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Pattern Recognition with Fuzzy Objective Function Algorithms

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

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Data clustering: a review

In the early 1980s, a strategy for graphical representation of multivariate (multi-species) abundance data was introduced into marine ecology by, among others, Field, et al. (1982). A decade on, it is instructive to: (i) identify which elements of this often-quoted strategy have proved most useful in practical assessment of community change resulting from pollution impact; and (ii) ask to what extent evolution of techniques in the intervening years has added self-consistency and comprehensiveness to the approach. The pivotal concept has proved to be that of a biologically-relevant definition of similarity of two samples, and its utilization mainly in simple rank form, for example ‘sample A is more similar to sample B than it is to sample C’. Statistical assumptions about the data are thus minimized and the resulting non-parametric techniques will be of very general applicability. From such a starting point, a unified framework needs to encompass: (i) the display of community patterns through clustering and ordination of samples; (ii) identification of species principally responsible for determining sample groupings; (iii) statistical tests for differences in space and time (multivariate analogues of analysis of variance, based on rank similarities); and (iv) the linking of community differences to patterns in the physical and chemical environment (the latter also dictated by rank similarities between samples). Techniques are described that bring such a framework into place, and areas in which problems remain are identified. Accumulated practical experience with these methods is discussed, in particular applications to marine benthos, and it is concluded that they have much to offer practitioners of environmental impact studies on communities.

Non-parametric multivariate analyses of changes in community structure

A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered. It reconciles, in a sense, two different approaches to the investigation of the spatial relationships between the points, viz., the agglomerative and the divisive methods. A graph, the shortest dendrite of Florek etal. (1951a), is constructed on a nearest neighbour basis and then divided into clusters by applying the criterion of minimum within cluster sum of squares. This procedure ensures an effective reduction of the number of possible splits. The method may be applied to a dichotomous division, but is perfectly suitable also for a global division into any number of clusters. An informal indicator of the "best number" of clusters is suggested. It is a"variance ratio criterion" giving some insight into the structure of the points. The method is illustrated by three examples, one of which is original. The results obtained by the dendrite method are compared with those...

A dendrite method for cluster analysis

The spatial heterogeneity of populations and communities plays a central role in many ecological theories, for instance the theories of succession, adaptation, maintenance of species diversity, community stability, competition, predator-prey interactions, parasitism, epidemics and other natural catastrophes, ergoclines, and so on. This paper will review how the spatial structure of biological populations and communities can be studied. We first demonstrate that many of the basic statistical methods used in ecological studies are impaired by autocorrelated data. Most if not all environmental data fall in this category. We will look briefly at ways of performing valid statistical tests in the presence of spatial autocorrelation. Methods now available for analysing the spatial structure of biological populations are described, and illustrated by vegetation data. These include various methods to test for the presence of spatial autocorrelation in the data: univariate methods (all-directional and two-dimensional spatial correlograms, and two-dimensional spectral analysis), and the multivariate Mantel test and Mantel correlogram; other descriptive methods of spatial structure: the univariate variogram, and the multivariate methods of clustering with spatial contiguity constraint; the partial Mantel test, presented here as a way of studying causal models that include space as an explanatory variable; and finally, various methods for mapping ecological variables and producing either univariate maps (interpolation, trend surface analysis, kriging) or maps of truly multivariate data (produced by constrained clustering). A table shows the methods classified in terms of the ecological questions they allow to resolve. Reference is made to available computer programs.

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Spatial pattern and ecological analysis

Minimum spanning trees (MST) and single linkage cluster analysis (SLCA) are explained and it is shown that all the information required for the SLCA of a set of points is contained in their MST. Known algorithms for finding the MST are discussed. They are efficient even when there are very many points; this makes a SLCA practicable when other methods of cluster analysis are not. The relevant computing procedures are published in the Algorithm section of the same issue of Applied Statistics. The use of the MST in the interpretation of vector diagrams arising in multivariate analysis is illustrated by an example.

