Deba Prasad Mandal

Linguistic recognition system based on approximate reasoning

A linguistic recognition system based on approximate reasoning has been described which is capable of handling various imprecise input patterns and of providing a natural decision. The input feature is considered to be of either linguistic form or quantitative form or mixed form or set form. An input has been viewed as consisting of various combinations of the three primary properties small, medium and high possessed by its different features to some degree. The various uncertainty (ambiguity) in the input statement has been managed by providing/modifying membership values heuristically to a great extent. Unlike the conventional fuzzy set theoretic approach, the sets small and high have been represented here by π-functions. The weight matrices corresponding to various properties and classes have been taken into account in the composition rule of inference in order to make the analysis more effective. The natural output decision is associated with a confidence factor denoting the degree of certainty of the decision, thus providing a low rate of misclassification as compared to the conventional two-state system. The effectiveness of the algorithm has been demonstrated on the speech recognition problem.

Formulation of a multivalued recognition system

A recognition system based on fuzzy set theory and approximate reasoning that is capable of handling various imprecise input patterns and providing a natural decision system is described. The input feature is considered to be of either quantitative form, linguistic form, mixed form, or set form. The entire feature space is decomposed into overlapping subdomains depending on the geometric structure and the relative position of the pattern classes found in the training samples. Uncertainty (ambiguity) in the input statement is managed by providing/modifying membership values to a great extent. A relational matrix corresponding to the subdomains and the pattern classes is used to recognize the samples. The system uses L.A. Zadehs (1977) compositional rule of inference and gives a natural (linguistic) multivalued output decision associated with a confidence factor denoting the degree of certainty of a decision. The effectiveness of the algorithm is demonstrated for some artificially generated patterns and for real-life speech data. >

Fuzzy Logic and Approximate Reasoning: An Overview

Approximate Reasoning is the process or processes by which a possible imprecise conclusion is deduced from a collection of imprecise premises. Fuzzy logic plays the major role in approximate reasoning. It has the ability to deal with different types of uncertainty.An overview of the different aspects of the theory of approximate reasoning has been provided here based on the existing literature. Suitable illustrations are included, whenever necessary, to make the concept clear. Some of the implementation of the theory to real life problems have been mentioned. Finally, a linguistic recognition system based on approximate reasoning has been described along with its implementation in speech recognition problem.

Selection of alpha for alpha-hull in R2

Abstract For finding the shape of a planar set, Edelsbrunner, Kirkpatrick and Seidel introduced the concept of α- hulls as a natural generalization of convex hulls. While the α-hull is elegant and efficient to compute, it still suffers from a major drawback, i.e. the single parameter, namely α, must nevertheless be tuned. This paper deals with finding a way to overcome this drawback, i.e. we proposed here a selection criterion of α for α-hulls corresponding to a point set in R 2 . The selection criterion of α is based on the concept of minimum spanning trees and certain existing results. The effectiveness of the proposed selection criterion is demonstrated on some artificially generated data sets. The convergence (with sample size) of the α-hull, based on the proposed selection criterion for α, to the original pattern class has also been verified using symmetric difference, the Hausdorff metric, and a similarity metric.

Determining the shape of a pattern class from sampled points in R2

An important problem in pattern recognition is determining the shape of a pattern class from its sampled points. A procedure which provides multivalued shape has been suggested here for a pattern class in R2. The procedure can be viewed in two phases. Phase I deals with the decomposition of sample set into some groups of nearly rectangular shape. Phase II determines each of the sub-classes corresponding to the groups separately, aggregates them and obtains the multivalued shape of the pattern class. The effectiveness of the procedure has been demonstrated on some artificially generated data sets or pattern classes as well as on the Indian Telugu vowel speech data set. The convergence of the estimated set to the original set has been verified successfully using two different metrics between sets. One is the well-known Hausdorff metric. The other is a new metric which has been defined in the paper

Partitioning of feature space for pattern classification

The article proposes a simple approach for finding a fuzzy partitioning of a feature space for pattern classification problems. A feature space is initially decomposed into some overlapping hyperboxes depending on the relative positions of the pattern classes found in the training samples. A few fuzzy if-then rules reflecting the pattern classes by the generated hyperboxes are then obtained in terms of a relational matrix. The relational matrix is utilized in the modified compositional rule of inference in order to recognize an unknown pattern. The proposed system is capable of handling imprecise information both in the learning and the processing phases. The imprecise information is considered to be either incomplete or mixed or interval or linguistic in form. Ways of handling such imprecise information are also discussed. The effectiveness of the system is demonstrated on some synthetic data sets in two-dimensional feature space. The practical applicability of the system is verified on four real data such as the Iris data set, an appendicitis data set, a speech data set and a hepatic disease data set.

Analysis of IRS imagery for detecting man-made objects with a multivalued recognition system

The present work describes a method of analyzing Indian Remote Sensing (IRS) satellite imagery for detecting various man-made objects, namely, roads, bridges, airports, seaports, city area and town-ship/industrial areas. A multivalued recognition system has initially been used to classify the image pixels into six land cover types by providing multiple choices of classes. In order to identify certain targets, some spatial knowledge about them and their inter-relationships have been incorporated on the clustered image using some heuristic rules. The use of multiple class choices makes the detection procedures effective.

Theoretical performance of a multivalued recognition system

A multivalued recognition system was formulated by the authors which has the ability of discriminating the nonoverlapping, and overlapping and no-class ( ambiguous/doubtful) regions and of analyzing the associated uncertainties by providing output decisions in four states, namely, single, first-second, combined, and null choices. The single choices correspond to the nonoverlapping regions, whereas the overlapping regions are reflected by the first-second and combined choices. The null choices reflect the portions outside the pattern classes and/or the portions of the pattern classes uncovered by the training samples. A theoretical analysis of these characteristics and of the performance of the recognition system is provided. It is shown theoretically that with the increase in the size of the training samples, the estimates of the overlapping, nonoverlapping, and no-class regions tend to their actual sizes. All analytical findings have been substantiated with experimental results various situations in one and two-dimensional feature spaces. Bayes decision boundaries are always found to lie within the combined choice region as provided by the multivalued recognition system. The present investigation, in turn, establishes analytically the justification of providing multivalued output decisions in four states for managing uncertainties arising from ambiguous regions. >

DETERMINING THE SHAPE OF A PATTERN CLASS: EXTENSION TO RN

Abstract An important problem in pattern recognition is determining the shape of a patient class from its sampled points. We have reported earlier a procedure in this regard which provides multivalued shape of a pattern class in fif2. In the present article, an extension of the procedure to higher dimensional space (TV) has been suggested. The effectiveness of the extended version has been demonstrated on some artificially generated pattern classes (in R3). The convergence of the estimated shape to the original set has also been verified using two different metrics.

SELECTION OF α FOR α-HULL AND FORMULATION OF FUZZY α-HULL IN IR2

A decade ago, Edelsbrunner et. al. introduced the concept of α-hulls for finding the shape of a planar set. But it still suffers from a major deficiency i.e., the single parameter α must be fine-tuned. The present article initially proposes a selection criterion of α for α-hulls in R2. Then the concept of α-hulls is extended to define the fuzzy α-hulls. The effectiveness of the fuzzy α-hulls and the proposed selection criterion of α is demonstrated on some artificially generated data sets. The convergence (with sample size) of both the crisp and fuzzy α-hulls, based on the proposed selection criterion of α, to the original pattern class has also been verified.