K. Chidananda Gowda

Symbolic clustering using a new dissimilarity measure

Abstract A new dissimilarity measure, based on “position”, “span” and “content” of symbolic objects is proposed for symbolic clustering. The dissimilarity measure is new in the sense that it is not just another aspect of a similarity measure. In the proposed hierarchical agglomerative clustering methodology, composite symbolic objects are formed using a Cartesian join operator whenever a mutual pair of symbolic objects is selected for agglomeration based on minimum dissimilarity. The minimum dissimilarity values of different merging levels are used to compute the cluster indicator values and hence to determine the number of clusters in the data. The results of the application of the algorithm on numeric data of known number of classes are described first so as to show the efficacy of the method. Subsequently, the results of the experiments on two data sets of Assertion type of symbolic objects drawn from the domains of fat-oil and microcomputers are presented.

Agglomerative clustering using the concept of mutual nearest neighbourhood

A method for determining the mutual nearest neighbours (MNN) and mutual neighbourhood value (mnv) of a sample point, using the conventional nearest neighbours, is suggested. A nonparametric, hierarchical, agglomerative clustering algorithm is developed using the above concepts. The algorithm is simple, deterministic, noniterative, requires low storage and is able to discern spherical and nonspherical clusters. The method is applicable to a wide class of data of arbitrary shape, large size and high dimensionality. The algorithm can discern mutually homogenous clusters. Strong or weak patterns can be discerned by properly choosing the neighbourhood width.

Divisive clustering of symbolic objects using the concepts of both similarity and dissimilarity

A new approach to clustering of symbolic objects which makes use of both similarity and dissimilarity measures is proposed. The proposed modified new similarity and dissimilarity measures will take into consideration the position, span and content of symbolic objects. The similarity and dissimilarity measures used are of new type. The advantages of the proposed modified measures are presented. A divisive clustering algorithm which makes use of both similarity and dissimilarity is proposed. The results obtained by the proposed method is compared with other methods.

Agglomerative clustering of symbolic objects using the concepts of both similarity and dissimilarity

A hierarchical, agglomerative clustering methodology is presented in which composite symbolic objects are formed using a cartesian join operator whenever symbolic objects are selected for agglomeration based on both similarity and dissimilarity.

An ISODATA clustering procedure for symbolic objects using a distributed genetic algorithm

Abstract A novel ISODATA clustering procedure for symbolic objects is presented using distributed genetic algorithms where in a structured organisation in the distribution of the population is introduced and selection and mating are made within locally distributed subgroups of individuals rather than the whole population.

Dimensionality reduction of symbolic data

Abstract Hitherto dimensionality/feature reduction techniques are studied with reference to conventional data, where the objects are represented by numerical vectors. This proposal is to extend the notion of dimensionality reduction to more generalised objects called Symbolic data. A mathematical model which achieves generation of symbolic features — particularly of span type — in transformed lower-dimensional space from a high n -dimensional feature space of span type symbolic data, is presented in this paper. This work is expected to open a new avenue in the area of symbolic data analysis.

A feature reduction and unsupervised classification algorithm for multispectral data

Abstract A new scheme, incorporating dimensionality reduction and clustering, suitable for classification of a large volume of remotely sensed data using a small amount of memory is proposed. The scheme involves transforming the data from multidimensional n-space to a 3-dimensional primary color space of blue, green and red coordinates. The dimensionality reduction is followed by data reduction, which involves assigning 3-dimensional samples to a 2-dimensional array. Finally, a multi-stage ISODATA technique incorporating a novel seedpoint picking method is used to obtain the desired number of clusters. The storage requirements are reduced to a low value by making five passes through the data and storing necessary information during each pass. The first three passes are used to find the minimum and maximum values of some of the variables. The data reduction is done and a classification table is formed during the fourth pass. The classification map is obtained during the fifth pass. The computer memory required is about 2K machine words. The efficacy of the algorithm is justified by simulation studies using multispectral LANDSAT data.

Dimensionality reduction using geometric projections: A new technique

Abstract A new method based on geometric projections for Dimensionality Reduction of multispectral, remotely sensed data is presented. A composite of four different parameters, called the “Clustering Tendency Index” (CTI) has been defined to quantify the suitability of the Dimensionality Reduction methods from the point of view of clustering. The Dimensionality Reduction scheme involves transformation of data from multi-dimensional n-space to a two-dimensional (2D) space, which reduces storage requirements and processing time in addition to facilitating representation in the Cartesian coordinate system. The efficacy of the algorithm is established by experimental studies using different data sets.

Learning with a mutualistic teacher

The concept of a “mutualistic teacher” is introduced for unsupervised learning of the mean vectors of the components of a mixture of multivariate normal densities, when the number of classes is also unknown. The unsupervised learning problem is formulated here as a multi-stage quasi-supervised problem incorporating a cluster approach. The mutualistic teacher creates a quasi-supervised environment at each stage by picking out “mutual pairs” of samples and assigning identical (but unknown) labels to the individuals of each mutual pair. The number of classes, if not specified, can be determined at an intermediate stage. The risk in assigning identical labels to the individuals of mutual pairs is estimated. Results of some simulation studies are presented.

Symbolic agglomerative clustering for quantitative analysis of remotely sensed data

An efficient nonparametric, hierarchical, symbolic agglomerative clustering procedure based on the mutual nearest neighbourhood concept is proposed for classifying remotely sensed multispectral data. The procedure utilized a data reduction technique and an innovative symbolic concept to minimize the memory and computational time requirements. A new non-metric similarity measure and a novel method of formulation of composite symbolic objects are proposed to enrich the performance of the algorithm. A Mean Difference Index (MDI) concept for identifying the optimal number of classes was used. Experiments were conducted on IRS (Indian Remote Sensing) satellite data to authenticate the efficacy of the procedure.