Complete Linkage Clustering Research Articles

A method for classifying commercial tree species of an uneven-aged mixed species tropical forest for growth and yield model construction

The sparse distribution of timber species in the tropical rainforest has been a major obstacle in the construction of timber growth and yield models for forest management planning. Models for individual species usually have biased parameter estimates because of the sparse representation of those species ( Vanclay, 1991). We present a technique for pooling species with similar growth characteristics into groups to minimize the level of bias in the estimation of model parameters. Principal component, canonical discriminant, and approximate covariance estimation for clustering procedures ( Milligan and Cooper, 1985) were used to transform and improve the sphericity and separation of multivariate diameter increment data. The k-th nearest neighbor clustering technique ( Wong and Lane, 1983) was used to evaluate the most likely number of species clusters within the population covered by the data. The average linkage, complete linkage, and Ward's minimum variance hierarchical clustering procedures ( Milligan, 1981) were separately applied to the transformed data to identify the characteristics of inherent structures as the basis for classifying similar species into groups. An objective reclassification criterion was used to evaluate the performance of the three clustering methods. Optimal species groupings were attained, with 86.3% cluster recovery, by applying Ward's minimum variance method to data transformed by the canonical discriminant procedure. Consequently, six species growth classes were formed on the basis of the similarities of species growth increment patterns. This objective procedure is guaranteed to produce optimal species groups, with minimal internal variations, suitable for developing unbiased estimates of growth model parameters. The analytic procedure should be applicable to most tropical forest ecological types similar to the moist semi-deciduous forest.

Fast Algorithms for Complete Linkage Clustering

It is shown that the complete linkage clustering of n points can be computed in O(n log 2 n) time. Furthermore, it is shown that the complete linkage clustering can be approximated within an arbitrarily small constant factor in O(n log n) time.

Definition of Climate Regions in the Northern Plains Using an Objective Cluster Modification Technique

Spatially homogeneous climate regions were developed from long-term monthly temperature and precipitation data for a subset of the U.S. Northern Plains. Climate regions were initially defined using the “best” of three agglomerative and hierarchical clustering methodologies, then the clusters were objectively modified using a “pseudohierarchical” iterative improvement technique. Under the premise of hierarchical cluster analysis, once an object has been assigned to a cluster, it cannot later he reassigned to a different cluster, even if it is statistically desirable. The objective modification technique used herein is employed to compensate for this problem. Principal component analysis (PCA) was used to reduce a 147-station dataset, consisting of 24 climatic variables averaged over the 1931–1990 period, to three orthogonal components. The new standardized mars, which explain 93% of the original dataset variance, were then subjected to the Ward's, average linkage, and complete linkage clustering methods. The average linkage method produced the most representative statistical results in identifying the climate regions. An iterative improvement technique was then utilized to test “border station” membership and to modify the climate region houses. Fifteen climate regions resulted from the clustering (with two single-station clusters in the Black Hills alone), although they age just one possible partitioning of the data. The within-cluster variability is generally the same for the 15 climate regions and the corresponding 21 National Climatic Data Center (NCM) climate divisions. However, since data within-cluster variability tends to decrease with increasing cluster number, this result favors the new climate regions. Additionally, the new climate regions am shown to be superior to the NCDC climate, divisions in wont of between-cluster variability. These results suggest that the NCDC climate divisions could be redefined, improving their climatic homogeneity.

Similarity and distance measures for cellular manufacturing. Part II. An extension and comparison

A new similarity measure that is easy to calculate, intuitively appealing, and overcomes the bias inherent in many existing similarity measures is proposed. This new similarity measure is particularly useful for reducing the size of the cell formation problem thus reducing the computational burden. Additionally, an investigation comparing several measures of association is presented. Included in this investigation is a comparison of single linkage clustering, average linkage clustering, complete linkage clustering, and Ward's method for clustering.

Relationships between amino acid sequences determined through optimum alignments, clustering, and specific distance patterns: application to a group of scorpion toxins.

