Concurrent disjoint and reciprocal classification by Cebus apella in seriation tasks: evidence for hierarchical organization

We report the results of a 4-year-long study of capuchin monkeys (Cebus apella ) on concurrent three-way classification and linear size seriation tasks using explicit ordering procedures, requiring subjects to select icons displayed on touch screens rather than manipulate and sort actual objects into groups. The results indicate that C. apella is competent to classify nine items concurrently, first into three disjoint classes where class exemplars are identical to one another, then into three reciprocal classes which share common exemplar (size) features. In the final phase we compare the relative efficiency of executive control under conditions where both hierarchical and/or linear organization can be utilized. Whilst this shows a superiority of categorical based size seriation for a nine item test set suggesting an adaptive advantage for hierarchical over linear organization, Cebus nevertheless achieved high levels of principled linear size seriation with sequence lengths not normally achieved by children below the age of six years.     

Do apes and monkeys rely upon conceptual reversibility?

The ability to seriate nesting cups as a sensorimotor task has posed interesting questions for cognitive scientists. Greenfield et al. [(1972) Cognit Psychol 3:291–310] found parallels between children's combinatorial activity with nesting cups and patterns of phonological and grammatical constructions. The parallels suggested the possibility of a neurally based developmental homology between language and instrumental action [Greenfield (1991) Behav Brain Sci 14:531–595]. Children who predominantly used subassembly, a hierarchical method of combining cups, succeeded at seriating nesting cups more often than those who did not. Greenfield and others [e.g., Piaget and Inhelder (1969) The psychology of the child. Basic Books, New York; DeLoache et al. (1985) Child Dev 56:928–939] argued that success in seriation reflects the child's growing recognition of a reversible relationship: a particular element in a series is conceived of as being smaller than the previous element and larger than the subsequent element. But is a concept of reversibility or a hierarchical form of object manipulation necessary to seriate cups? In this article, we review studies with very young children and nonhuman primates to determine how individuals that do not evidence conceptual reversibility manage the seriation task. We argue that the development of skill in seriation is experientially, rather than conceptually, driven and that it may be unnecessary to link seriation with cognitive conceptions of reversibility or linguistic capacities. Rather, in ordering a set of objects by size, perceptual-motor learning may enable contemplative refinement. Accepted after revision: 10 September 2001 Electronic Publication     

Analysis of meteorological conditions in Spain by means of clustering techniques

A comprehensive analysis of clustering techniques is presented in this paper through their application to data on meteorological conditions. Six partitional and hierarchical clustering techniques (k-means, k-medoids, SOM k-means, Agglomerative Hierarchical Clustering, and Clustering based on Gaussian Mixture Models) with different distance criteria, together with some clustering evaluation measures (Calinski–Harabasz, Davies–Bouldin, Gap and Silhouette criterion clustering evaluation object), present various analyses of the main climatic zones in Spain. Real-life data sets, recorded by AEMET (Spanish Meteorological Agency) at four of its weather stations, are analyzed in order to characterize the actual weather conditions at each location. The clustering techniques process the data on some of the main daily meteorological variables collected at these stations over six years between 2004 and 2010.     

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [_?1¹₁^?1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.     

ETUDE INTERCULTURELLE DE LA GENERALISATION DES OPERATIONS: SIMILITUDE ET COHERENCE DES ACTIVITES DE CLASSIFICATION ET DE SERIATION CHEZ DES SUJETS CANADIENS-FRANÇAIS,RWANDAIS SCOLARISES ET RWANDAIS NON SCOLARISES*

Sixty-two French-Canadian children, seven to ten years old; 64 schooled Rwandese children, ten to thirteen years old; and 32 unschooled Rwandese subjects aged 15 and 17 were tested on four piagetian logico-mathematical tasks: hierarchical classification (CA), multiple classification (CM), seriation of weight (RA) and double seriation (RM). Due to the effect of order, separate analyses were performed for tasks done during the same test session. When the results of tasks CA and RM, on the one hand, and of RA and CM, on the other hand, are combined, it is observed, firstly, that the items alternate in order of difficulty and, secondly, that the number of coherent patterns of responses exceeds the null hypothesis in French-Canadian and schooled Rwandese populations, supporting the hypothesis of a complementary and partially synchronous modality of structuration of logical abilities. From another point of view, when the items from all four tasks are combined in a single scale of difficulty, the very close similarity observed between the ranks of the items in the three populations strengthens the hypothesis of a universally determined cognitive development based mainly on the equilibration process.     

