Fuzzy geometry, entropy, and image information

Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described

A fuzzy measure approach to motion frame analysis for scene detection

This paper addresses a solution to the problem of scene estimation of motion video data in the fuzzy set theoretic framework. Using fuzzy image feature extractors, a new algorithm is developed to compute the change of information in each of two successive frames to classify scenes. This classification process of raw input visual data can be used to establish structure for correlation. The algorithm attempts to fulfill the need for nonlinear, frame-accurate access to video data for applications such as video editing and visual document archival/retrieval systems in multimedia environments

Soft data mining, computational theory of perceptions, and rough-fuzzy approach

Data mining and knowledge discovery is described from pattern recognition point of view along with the relevance of soft computing. Key features of the computational theory of perceptions and its significance in pattern recognition and knowledge discovery problems are explained. Role of fuzzy-granulation (f-granulation) in machine and human intelligence, and its modeling through rough-fuzzy integration are discussed. Merits of fuzzy granular computation, in terms of performance and computation time, for the task of case generation in large scale case-based reasoning systems are illustrated through an example

Gene ordering in partitive clustering using microarray expressions

A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering and ordering the genes using gene expression data into homogeneous groups was shown to be useful in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on gene ordering in hierarchical clustering framework for gene expression analysis, there is no work addressing and evaluating the importance of gene ordering in partitive clustering framework, to the best knowledge of the authors. Outside the framework of hierarchical clustering, different gene ordering algorithms are applied on the whole data set, and the domain of partitive clustering is still unexplored with gene ordering approaches. A new hybrid method is proposed for ordering genes in each of the clusters obtained from partitive clustering solution, using microarry gene expressions. Two existing algorithms for optimally ordering cities in travelling salesman problem (TSP), namely, FRAG_GALK and Concorde, are hybridized individually with self organizing MAP to show the importance of gene ordering in partitive clustering framework. We validated our hybrid approach using yeast and fibroblast data and showed that our approach improves the result quality of partitive clustering solution, by identifying subclusters within big clusters, grouping functionally correlated genes within clusters, minimization of summation of gene expression distances, and the maximization of biological gene ordering using MIPS categorization. Moreover, the new hybrid approach, finds comparable or sometimes superior biological gene order in less computation time than those obtained by optimal leaf ordering in hierarchical clustering solution

Theoretical quantification of shape distortion in fuzzy hough transform

We present a generalization of classical Hough transform in fuzzy set theoretic framework (called fuzzy Hough transform or FHT) in order to handle the impreciseness/ill-definedness in shape description. In addition to identifying the shapes, the methodology can quantify the amount of distortion present in each shape by suitably characterizing the parametric space. We extended FHT to take care of gray level images (gray FHT) in order to handle the gray level variation along with shape distortion. The gray FHT gives rise to a scheme for image segmentation based on the a priori knowledge about the shapes

Case-based reasoning: concepts, features and soft computing

Here we first describe the concepts, components and features of CBR. The feasibility and merits of using CBR for problem solving is then explained. This is followed by a description of the relevance of soft computing tools to CBR. In particular, some of the tasks in the four REs, namely Retrieve, Reuse, Revise and Retain, of the CBR cycle that have relevance as prospective candidates for soft computing applications are explained

Unsupervised feature extraction using neuro-fuzzy approach

The present article demonstrates a way of formulating a neuro-fuzzy approach for feature extraction under unsupervised training. A fuzzy feature evaluation index for a set of features is newly defined in terms of degree of similarity between two patterns in both the original and transformed feature spaces. A concept of flexible membership function incorporating weighted distance is introduced for computing membership values in the transformed space that is obtained by a set of linear transformation on the original space. A layered network is designed for performing the task of minimization of the evaluation index through unsupervised learning process. This extracts a set of optimum transformed features, by projecting n-dimensional original space directly to n'-dimensional (n'<n) transformed space, along with their relative importance. The extracted features are found to provide better classification performance than the original ones for different real life data with dimensions 3, 4, 9, 18 and 34. The superiority of the method over principal component analysis network, nonlinear discriminant analysis network and Kohonen self-organizing feature map is also established

Fuzzy feature evaluation index and connectionist realization

A new feature evaluation index based on fuzzy set theory and a connectionist model for its evaluation are provided. A concept of flexible membership function incorporating weighting factors, is introduced which makes the modeling of the class structures more appropriate. A neuro-fuzzy algorithm is developed for determining the optimum weighting coefficients representing the feature importance. The overall importance of the features is evaluated both individually and in a group considering their dependence as well as independence. Effectiveness of the algorithms along with comparison is demonstrated on speech and Iris data

Fuzzy rough granular neural networks, fuzzy granules, and classification

AbstractWe introduce a fuzzy rough granular neural network (FRGNN) model based on the multilayer perceptron using a back-propagation algorithm for the fuzzy classification of patterns. We provide the development strategy of the network mainly based upon the input vector, initial connection weights determined by fuzzy rough set theoretic concepts, and the target vector. While the input vector is described in terms of fuzzy granules, the target vector is defined in terms of fuzzy class membership values and zeros. Crude domain knowledge about the initial data is represented in the form of a decision table, which is divided into subtables corresponding to different classes. The data in each decision table is converted into granular form. The syntax of these decision tables automatically determines the appropriate number of hidden nodes, while the dependency factors from all the decision tables are used as initial weights. The dependency factor of each attribute and the average degree of the dependency factor of all the attributes with respect to decision classes are considered as initial connection weights between the nodes of the input layer and the hidden layer, and the hidden layer and the output layer, respectively. The effectiveness of the proposed FRGNN is demonstrated on several real-life data sets