Hierarchical Clustering Scheme Research Articles

A Graph Theoretic Analysis of Pattern Classification via Tamura's Fuzzy Relation

Graph theoretical arguments are used to show that the hierarchical clustering scheme induced by Tamura's N-step fuzzy relation f is contained in the maximal single linkage hierarchy. A method of computing f is proposed, based upon Prim's algorithm for generating maximal spanning trees and a result reported by Hu on maximal capacity routes in maximal spanning trees. It is shown that this procedure is superior to Tamura's generalized matrix multiplication algorithm with regard to both computing time and storage requirements.

Free-recall learning of word lists by prelingual deaf subjects

This study examined the extent of influence which an extremely impoverished acoustic-linguistic system exerted on multitrial free recall of word lists, using 36 prelingual deaf and 36 normal-hearing S s of two age levels. In comparison with the hearing S s, the deaf S s′ recall performance was poor and their span of “echoic” memory tended to be short. Between the two groups, there was a considerable amount of common features in mnemonic organizations, as assessed by Tulving's subjective organization, Bousfield's clustering, and Johnson's hierarchical clustering schemes. The deaf S s were, however, less efficient and showed no developmental improvement in these measures. These results suggest that acoustic-linguistic mediation is also crucial for deaf S s′ free-recall learning of verbal materials.

Adaptive Hierarchical Clustering Schemes

Rohlf, F. J. (Biological Sciences, State Univ., Stony Brook, N. Y. 11790) 1970. Adaptive hierarchical clustering schemes. Syst. Zool., 18:58-82.-Various methods of summarizing phenetic relationships are briefly reviewed (including a comparison of principal components analysis and non-metric scaling). Sequential agglomerative hierarchical clustering schemes are considered in particular detail, and several new methods are proposed. The new algorithms are characterized by their ability to adapt to the possible trends of variation found within clusters as they are being formed. A nonlinear version allows the isolation and description of clusters which are parabolic, ring-shaped, etc., by the introduction of appropriate dummy variables. Procedures for computing the fitting trend line through the cluster are also presented, and problems in measuring the amount of information lost by clustering are discussed. [Phenetics; cluster analysis; numerical taxonomy.] This paper is concerned with a brief review of some of the techniques of summarizing phenetic similarities that have been proposed for use in numerical taxonomy. One class of methods (sequential agglomera'tive) is considered in detail and new procedures which allow for elongated and curvilinear clusters are proposed. The problem in biology can be described as follows: Given a set of specimens (operational taxonomic units or OTU's, Sokal and Sneath, 1963, which may represent taxa of any rank) known only by a list of their properties or characters, we wish to find the best way of describing their often complex patterns of mutual similarities (phenetic relationships). Such relationships do not necessarily imply evolutionary (cladistic) relationships (for a discussion of these approaches, see Sokal and Camin, 1965). The methods that have been developed appear to have a more general application than just in biological taxonomy, but there are certain facts and assumptions that can be made in biology which influence our choice of methods. As a result, the techniques may or may not be completely valid in other fields. Some of the considerations which influence the development of cluster analyses in biological taxonomy are the following: (1) All things being equal we would hope that a system of nested clusters would be found. This is due to the fact that evolution is believed usually to be a divergent process and the distribution of OTU's in a phenetic space should to some extent reflect this. There are, of course, exceptions to this overall rule which are very important, such as those provided by hybridization and clinal variation. (2) Another consideration is the nature of the character set representing each OTU. We would like to use a random sampling of or at least a representative sampling of characters. But since different sets of characters seem to yield slightly different systems of relationships (Rohlf, 1963; Ehrlich and Ehrlich, 1967; Michener and Sokal, 1966), biologists may have to get used to the idea of using different classifications, based upon different sets of characters, each for its own special purpose, with overall similarities based on the total character set available at any one time. (3) The selection of OTU's is also not random. Since we cannot study all organisms, we must select those which are of immediate interest. But even with a specified group of organisms, we usually cannot sample at random. This is so because the distributions of recent (and even fossil) organisms are clumped in a phenetic hyperspace. One needs to pass up many very similar, common specimens to obtain a more interesting sampling of different kinds of organisms. Thus, a preliminary screening of individuals according to their apparent similarities must be made before one can make detailed measurements to analyze their phenetic relationships quan-

Hierarchial chunking in sentence processing

In order to evaluate a left-to-right hierarchical chunking model of sentence perception, Johnson’s Hierarchical Clustering Scheme (HCS) technique was applied to data obtained from sentence intelligibility tests. One hundred and twenty Ss listened to sentences disturbed by white noise. After each presentation they wrote down what they had heard. For each sentence, a table of conditional probabilities p(j/i) was computed, where p(j/i) is the probability that word j had been correctly identified. given correct identification of word i. This was done for all i’s and j’s from the sentence. HCS analysis of the off-diagonal submatrices for which words i precede words j (“forward conditional probabilities ”) yielded satisfactory results. Apparently there is a latent hierarchical structure to these data. The large chunks that appear from these analyses do generally correspond to major syntactic constituents. Minor constituents, however, are very often not reflected in the chunking pattern.

Perceptual Structure of English Vowels

Twelve isolated sustained English vowels were magnetically recorded and then presented to English speaking subjects in pairs. The subjects were asked to estimate the perceptual similarity of each pair by drawing a horizontal line. The length of the line corresponded to the degree of similarity. A short line represented a more similar pair; a long line, a less similar pair. The average length of all lines for all auditors was computed for each pair of vowels. These average values were summarized in a matrix and were used in subsequent analysis. Two statistical models were used in the analysis: Multidimensional Scaling (MDS: Shepard, Kruskal) and Hierarchical Clustering Schemes (HCS: Johnson). These models bring out the most prominent dimensions in the set of similarity values and are interpretable generally as phonetic features. Feature strength and feature markedness were also computed. [This work was supported by The National Institutes of Health, U. S. Department of Health, Education, and Welfare.]

Measuring Distances of English Phonemes Using Magnitude Estimation

The dissimilarity between English phonemes was determined (separately for consonants and vowels) using a method of magnitude estimation. The stimuli were 23 consonants and 12 vowels of English. The consonants were presented before the vowel [a]; the vowels were presented in isolation. The auditors (18 female students of Speech) were presented 506 pairs of consonants and 132 pairs of vowels [n(n−1)] as recorded by a speaker of English. The auditors' task was to draw horizontal lines estimating the similar soundingness of each pair of stimuli. The results showed a direct relationship between the phonological account of dissimilarity and psychological estimates of magnitude of difference. The statistical models of Multidimensional Scaling (MDS) (Shepardd, Kruskal) and the Hierarchical Clustering Schemes (HCS) (Johnson) were used to indicate the appropriate number of dimensions needed to classify English phonemes and the differing degrees of weights on the different phonological features—i.e. the degree of intensity with which the phonemes relate to each other. [This work was partially supported by a grant from the Office of the Academic Vice-President, Howard University.]