A Repetitive Branch-and-Bound Procedure for Minimum Within-Cluster Sums of Squares Partitioning

Minimization of the within-cluster sums of squares (WCSS) is one of the most important optimization criteria in cluster analysis. Although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion, optimal approaches can be computationally feasible for problems of modest size. This paper presents a new branch-and-bound algorithm for minimizing WCSS. Algorithmic enhancements include an effective reordering of objects and a repetitive solution approach that precludes the need for splitting the data set, while maintaining strong bounds throughout the solution process. The new algorithm provided optimal solutions for problems with up to 240 objects and eight well-separated clusters. Poorly separated problems with no inherent cluster structure were optimally solved for up to 60 objects and six clusters. The repetitive branch-and-bound algorithm was also successfully applied to three empirical data sets from the classification literature.     

Order-Constrained Solutions in <Emphasis Type="Italic">K</Emphasis>-Means Clustering: Even Better Than Being Globally Optimal

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that although the usual K-means sum-of-squared-error criterion is not guaranteed to be minimal, a true underlying cluster structure may be more accurately recovered. Also, substantive interpretability seems generally improved when constrained solutions are considered. We illustrate the procedure with several data sets from the literature.     

A study of the classification capabilities of neural networks using unsupervised learning: A comparison withK-means clustering

Several neural networks have been proposed in the general literature for pattern recognition and clustering, but little empirical comparison with traditional methods has been done. The results reported here compare neural networks using Kohonen learning with a traditional clustering method (K-means) in an experimental design using simulated data with known cluster solutions. Two types of neural networks were examined, both of which used unsupervised learning to perform the clustering. One used Kohonen learning with a conscience and the other used Kohonen learning without a conscience mechanism. The performance of these nets was examined with respect to changes in the number of attributes, the number of clusters, and the amount of error in the data. Generally, theK-means procedure had fewer points misclassified while the classification accuracy of neural networks worsened as the number of clusters in the data increased from two to five.Acknowledgements: Sara Dickson, Vidya Nair, and Beth Means assisted with the neural network analyses.     

Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima

Cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low-dimensional spatial representation ofK cluster points, to model a given square table of dissimilarities amongn stimuli or objects. The least squares loss function of cluster differences scaling, originally defined only on the residuals of pairs of objects that are allocated to different clusters, is extended with a loss component for pairs that are allocated to the same cluster. It is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described, including the appropriate degrees of freedom for each source. After developing a convergent algorithm for fitting the cluster differences model, it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by-product of the optimization. Finally, the paper introduces a fuzzy version of the loss function, which can be used in a successive approximation strategy for avoiding local minima. A simulation study demonstrates that this strategy significantly outperforms two other well-known initialization strategies, and that it has a success rate of 92 out of 100 in attaining the global minimum.     

Optimal Partitioning of a Data Set Based on the p-Median Model

Although the K-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The p-median model is an especially well-studied clustering problem that requires the selection of p objects to serve as cluster centers. The objective is to choose the cluster centers such that the sum of the Euclidean distances (or some other dissimilarity measure) of objects assigned to each center is minimized. Using 12 data sets from the literature, we demonstrate that a three-stage procedure consisting of a greedy heuristic, Lagrangian relaxation, and a branch-and-bound algorithm can produce globally optimal solutions for p-median problems of nontrivial size (several hundred objects, five or more variables, and up to 10 clusters). We also report the results of an application of the p-median model to an empirical data set from the telecommunications industry.     

Identifying g: A review of current factor analytic practices in the science of mental abilities

Factor analysis is arguably one of the most important tools in the science of mental abilities. While many studies have been conducted to make recommendations regarding “best practices” concerning its use, it is unknown the degree to which contemporary ability researchers abide by those standards. The current study sought to evaluate the typical practices of contemporary ability researchers. We analyzed articles reporting factor analyses of cognitive ability tests administered to adult samples over a 12 year period. Results suggest that, in aggregate, the science of mental abilities seems to be doing well with respect to the issues of sample size, number of indicators (relative to number of factors) and breadth of indicators. Further, our results suggest that the majority of ability researchers are using methods of factor analysis that allow for the identification of a g factor. However, 14.57% failed to use a method that allowed a common factor to emerge. These results provide insights regarding the methodological quality of the science of mental abilities, and will hopefully encourage further “introspective” research into the science of mental abilities.     

