Abstract - Spatial Decision Support Systems have received increasing interest in geographical, political, and economical applications such as agricultural cultivation, disaster management, and industrial settlement. For instance, farmers want to know what the best farmland areas are to grow a specific crop, political decision makers want to know what the areas are that should be protected based on risk zones, and companies would like to know the best location to place a new production facility. In many cases, the spatial phenomena of interest have a vague and imprecise extent and can be adequately represented by fuzzy spatial objects such as fuzzy regions. In this paper, we formally propose a general-purpose model named Fuzzy Inference on Fuzzy Spatial Objects (FIFUS) that incorporates fuzzy spatial objects into its inference strategy and supplies the user with recommendations, estimations, and predictions based on fuzzy inference rules and expert knowledge.
Abstract - The fuzzy co-clustering algorithms are considered as effective technique for clustering the complex data, such as high-dimensional and large size. In general, features of data objects are considered the same importance. However, in reality, the features have different roles in data analyses; even some of them are considered redundancy in the individual case for data sets. Removing these features is a way for the dimensionality reduction, which needs to improve the performance of data processing algorithms. In this paper, we proposed an improved fuzzy co-clustering algorithm called feature-reduction fuzzy co-clustering (FRFCoC), which can automatically calculate the weight of features and put them out of the data processing. We considered the objective function of the FCoC algorithm with feature- weighted entropy and build a learning procedure for components of the objective function, then reducing the dimension of data by eliminating irrelevant features with small weights. Experiments were conducted on synthetic data sets and hyperspectral image using the robust assessment indexes. Experimental results demonstrated the proposed algorithm outperformed the previous algorithms.
Abstract - Data clustering is an important step which evolves in many pattern recognition problems and decision making applications. This step had gained great interest and several approaches were proposed to improve the clustering quality. In this context, we proposed a new ensemble clustering system based on the use of a dynamic fuzzy exponent within fuzzy C-Means clustering, an unsupervised feature selection based on the building of a strong feature vector and the use of a modified version of normalized cuts spectral image clustering algorithm applied to general data clustering. The proposed clustering algorithm was validated on eight benchmarks from UC Irvine Machine Learning Repository. Our findings are very promising and prove the effectiveness of our algorithm.
Abstract - In this study, a new fuzzy co-clustering algorithm based on a q-multinomial mixture model is proposed. A conventional fuzzy co-clustering model was constructed by fuzzifying a multinomial mixture model (MMM) via regularizing Kullback-Leibler divergence appearing in a pseudo likelihood of an MMM. Furthermore, a q-multinomial distribution was formulated, which acts as the Tsallis statistical counter for multinomial distributions in standard statistics. The proposed algorithm is constructed by fuzzifying a q-multinomial mixture model, by means of regularizing q-divergence appearing in a pseudo likelihood of the model. The proposed algorithm not only reduces into the q-multinomial mixture model, but also reduces into conventional fuzzy co-clustering models with specified sets of parameter values. In numerical experiments, the properties of the membership of the proposed method are observed.
Abstract - This paper proposes a partitioning fuzzy clustering algorithm with automatic variable selection and entropy regularization. The proposed method is an iterative three steps algorithm which provides a fuzzy partition, a representative for each fuzzy cluster, and learns a relevance weight for each variable in each cluster by minimizing a suitable objective function that includes a multi-dimensional distance function as the dissimilarity measure and entropy as the regularization term. Experiments on real-world datasets corroborate the usefulness of the proposed algorithm.
Abstract - Possibilistic c-means (PCM) based clustering algorithms are widely used in the literature. In this paper, we develop a noise level based PCM (NPCM) clustering algorithm. The advantage of NPCM is that strong prior information of the dataset is not required, and NPCM needs two kinds of information that is intuitive to specify for the clustering task, i.e., information of the cluster number and information of the property of clusters. More specifically, there are two parameters in NPCM: one specifies the possibly over-specified cluster number, and the other characterizes the closeness of clusters in the clustering result. Both parameters are not required to be exactly specified. Furthermore, we find that the update of bandwidth in adaptive PCM (APCM) is a positive feedback process and the adaptive bandwidth-uncertainty mechanism adopted in NPCM makes this positive feedback process more stronger, which leads to a faster convergence rate. Experiments show that the clustering process can be effectively controlled by the parameters.