Optimum alignment in all pairwise combinations among a group of amino acid sequences generated a distance matrix. These distances were clustered to evaluate relationships among the sequences. The degree of relationship among sequences was also evaluated by calculating specific distances from the distance matrix and examining correlations between patterns of specific distances for pairs of sequences. The sequences examined were a group of 20 amino acid sequences of scorpion toxins originally published and analyzed by M.J. Dufton and H. Rochat in 1984. Alignment gap penalties were constant for all 190 pairwise sequence alignments and were chosen after assessing the impact of changing penalties on resultant distances. The total distances generated by the 190 pairwise sequence alignments were clustered using complete (farthest neighbour) linkage. The square, symmetrical input distance matrix is analogous to diallel cross data where reciprocal and parental values are absent. Diallel analysis methods provided analogues for the distance matrix to genetical specific combining abilities, namely specific distances between all sequence pairs that are independent of the average distances shown by individual sequences. Correlation of specific distance patterns, with transformation to modified z values and a stringent probability level, were used to delineate subgroups of related sequences. These were compared with complete linkage clustering results. Excellent agreement between the two approaches was found. Three originally outlying sequences were placed within the four new subgroups.

Resource-requirements planning in flexible manufacturing systems

In this paper, we address the problem of planning the requirements of some of the important resources in flexible manufacturing systems. Specifically, we model the problem of estimating the required numbers and types of machines and tools in the context of a cellular layout. A two-stage procedure is developed which first forms the part families, using the complete-linkage clustering method based on a new similarity index defined in terms of the tooling requirements, and then subsequently estimates the resource requirements to manufacture the part families using an integer programming model. Several variations of the model are discussed and a numerical example is given.

Automated conformational analysis from crystallographic data. 2. Symmetry-modified Jarvis–Patrick and complete-linkage clustering algorithms for three-dimensional pattern recognition

The complete-linkage and Jarvis-Patrick clustering algorithms are used to identify discrete conformational subgroups for a chemical fragment from crystal structure data. Fragment conformations are defined by Nt torsion angles for N s occurrences of the fragment in the Cambridge Structural Database. Both algorithms are extensively modified to handle 2D topological symmetry of the fragment and the 3D conformational enantiomers which occur in crystal structures. The modified procedures ensure that symmetry equivalents of a given conformation are optimally superimposed in a unique cluster. A modified single-linkage algorithm, based on cluster centroids, is used to place the discrete clusters in a single asymmetric unit of conformational space. Principal-component analysis provides a graphical representation of the clustering process. The complete-linkage and Jarvis-Patrick algorithms may be preferable to single-linkage cluster analysis [Allen, Doyle & Taylor (1991). Aeta Cryst. B47, 29-40] since they minimize the effects of 'chaining' i.e. the linkage of major clusters through a chain of outlying observations. Both of the new algorithms have been tested using a trial data set of 222 six-membered carbocycles of known conformational complexity. The new algorithms are judged to provide a more effective conformational breakdown of the trial data set (in chemical terms) than that obtained with the single-linkage method alone.

Clustering algorithms for the design of a cellular manufacturing system—an analysis of their performance

The heuristic clustering methods based on similarity coefficient are considered to be very efficient for providing modularity and flexibility in a cellular manufacturing systems (CMS's). Various algorithms have been implemented in these heuristic methods. However, these algorithms suffer from string effect which is also known as “chaining”. Sedveral studies have reported this problem, yet not much research has been conducted to investigate its impact on actual clustering process. This paper presents results from an analytical study performed to determine the severity of chaining problem and other characteristics associated with the clustering process of four selected algorithms. The four algorithms are Single linkage clustering (SLINK), Average linkage clustering (ALINK), Weighted average linkage clustering (WLINK), and Complete linkage clustering (CLINK). A sample of fifty problems with randomly generated data sets was used to determine feasible solutions consisting of machine cells and corresponding part families from each of the four algorithms. A quantitative measure is proposed for evaluating the performance of different algorithms. The study concludes that the chaining effect for CLINK, WLINK, ALINK and SLINK progresively worsens from CLINK to SLINK in the same order. The study also provides important guidelines to designers of a CMS in selecting the most efficient algorithm for a given problem data. Several important statistical results are also presented.

Concepts and effectiveness of the cover-coefficient-based clustering methodology for text databases

A new algorithm for document clustering is introduced. The base concept of the algorithm, the cover coefficient (CC) concept, provides a means of estimating the number of clusters within a document database and related indexing and clustering analytically. The CC concept is used also to identify the cluster seeds and to form clusters with these seeds. It is shown that the complexity of the clustering process is very low. The retrieval experiments show that the information-retrieval effectiveness of the algorithm is compatible with a very demanding complete linkage clustering method that is known to have good retrieval performance. The experiments also show that the algorithm is 15.1 to 63.5 (with an average of 47.5) percent better than four other clustering algorithms in cluster-based information retrieval. The experiments have validated the indexing-clustering relationships and the complexity of the algorithm and have shown improvements in retrieval effectiveness. In the experiments two document databases are used: TODS214 and INSPEC. The latter is a common database with 12,684 documents.