Validating the coping scale for Chinese athletes using multidimensional Rasch analysis

Objective

The Coping Scale for Chinese Athletes (CSCA) was developed and validated using classic testing theory in 2004 (Chung, Si, Lee, & Liu, 2004). This study aimed to validate CSCA using multidimensional Rasch analysis with the ConQuest software programme.

Method

The sample in this study comprised 367 athletes from mainland China. A Multidimensional Rating Scale model was applied to investigate the validity of the four-dimension scale. Standard fit statistics (Infit and Outfit MNSQ) and Differential item functioning (DIF) were computed to examine the model-data fit. Test reliability and category functioning were also checked.

Results

The item difficulty and the athletes’ trait level of coping were calibrated along the same latent trait scale. Three items were removed from the scale due to misfit with the Rasch model. No DIF across gender was found for the remaining 21 items. Test reliabilities for the four subscales ranged from 0.66 to 0.76. The results also indicated that the original 5-category rating scale structure did not function well.

Conclusion

The multidimensional Rasch analysis supported that the 21-item CSCA measures four latent traits of coping of Chinese athletes as expected. The results also demonstrated advantages of multidimensional Rasch analysis over unidimensional Rasch analysis as well as traditional approach in examining the quality of multidimensional scale in sport settings.     

Schizotypy and affective temperament: Relationships with divergent thinking and creativity styles

Schizotypy and affective temperament have both been linked to creativity using measures such as divergent thinking (DT) but not in terms of creativity styles. The relationship between schizotypy and affective temperament has also not been examined directly in a creativity paradigm. Seventy-eight (44 female, 34 male) university students completed two DT tasks and measures of schizotypy, affective temperament, and creativity styles. Positive schizotypy was correlated with creativity styles, and affective temperament was correlated with both creativity styles and DT scores. Furthermore, schizotypy and affective temperament differentially predicted DT scores and creativity styles. Finally, the relationship between schizotypy and affective temperament gave evidence towards a unitary psychosis theory. Results are discussed in terms of current theories about psychosis and psychoticism and their association to creativity.     

Concurrent Validity Studies of the Facial Discrimination Task

We examined the concurrent validity properties of the Facial Discrimination Task (FDT), an instrument for the assessment of facial emotion recognition by comparing it with the widely used Pictures of Facial Affect (PFA). In Study 1, 100 adults with heterogeneous psychiatric diagnoses were administered items of the FDT Emotion Task, the FDT Age Task, and PFA. In Study 2, 25 normally developing preschool children were instructed to label happy, sad, or neutral facial expressions from the FDT and the PFA. Despite methodological differences between the two studies, very similar and high correlations were found between the FDT and the PFA overall correct scores (r = .79 and r = .77, respectively). The data suggest that the FDT and the PFA measure similar competencies in preschoolers and in adults with psychiatric disorders. This finding is important because it establishes the concurrent validity of the FDT in child and adult populations.     

On the Dao in the Commentary of the Book of Change

The existence of the Dao 道 (the Way), according to the Yizhuan 易传 (the Commentary), is something intangible. The connotation of the Dao is the law of change caused by the interaction between yin and yang. The main functions of the Dao are “to change” and “to generate”. The intangible refers to the law of change caused by the interaction between yin and yang, and the law is expressed by the divinatory symbolic system (卦爻符号, the trigrams or hexagrams). It is through the unique permutation of yin and yang lines of a trigram or hexagram that the law of change is explained as a universal model uniting celestial, terrestrial and human laws. The symbolic system is used to express the universal nature of continual generation of life. __________ Translated from Zhongguo Zhexue Shi 中国哲学史 (History of Chinese Philosophy), 2005(4) by Yun Yufen     

Old Foundations for the Logic of Agency and Action

The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how the formal machinery of our systems can be used to reconstruct a number of interesting ideas in the Logic of Agency and Action that have been proposed by authors like von Wright, von Kutschera, Belnap and Segerberg.     

Culturally adapted CBT (CA-CBT) for Latino women with treatment-resistant PTSD: a pilot study comparing CA-CBT to applied muscle relaxation

We examined the therapeutic efficacy of a culturally adapted form of CBT (CA-CBT) for PTSD as compared to applied muscle relaxation (AMR) for female Latino patients with treatment-resistant PTSD. Participants were randomized to receive either CA-CBT (n = 12) or AMR (n = 12), and were assessed before treatment, after treatment, and at a 12-week follow-up. The treatments were manualized and delivered in the form of group therapy across 14 weekly sessions. Assessments included a measure of PTSD, anxiety, culturally relevant idioms of distress (nervios and ataque de nervios), and emotion regulation ability. Patients receiving CA-CBT improved significantly more than in the AMR condition. Effect size estimates showed very large reductions in PTSD symptoms from pretreatment to posttreatment in the CA-CBT group (Cohen’s d = 2.6) but only modest improvements in the AMR group (0.8). These results suggest that CA-CBT can be beneficial for previously treatment-resistant PTSD in Latino women.     