Minimum Spanning Trees and Single Linkage Cluster Analysis

Kiwifruit (Actinidia spp.) are a relatively new, but economically important crop grown in many different parts of the world. Commercial success is driven by the development of new cultivars with novel consumer traits including flavor, appearance, healthful components and convenience. To increase our understanding of the genetic diversity and gene-based control of these key traits in Actinidia, we have produced a collection of 132,577 expressed sequence tags (ESTs). The ESTs were derived mainly from four Actinidia species (A. chinensis, A. deliciosa, A. arguta and A. eriantha) and fell into 41,858 non redundant clusters (18,070 tentative consensus sequences and 23,788 EST singletons). Analysis of flavor and fragrance-related gene families (acyltransferases and carboxylesterases) and pathways (terpenoid biosynthesis) is presented in comparison with a chemical analysis of the compounds present in Actinidia including esters, acids, alcohols and terpenes. ESTs are identified for most genes in color pathways controlling chlorophyll degradation and carotenoid biosynthesis. In the health area, data are presented on the ESTs involved in ascorbic acid and quinic acid biosynthesis showing not only that genes for many of the steps in these pathways are represented in the database, but that genes encoding some critical steps are absent. In the convenience area, genes related to different stages of fruit softening are identified. This large EST resource will allow researchers to undertake the tremendous challenge of understanding the molecular basis of genetic diversity in the Actinidia genus as well as provide an EST resource for comparative fruit genomics. The various bioinformatics analyses we have undertaken demonstrates the extent of coverage of ESTs for genes encoding different biochemical pathways in Actinidia.

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Analysis of expressed sequence tags from Actinidia: Applications of a cross species EST database for gene discovery in the areas of flavor, health, color and ripening

Analyse Statistique à Plusieurs Variables

A β-galactosidase (EC 3.2.1.23) capable of degrading a number of fruit cell-wall polysaccharides in vitro, was isolated from ripening kiwifruit (Actinidia deliciosa [A. Chev.] C.F. Liang et A.R. Ferguson cv. Hayward). The enzyme has a molecular weight of approximately 60 kDa by gel permeation and consists of several basic isoforms. Several polypeptides were enriched during purification, with 33-, 46- and 67-kDa bands being predominant after sodium dodecyl sulphate-polyacrylamide gel electrophoresis. The optimum activity of the enzyme against p-nitrophenyl-β-d-galactopyranoside was at pH 3.2, but against a galactan purified from kiwifruit cell walls, it was at pH 4.9. The enzyme was specific for galactosyl residues in the β-configuration, releasing galactose from a variety of kiwifruit cell-wall polysaccharide fractions including cell wall material, Na2CO3-soluble pectin, high-molecular-weight galactan, xyloglucan, and galactoglucomannan. A galactosylated glucuronomannan found throughout the kiwifruit plant was also a substrate for the enzyme. The results indicate that the enzyme attacks the non-reducing end of galactose side chains, cleaving single galactose residues which may be attached to the 2, 3, 4, or 6 position of the aglycone. Activity of the enzyme in-vitro was too low to account for the total loss of galactose from the cell walls during ripening. If the β-galactosidase of this study is solely responsible for the removal of galactose from the cell wall during ripening then its in-vivo activity must be much greater than that observed in-vitro.

Kiwifruit β-galactosidase: Isolation and activity against specific fruit cell-wall polysaccharides

Maximum‐likelihood estimation problems can be solved numerically using function minimization algorithms, but the amount of computing required and the accuracy of the results depend on the way the algorithms are used. Attention to the analytical properties of the model, to the relationship between the model and the data, and to descriptive properties of the data can greatly simplify the problem, sometimes providing a method of solution on a desk calculator. This paper describes how parameter transformation, sequential minimization and nested minimization can be used to solve particular problems. Applications to well‐known problems of distribution fitting, quantal responses and least‐squares curve fitting are described. The implications for computer programming are discussed.

https://www.jstor.org/stable/pdfplus/2346325.pdf

G. J. S. Ross

Papers

Minimum Spanning Trees and Single Linkage Cluster Analysis

Analysis of expressed sequence tags from Actinidia: Applications of a cross species EST database for gene discovery in the areas of flavor, health, color and ripening

Analyse Statistique à Plusieurs Variables

Kiwifruit β-galactosidase: Isolation and activity against specific fruit cell-wall polysaccharides

The efficient use of function minimization in non-linear maximum-likelihood estimation