relevan...

A relationship between the discrete F-transform and aggregation functions is analyzed. We show that the discrete F-transform (direct or inverse) can be associated with a set of linear aggregation functions that respect a fuzzy partition of a universe. On the other side, we discover conditions that should be added to a set of linear aggregation functions in order to obtain the discrete F-transfo...

In this work, we present the induction of a fuzzy model that represents the behavior of a partial known function. We extend the approach of classical induction of a classifier by building a decision tree, and its generalization for regression problems by CART, to build a fuzzy model. It is defined by a collection of fuzzy regions fixed in the input domain of the function. To obtain fuzzy region...

A design methodology of interval type-2 fuzzy c-means clustering algorithm-based fuzzy inference systems (IT2FCMFIS) is introduced in this paper. An interval type-2 fuzzy c-means (IT2FCM) clustering algorithm is developed to generate the fuzzy rules in the form of the scatter partition of input space. And the individual partitioned spaces describe the fuzzy rules equal to the number of clusters...

In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely ...

Clustering is a useful approach in image segmentation, data mining and other pattern recognition problems for which unlabeled data exist. Fuzzy clustering using fuzzy c-means or variants of it can provide a data partition that is both better and more meaningful than hard clustering approaches. The clustering process can be quite slow when there are many objects or patterns to be clustered. This...

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions fro...

When clustering algorithms are applied to image seg-mentation, the goal is to solve a classification problem. However, these algorithms do not directly optimize classification quality. As a result, they are susceptible to two problems: P1) the criterion they optimize may not be a good estimator of " true " classification quality, and P2) they often admit many (suboptha€) solutions. This paper i...

Several information measures such as entropy, mutual information, and f-information have been shown to be successful for selecting a set of relevant and nonredundant genes from a high-dimensional microarray data set. However, for continuous gene expression values, it is very difficult to find the true density functions and to perform the integrations required to compute different information me...