Clustering algorithms for the design of a cellular manufacturing system - an analysis for their performance

Abstract The heuristic clustering methods based on similarity coefficient are considered to be very efficient for providing modularity and flexibility in a cellular manufacturing systems (CMS's). Various algorithms have been implemented in these heuristic methods. However, these algorithms suffer from string effect which is also known as “chaining”. Sedveral studies have reported this problem, yet not much research has been conducted to investigate its impact on actual clustering process. This paper presents results from an analytical study performed to determine the severity of chaining problem and other characteristics associated with the clustering process of four selected algorithms. The four algorithms are Single linkage clustering (SLINK), Average linkage clustering (ALINK), Weighted average linkage clustering (WLINK), and Complete linkage clustering (CLINK). A sample of fifty problems with randomly generated data sets was used to determine feasible solutions consisting of machine cells and corresponding part families from each of the four algorithms. A quantitative measure is proposed for evaluating the performance of different algorithms. The study concludes that the chaining effect for CLINK, WLINK, ALINK and SLINK progresively worsens from CLINK to SLINK in the same order. The study also provides important guidelines to designers of a CMS in selecting the most efficient algorithm for a given problem data. Several important statistical results are also presented.

Classification of the family Plectonemertidae (Nemertea): a phenetic comparison

A phenetic classification based on overall morphological similarity between the species in the family Plectonemertidae (genera Plectonemertes, Campbellonemertes, Potamonemertes, Leptonemertes, Katechonemertes, Argonemertes, Anliponemertes, and Acteonemertes) was undertaken and the result compared with a cladistic and an evolutionary classification. Similarity between species was computed by Gower's general coefficient of similarity and various techniques were used to find patterns in the similarity matrix: single-linkage, average-linkage, and complete-linkage clustering, together with principal coordinate analysis. Although the explicit aim of phenetics is not to estimate the phylogeny, the classification based on overall similarity still portrays phylogeny better than an intuitive assessment of morphological similarity, as judged by the cladistic analysis. The classification does not support the previously proposed hypothesis that the two freshwater genera Campbellonemertes and Potamonemertes have descended from a terrestrial ancestor.

How many clusters are best? - An experiment

This paper reports the results of a Monte Carlo study on the relative effectiveness of two internal indices in estimating the true number of clusters in multivariate data. The two indices are the Davies and Bouldin(1) index and a new modification of the Hubert Γ statistic(2). Data in d dimensions are clustered to create sequences of partitions. Estimates are based on plots of the indices as functions of the number of recovered clusters. Neither index uses a-priori information. The effects of sample size, dimensionality, cluster spread, number of true clusters, and sampling window are examined. Clustered data are generated to assure a given number of distinct clusters. The degree of clustering in the data is verified by a separate Monte Carlo study based on the Jaccard and corrected Rand indices that exhibits the importance of correcting external indices for chance.The modified Hubert index, proposed here for the first time, is shown to perform better than the Davies-Bouldin index under all experimental conditions. Recovery of the true number of clusters gets better as the number of true clusters decreases and as the number of dimensions increases. No effect occurs due to sampling window. The complete link clustering method and a square error clustering method recognize the true number of clusters consistently better than the single link method. This study demonstrates the difficulty inherent in estimating the number of clusters.

Abstracts

The first part of this paper reports a comparative study of the document classifications produced by the use of the single linkage, complete linkage, group average, and Ward clustering methods. Studies of cluster membership and of the effectiveness of cluster searches support previous findings that suggest that the single linkage classifications are rather different from those produced by the other three methods. These latter methods all produce large numbers of small clusters containing just pairs of documents. This finding motivates the work reported in the second part of the paper, which considers the use of clusters consisting of a document together with that document with which it is most similar. A comparison of the use of such clusters with conventional best match searches using seven documents test collections suggest that the two types of search are of comparable effectiveness, but they retrieve noticeably different sets of relevant documents.

Using interdocument similarity information in document retrieval systems

Etude comparative de quatre methodes de constitution de grappes de documents et de leur efficacite lors de la recherche documentaire, testee sur sept collections de documents

Investigation of proportional link linkage clustering methods

Proportional link linkage (PLL) clustering methods are a parametric family of monotone invariant agglomerative hierarchical clustering methods. This family includes the single, minimedian, and complete linkage clustering methods as special cases; its members are used in psychological and ecological applications. Since the literature on clustering space distortion is oriented to quantitative input data, we adapt its basic concepts to input data with only ordinal significance and analyze the space distortion properties of PLL methods. To enable PLL methods to be used when the numbern of objects being clustered is large, we describe an efficient PLL algorithm that operates inO(n 2 logn) time andO(n 2) space.

