Fuzzy Covering-Based Three-Way Clustering

This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

Feature Genes Selection Using Fuzzy Rough Uncertainty Metric for Tumor Diagnosis

To select more effective feature genes, many existing algorithms focus on the selection and study of evaluation methods for feature genes, ignoring the accurate mapping of original information in data processing. Therefore, for solving this problem, a new model is proposed in this paper: rough uncertainty metric model. First, the fuzzy neighborhood granule of the sample is constructed by combining the fuzzy similarity relation with the neighborhood radius in the rough set, and the rough decision is defined by using the fuzzy similarity relation and the decision equivalence class. Then, the fuzzy neighborhood granule and the rough decision are introduced into the conditional entropy, and the rough uncertainty metric model is proposed; in the meantime, the definition of measuring the significance of feature genes and the proof of some related theorems are given. To make this model tolerate noises in data, this paper introduces a variable precision model and discusses the selection of parameters. Finally, based on the rough uncertainty metric model, we design a feature genes selection algorithm and compare it with some existing similar algorithms. The experimental results show that the proposed algorithm can select the smaller feature genes subset with higher classification accuracy and verify that the model proposed in this paper is more effective.

A Distributed Execution Pipeline for Clustering Trajectories Based on a Fuzzy Similarity Relation

The proliferation of indoor and outdoor tracking devices has led to a vast amount of spatial data. Each object can be described by several trajectories that, once analysed, can yield to significant knowledge. In particular, pattern analysis by clustering generic trajectories can give insight into objects sharing the same patterns. Still, sequential clustering approaches fail to handle large volumes of data. Hence, the necessity of distributed systems to be able to infer knowledge in a trivial time interval. In this paper, we detail an efficient, scalable and distributed execution pipeline for clustering raw trajectories. The clustering is achieved via a fuzzy similarity relation obtained by the transitive closure of a proximity relation. Moreover, the pipeline is integrated in Spark, implemented in Scala and leverages the Core and Graphx libraries making use of Resilient Distributed Datasets (RDD) and graph processing. Furthermore, a new simple, but very efficient, partitioning logic has been deployed in Spark and integrated into the execution process. The objective behind this logic is to equally distribute the load among all executors by considering the complexity of the data. In particular, resolving the load balancing issue has reduced the conventional execution time in an important manner. Evaluation and performance of the whole distributed process has been analysed by handling the Geolife project’s GPS trajectory dataset.

Using Fuzzy Segmentation for Colour Image Enhancement of Computed Tomography Perfusion Images

This chapter presents a methodology for an image enhancement process of computed tomography perfusion images by means of partition generated with appropriately defined fuzzy relation. The proposed image processing is used to improve the radiological analysis of the brain perfusion. Colour image segmentation is a process of dividing the pixels of an image in several homogenously- coloured and topologically connected groups, called regions. As the concept of homogeneity in a colour space is imprecise, a measure of dependency between the elements of such a space is introduced. The proposed measure is based on a pixel metric defined in the HSV colour space. By this measure a fuzzy similarity relation is defined, which next is used to introduce a clustering method that generates a partition, and so a segmentation. The achieved segmentation results are used to enhance the considered computed tomography perfusion images with the purpose of improving the corresponding radiological recognition.

The Uncertainty Measure of Hierarchical Quotient Space Structure

In the application of fuzzy reasoning, researchers usually choose the membership function optionally in some degree. Even though the membership functions may be different for the same concept, they can generally get the same (or approximate) results. The robustness of the membership function optionally chosen has brought many researchers' attention. At present, many researchers pay attention to the structural interpretation (definition) of a fuzzy concept, and find that a hierarchical quotient space structure may be a better tool than a fuzzy set for characterizing the essential of fuzzy concept in some degree. In this paper, first the uncertainty of a hierarchical quotient space structure is defined, the information entropy sequence of a hierarchical quotient space structure is proposed, the concept of isomorphism between two hierarchical quotient space structures is defined, and the sufficient condition of isomorphism between two hierarchical quotient space structures is discovered and proved also. Then, the relationships among information entropy sequence, hierarchical quotient space structure, fuzzy equivalence relation, and fuzzy similarity relation are analyzed. Finally, a fast method for constructing a hierarchical quotient space structure is presented.