Personalized interactive characters for toddlers' learning of seriation from a video presentation

Children's media is rooted in relationships with onscreen characters. In this study, 18-month-old toddlers were initially exposed to one of two unfamiliar interactive media characters for 3 months. Conditions varied whether the character was personalized to them or not. At age 21 months, toddlers were tested on a seriation task that was presented onscreen by the character and compared to the performance of a 21-month-old control group who did not view a video demonstration (total N = 48). Toddlers learned significantly more from the personalized character, but not from the non-personalized character, when compared to the control group. Children in the personalized condition also increased in parasocial, nurturing behaviors directed at the character during play sessions, and these scores were linked to better seriation performance. The results suggest an important role for social relationships with interactive characters to teach early seriation skills.     

The sources of skill in seriating cups in children,monkeys and apes

Is a concept of either reversibility or of hierarchical forms of combination necessary for skilled seriation? We examined this question by presenting seriating cups to adult capuchin monkeys and chimpanzees and to 11‐, 16‐ and 21‐month‐old children. Capuchins and chimpanzees consistently created seriated sets with five cups, and placed a sixth cup into a previously seriated set. Children of all three ages created seriated five‐cup sets less consistently than the capuchins and chimpanzees, and were rarely able to place a sixth cup into a seriated set. Twenty‐one‐month‐olds produced more structures containing three or more cups than did the younger age groups, and these children also achieved seriated sets more frequently. Within all participant groups, success at seriating five cups was associated with the frequency of combining three or more cups, regardless of form. The ability to integrate multiple elements in persistent combinatorial activity is sufficient for the emergence of seriation in young children, monkeys and apes. Reliance on particular methods of combination and a concept of reversibility are later refinements that can enhance skilled seriation.     

Nonmetric grouping: Clusters and cliques

A class of related nonmetric (“monotone invariant”) hierarchical grouping methods is presented. The methods are defined in terms of generalized cliques, based on a systematically varying specification of the degree of indirectness of permitted relationships (i.e., degree of “chaining”). This approach to grouping is shown to provide a useful framework for grouping methods based on ana priori specification of the properties of the desired subsets, and includes a natural generalization for “complete linkage” and “single linkage” clustering, such as the methods of Johnson [1967]. The central feature of the class of methods is a simple iterative matrix operation on the original disparities (“inverse-proximities” or “dissimilarities”) matrix, and one of the methods also constitutes a very efficient single linkage clustering procedure.     

Building Meaningful Parasocial Relationships Between Toddlers and Media Characters to Teach Early Mathematical Skills

Very young children have difficulty transferring what they view onscreen to their offscreen worlds. This study examined whether familiarizing toddlers with a character would improve toddlers' performance on a subsequent seriation task. Toddlers were randomly assigned to one of three conditions: (1) a familiarized character condition where toddlers viewed character-based videos and engaged in character-based play over a 3-month period before viewing the seriation video demonstration; (2) an unfamiliarized character condition where the toddler only saw the seriation video demonstration; and (3) a no-exposure control group where the toddler did not see the seriation video demonstration or have any involvement with the character. All toddlers were tested on the same seriation task at age 21 months, with the familiarized character group beginning the study at age 18 months and the other groups participating only at age 21 months. Toddlers in the familiarized character condition, but not the unfamiliarized character condition, completed the seriation task significantly better than the no-exposure control group. Within the familiarized character condition, toddlers who nurtured the character during play subsequently had higher seriation scores. The results suggest that meaningful relationships with media characters can help toddlers learn early mathematical skills.     