老庄哲学与上博竹书《恒先》

The bamboo slip essay Hengxian 恒先is historically valuable because it serves to further the ontological understanding and comprehension of issues related to the existence of the universe from the perspective of Laozi’s Daoist thought. Hengxian explores important propositions such as how “Qi originated and activated itself” and “they came out of the same source but differed in nature” from several aspects. The idea that “Hengxian is ‘being’ without any definiteness” responds to the issue of the relationship of difference and identity of all things in the world, and thus examines the interdependent relationships between subjects and objects. It proposes that humans can further understand the existence of the universe through cognitive activities and practices such as “analysis and comparison” in which objective realities are checked. The issues discussed in Hengxian are consistent with Laozi’s Dao de jing, the works of Zhuangzi, Huangdi sijing 黄帝四经 (The Four Classics from the Emperor Yellow) and other Daoist works, and deserve significant attention. Translated by Huang Deyuan from Daojia wenhua yanjiu 道家文化研究 (Research of Daoist Culture), 2007, (22): 539–563     

Amount of General Factor Saturation in the Beck Anxiety Inventory Responses of Outpatients with Anxiety Disorders

To ascertain the amount of general factor saturation underlying the Beck Anxiety Inventory (BAI; Beck and Steer 1993) responses of anxious patients, the BAI was administered to 525 outpatients with DSM-IV-TR anxiety disorders. McDonald’s omega_hierarchical(ω _h) (Zinbarg et al. 2005) was calculated to estimate the amount of general factor saturation; ω _h is the amount of variance explained by a general (second-order) factor underlying a scale composed of multiple items divided by the total amount of variance explained by all of the scale’s items. An iterated principal-factor analysis was first performed and followed by a Schmid-Leiman transformation to determine the amount of variance explained by the second-order factor. ω _h was 0.70 [95% CI 0.66–0.72], and this value was discussed as supporting the current practice of summing the 21 symptom ratings of the BAI to estimate the overall severity of self-reported anxiety.

Writing Effective Insurance Justification Letters for Cancer Genetic Testing: A Streamlined Approach

The topic of insurance coverage and justification letters for cancer predisposition testing has been the subject of much discussion on the National Society of Genetic Counselors Cancer Special Interest Group (NSGC Cancer-SIG) listserv. Some counselors have stated that they have had difficulty in obtaining insurance coverage for their patients, while others have indicated that they would appreciate seeing examples of successful letters. The purpose of this paper is to provide practical guidance in writing successful letters of justification and to share insurance success stories in the area of cancer genetic testing.     

A brief explanation of the Chu bamboo slips Hengxian

The discovery of Hengxian and the formation of the category of hengxian are an important recapitulation and creative integration of the theory of the ontological Dao (Tao) in the Pre-Qin period. The cosmology of “self-creating and self-functioning” in Hengxian and the theory of “self-creating and self-evolving” in Liezi and Zhuangzi can be mutually interpreted. It indicates that the theory of transformation of qi entered a quite mature state in the Warring States Period. __________ Translated from Qilu Xuekan 齐鲁学刊 (Qilu Academic Journal), 2005 (1) by Yan Xin     

Power and sample size calculations for multivariate linear models with random explanatory variables

This article considers the problem of power and sample size calculations for normal outcomes within the framework of multivariate linear models. The emphasis is placed on the practical situation that not only the values of response variables for each subject are just available after the observations are made, but also the levels of explanatory variables cannot be predetermined before data collection. Using analytic justification, it is shown that the proposed methods extend the existing approaches to accommodate the extra variability and arbitrary configurations of the explanatory variables. The major modification involves the noncentrality parameters associated with the F approximations to the transformations of Wilks likelihood ratio, Pillai trace and Hotelling-Lawley trace statistics. A treatment of multivariate analysis of covariance models is employed to demonstrate the distinct features of the proposed extension. Monte Carlo simulation studies are conducted to assess the accuracy using a child’s intellectual development model. The results update and expand upon current work in the literature.The author wishes to thank the associate editor and the referees for comments which improve the paper considerably. This research was partially supported by a grant from the Natural Science Council of Taiwan.