Phylogeny of the Vibrionaceae, and Recommendation for Two New Genera, Listonella and Shewanella

Ribonucleotide sequences were determined for 5S rRNAs purified from 31 type cultures and freshly isolated strains representing species of the eubacterial family Vibrionaceae. These were compared with published 5S rRNA sequences for 11 other species of rRNA superfamily I (Vibrionaceae, Enterobacteriaceae) for the purpose of constructing a phylogenetic taxonomy of the Vibrionaceae. Sequence data were compiled and analyzed, using single, average, and complete linkage clustering methods, resulting in the generation of evolutionary trees. Results of this study indicate a good correlation between the taxonomy of the Vibrionaceae established using conventional and molecular genetic data and evolutionary relationships deduced from 5S rRNA sequences. However, several species, including V. anguillarum, V. pelagius, V. damsela, V. fischeri, V. logei, V. psychroerythrus, V. marinus, and Plesiomonas shigelloides require reconsideration of their taxonomic status, based on the new information obtained in this study. Furthermore, the genus Aeromonas appears to be sufficiently distantly related to the Vibrionaceae to warrant exclusion from the family Vibrionaceae. We propose a restructuring of the family Vibrionaceae along phylogenetic lines, and establishment of two new genera Listonella and Shewanella, and a new family Aeromonadaceae.

REDUCING THE PARETO OPTIMAL SET IN MULTICRITERIA OPTIMIZATION(With Applications to Pareto Optimal Dynamic Programming)

This paper describes the rationale for using clustering methods to reduce the size of the Pareto optimal set whilst retaining its shape. It proceeds lo describe an implementation of the complete-linkage clustering method and demonstrates its application. Finally, the method is incorporated into a Pareto optimal serial dynamic programming process to reduce the size of the Pareto optimal set generated at each stage of the optimization.

HIERARCHIC AGGLOMERATIVE CLUSTERING METHODS FOR AUTOMATIC DOCUMENT CLASSIFICATION

This paper considers the classifications produced by application of the single linkage, complete linkage, group average and Ward clustering methods to the Keen and Cranfield document test collections. Experiments were carried out to study the structure of the hierarchies produced by the different methods, the extent to which the methods distort the input similarity matrices during the generation of a classification, and the retrieval effectiveness obtainable in cluster based retrieval. The results would suggest that the single linkage method, which has been used extensively in previous work on document clustering, is not the most effective procedure of those tested, although it should be emphasized that the experiments have used only small document test collections.

Sex differences in the levels of generality of values/preferences related to work

The current literature on sex differences in values/preferences related to work appears polarized around two apparently contradictory sets of findings and conclusions. One set of studies fails to detect sex differences. The other set of studies indicates that males are more concerned about money, independence, security, and career goals, while females appear more concerned about people and environmental issues at work. Following W. D. Siegfried, I. MacFarlane, D. B. Graham, N. A. Moore, and P. L. Young ( Journal of Vocational Behavior, 1981, 18, 30–42) it is suggested that level of analysis may be a crucial factor accounting for much of the prevailing confusion in the literature. This study investigated sex differences in values/preferences related to work at various levels of generality. A sample of 1081 senior high school students was administered the Work Aspect Preference Scale (WAPS). Complete-link cluster analyses were performed for males and females separately. Comparison of the two dendrograms reveals the substantial similarity of the preference patterns of males and females. However, the basic difference in the patterns focused on the Altruism and Physical Activity subscales. Females appeared more likely to associate helping others with personal achievement whereas males tended to see helping people in terms of controlling and organizing them. Females also linked physical activity with helping others and self-development whereas males tended to associate physical activity with extrinsic rewards of work. It is concluded that the use of cluster analysis techniques may provide the best procedure to effect an adequate reconciliation of the conflicting results to be found in the current literature.

Interpersonal Resource Exchanges as Indicators of Quality of Marriage

This study was designed to test Foa and Foa's (1974) resource exchange theory in predicting satisfaction with marriage. Data were obtained by survey using self-administered questionnaires from 224 husband-wife couples. Respondents provided information concerning feelings about perceived quality of marriage, resources received from spouse, and shared time. It was hypothesized that the order of resource classes on the particularism dimension would correspond to the order of their effectiveness in contributing to marital satisfaction. Questionnaire items chosen to represent resource classes were verified by hierarchical complete-linkage clustering. The forward method of multiple regression indicated that the theory is useful and that additional testing is needed.