Piaget's data and spearman's theory—An empirical reconciliation and its implications for academic achievement

A hierarchical simple structure factor solution was obtained for item scores from a psychometrized battery of Piagetian-type tasks individually administered to 660 kindergarten children. At the first level of factors were the Piagetian theoretical entities of seriation, classification, conservation of number, and temporal and spatial reasoning, with numeration loading on seriation and classification as indicated by the theory. At the second level were two factors identified as Piaget's logicomathematical and infralogical operations. A third-level factor was identified as a g factor. The association of the Piagetian-type tasks with kindergarden and first grade academic achievement was through the third-level g factor. The second-level factors appeared to be similar to Vernon's k:m and v:ed but, like the first level factors, made no important contribution to predicted achievement above that contributed by the g factor. A socioeconomic factor made no unique contribution to predicted first grade achievement. It was concluded that the Piagetian concrete operations variables have no unique role in the prediction of kindergarten or first grade academic achievement.     

Hierarchical Vs. Generally Overlapping Models In Psychiatric Classification

This paper illustrates two formal models for psychiatric classification. The first model, called a hierarchical or tree structure, requires patient categories to be disjoint or strictly nested. The second model, called the generally overlapping or network model, allows patient categories to cut across each other in a variety of different ways. Thus, patient groups can be disjoint, strictly nested (as in a hierarchy), or partially overlapping. To derive classification schemes consistent with the structural models, two different clustering techniques were applied to interpatient similarity data collected on 50 psychiatric patients. A hierarchical clustering technique was applied to the similarity data to obtain a hierarchical classification. To obtain a generally overlapping classification, Peay's cliquing procedure was applied to the same data. Two criteria were used to compare the clustering solutions. First, a solution's goodness-of-fit to the original data was examined by calculating the proportion of variance accounted for by cluster categories. Second, the predictive accuracy of a solution was analyzed by looking at the categories' ability to predict treatment assignment. The generally overlapping solution produced the best fit to the original similarity data; however, the hierarchical solution's clusters tended to be more readily interpretable in terms of psychiatric syndromes. Both clustering solutions were relatively poor predictors of treatment assignment. It was concluded that the hierarchical and generally overlapping approaches, although not conclusively demonstrated, represented promising models for psychiatric classification.     

Cross-category structure in semantic memory

In Experiment I, subjects made similarity judgments about all 56 category terms listed in the Battig and Montague (1969) norms. These judgments were then subjected to a hierarchical clustering analysis. Experiment II demonstrated that the relations among the category labels are very similar to the relations among the high dominance exemplars of these categories. Experiment III showed that the distances between the category terms in the hierarchical clustering analysis could predict RTs in a same-different paradigm.     

Inducing a blockmodel structure of two-mode binary data using seriation procedures

We show that seriation of the rows and columns of a two-mode, binary matrix can be an effective method for producing a reordering of the matrix that reveals a blockmodel structure of the data. The objective criterion of the seriation process is based on Robinson patterning of matrix elements. The key advantages of the proposed method are: (a) it can be used in conjunction with existing two-mode blockmodeling algorithms by facilitating selection of the number of classes for the rows and columns of the matrix and the appropriate types of ideal blocks; (b) the model uses a well-grounded index based on Robinson structure, (c) guaranteed optimal solutions can be obtained for problems of practical size, and (d) the seriation method is frequently capable of producing a solution that has a substantive interpretation with respect to the orderings of the row objects and column items.     

The advantages of mathematical modeling over traditional methods in the analysis of category clustering

A mathematical model for the analysis of category clustering is developed and testd. The model, which can be applied to categories of any size, is an extension of a two-item statistical model developed by Batchelder and Riefer (Psychological Review, 1980, 87, 375–397), and is equivalent to their model when categories consist of two items. The model is based on a current theory of clustering which postulates that the learning of a list of category items occurs on different hierarchical levels. Two category list-learning experiments are presented, and the data from these experiments are analyzed using the general statistical model. The first experiment reveals that the probabilities of storing and retrieving a cluster increase with category size, while the learning of items as singletons decreases. The effects of within-category spacing indicate that the storage of clusters decreases while cluster retrievability increases with an increase in input spacing. In the second experiment, the storage and retrieval of clusters are shown to be unaffected by whether the presentation of items is uncued or cued with the name of the category. However, the association of items decreases and the learning of items as singletons increases with uncued presentation. In the final sections, the general statistical model is compared to other methods for the measurement of category clustering. The model is shown to be superior to numerical indices of clustering, since these measures are not based on any theory of clustering, and because unitary measures cannot capture the multiprocess nature of categorized recall. The model is also argued to have certain advantages over other mathematical models that have been applied to category clustering, since these models cannot account for situations in which a portion of the items are clustered while others are learned singularly.     

Identifying similarities in cognitive subtest functional requirements: An empirical approach

In the cognitive test interpretation literature, a Rational/Intuitive, Indirect Empirical, or Combined approach is typically used to construct conceptual taxonomies of the functional (behavioral) similarities between subtests. To address shortcomings of these approaches, the functional requirements for 49 subtests from six individually administered scales of cognitive ability (WISC-IV, WPPSI-III, SB-V, WJ-III, CAS, and UNIT) were typed on index cards. Forty-eight (48) in-service and/or pre-service school psychologists were asked to sort the cards into two, three, five, or eight functionally similar piles. A multidimensional scaling analysis was performed on a 49 × 49 matrix of similarity scores collapsed across all 48 subjects. Three dimensions were extracted from the data: Reproduction of Stimuli Sequences versus Picture Viewing (Dimension 1), Timed Speed versus Untimed Power (Dimension 2), and Verbal versus Performance (Dimension 3). A hierarchical clustering procedure was then applied to the matrix data, and results were compared to previous categorization schemes identified in the test interpretation literature.     

Relation of cognitive operational performance to comprehension and production of dimensional adjectives

This study compared normal developing children, aged 34 to 51 mo., on comprehension and production of relative dimensional adjectives using object manipulations in a close elicitation procedure and on Piagetian operational tests of conservation of continuous quantity, length, reversibility and seriation. Analysis indicated a significant difference on the expressive language performance of the transitional and the concrete operational children over the preoperational children, but no significant differences occurred between the first two groups. Children who performed better on seriation were significantly better on expressive language performance. Children classified as operational for length performed better on all language measures than those classified as nonoperational. Reversibility and conservation of a continuous quantity did not differentiate children.     

Ultrametric hierarchical clustering algorithms

Johnson has shown that the single linkage and the complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Through the use of the Lance and Williams recurrence formula, Johnson's proof is extended to four other common clustering algorithms. It is also noted that two additional methods produce hierarchical structures which can violate the ultrametric inequality.     

Cross validation issues in multiobjective clustering

The implementation of multiobjective programming methods in combinatorial data analysis is an emergent area of study with a variety of pragmatic applications in the behavioural sciences. Most notably, multiobjective programming provides a tool for analysts to model trade offs among competing criteria in clustering, seriation, and unidimensional scaling tasks. Although multiobjective programming has considerable promise, the technique can produce numerically appealing results that lack empirical validity. With this issue in mind, the purpose of this paper is to briefly review viable areas of application for multiobjective programming and, more importantly, to outline the importance of cross‐validation when using this method in cluster analysis.     

Some applications of graph theory to clustering

This paper attempts to review and expand upon the relationship between graph theory and the clustering of a set of objects. Several graphtheoretic criteria are proposed for use within a general clustering paradigm as a means of developing procedures in between the extremes of complete-link and single-link hierarchical partitioning; these same ideas are then extended to include the more general problem of constructing subsets of objects with overlap. Finally, a number of related topics are surveyed within the general context of reinterpreting and justifying methods of clustering either through standard concepts in graph theory or their simple extensions.     

Bicriterion seriation methods for skew‐symmetric matrices

The decomposition of an asymmetric proximity matrix into its symmetric and skew‐symmetric components is a well‐known principle in combinatorial data analysis. The seriation of the skew‐symmetric component can emphasize information corresponding to the sign or absolute magnitude of the matrix elements, and the choice of objective criterion can have a profound impact on the ordering. In this research note, we propose a bicriterion approach for seriation of a skew‐symmetric matrix incorporating both sign and magnitude information. Two numerical demonstrations reveal that the bicriterion procedure is an effective alternative to direct seriation of the skew‐symmetric matrix, facilitating favourable trade‐offs among sign and magnitude information.