Beyond principal component analysis: A trilinear decomposition model and least squares estimation

The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.     

Kernel principal component analysis combining rotation forest method for linearly inseparable data

Rotation forest (RoF) is an ensemble classifier combining linear analysis theories and decision tree algorithms. In recent existing works, RoF was widely applied to various fields with outstanding performance compared to traditional machine learning techniques, given that a reasonable number of base classifiers is provided. However, the conventional RoF algorithm suffers from classifying linearly inseparable datasets. In this study, a hybrid algorithm integrating kernel principal component analysis (KPCA) and the conventional RoF algorithm is proposed to overcome the classification difficulty for linearly inseparable datasets. The radial basis function (RBF) is selected as the kernel for the KPCA method to establish the nonlinear mapping for linearly inseparable data. Moreover, we evaluate various kernel parameters for better performance. Experimental results show that our algorithm improves the performance of RoF with linearly inseparable datasets, and therefore provides higher classification accuracy rates compared with other ensemble machine learning methods.     

Influential observations in principal factor analysis

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functionsI(x; LL ^T ) andI(x; ) for the common variance matrixT =LL ^T and the unique variance matrix , respectively, in the common factor decomposition =LL ^T + . A numerical example is given for illustration.The authors are grateful to Tomoyuki Tarumi and Atsuhiro Hayashi for their kind permission to use their software Seto/B for drawing Figures 1 and 2 and to anonymous reviewers for comments on the paper.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

Concise formulas for the standard errors of component loading estimates

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.The author is indebted to anonymous reviewers for the corrections and suggestions on this study, which have led to improvements of earlier versions of this article.     

Determining the number of components from the matrix of partial correlations

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.     

Compressing movement information via principal components analysis (PCA): Contrasting outcomes from the time and frequency domains

PCA has become an increasingly used analysis technique in the movement domain to reveal patterns in data of various kinds (e.g., kinematics, kinetics, EEG, EMG) and to compress the dimension of the multivariate data set recorded. It appears that virtually all movement related PCA analyses have, however, been conducted in the time domain (PCA_t). This standard approach can be biased when there are lead-lag (phase-related) properties to the multivariate time series data. Here we show through theoretical derivation and analysis of simulated and experimental postural kinematics data sets that PCA_t and, PCA in the frequency domain (PCA_f), can lead to contrasting determinations of the dimension of a data set, with the tendency of PCA_t to overestimate the number of components. PCA_f also provides the possibility of obtaining amplitude and phase-difference spectra for each principal component that are uniquely suitable to reveal control mechanisms of the system. The bias in the PCA_t estimate of the number of components can have significant implications for the veracity of the interpretations drawn in regard to the dynamical degrees of freedom of the perceptual-motor system.     

The problem: American education the solution: Use behavior analytic technology

In spite of numerous demonstrations that America's youth can be effectively educated with behavior analytic teaching techniques, few of the country's children are benefiting from the technology. In addition scholarly reviews of effective teaching strategies have often omitted reference to behavior analysis. One way to look at this problem is as a two-step operation. First, it is necessary to determine procedures that work; second it is necessary to devise strategies for effective dissemination. The present issue of JOBE (Vol. 1, No. 3, Sept. 1991) contains the recommendations of six outstanding behavioral educators as to how to deal with the dissemination problem. The initial article by Pumroy and McIntire describes the activities of an organization which trains school psychologists and teachers to use behavioral procedures and advocates for the techniques with a number of audiences. Next, Engelmann suggests that the public have more control over school activities and that legal action be taken against irresponsible administrative decisions. Hall advocates for less labor-intensive procedures and the sale of curricular materials based on behavioral principles. Binder proposes that dissemination of the technology become a private endeavor that responds to consumer needs. Rosenfield describes a collaborative model of consultation that increases treatment adherence. Finally, Albers and Greer describe research that isolates a key teacher behavior that results in greater academic proficiency.     

The indirect effect of cognitive reserve on the relationship between age and cognition in pathological ageing: A cross-sectional retrospective study in an unselected and consecutively enrolled sample

Cognitive reserve (CR) allows individuals to maintain cognitive functionality even in the presence of pathologies. The compensation hypothesis suggests that CR plays an indirect role between age and cognitive decline, contrasting the negative effect of ageing on cognition. We test this hypothesis in an unselected and consecutively enrolled sample of memory clinic attendees (n = 134) who completed the CR Index questionnaire and three neuropsychological tests assessing global cognition (MMSE, FAB, CDT). Participants were divided into two groups based on standard diagnostic criteria (DSM-5): those who were cognitively impaired (n = 92) and those who were preserved (n = 42). A principal component analysis was used to extract a composite measure of global cognitive functioning from the three neuropsychological tests, and mediation analysis was used to examine the relationship between CR, age and global cognitive functioning in the two groups. Results revealed that: (i) age had a significant direct negative effect on the global cognitive score in both groups; (ii) the three socio-behavioural proxies of CR together suppress the direct negative relationship between age and global cognitive score in cognitively impaired patients but not in cognitively preserved participants. This study confirms the association between CR, age and cognition and allows us to validate its role in a population with cognitive impairment and extend findings to a low-to-middle educated population. These results hold important implications for public health and wellness promotion, emphasising the beneficial role of maintaining healthy and active physical, cognitive and social lifestyles.     

The personality of meaning in life: Associations between dimensions of life meaning and the Big Five

The goal of the current study was to identify aspects of personality that are associated with different ways in which people find meaning in life. This was achieved using constrained principal component analysis (CPCA) on data from 322 university students, who completed the Sources of Meaning and Meaning in Life questionnaire and the Big Five Aspects Scale. CPCA demonstrated that personality traits and life meaning are associated, but not redundant, with one another. Specifically, respondents with high scores on lower-level aspects of Openness to Experience tended to derive meaning from questioning, learning and challenging tradition, whereas those with high scores on aspects of Conscientiousness and Extraversion tended to derive meaning from success at work, health, and family. Results suggest that personality traits are associated with variations in the domains used to derive meaning in life, and demonstrate the utility of CPCA as an innovative statistical technique for the study of individual differences.     

Interactions of persistent slip bands with a grain boundary on the common primary slip plane in a copper bicrystal

In this letter, the dislocation patterns on the common primary slip plane in a fatigued \[1-34]-\[182-7] copper bicrystal with a Sigma=19b grain boundary (GB) have been investigated using the electron channelling contrast technique in a scanning electron microscope. The results show that the two-phase dislocation structure, such as veins and persistent slip band (PSB) walls, embedded within veins, can be clearly seen on the common primary slip plane. In particular, the interactions of PSBs with the GB are clearly revealed. It is found that there are three kinds of interaction mode between the GB and the dislocations during cyclic deformation, and those are discussed. It is suggested that the dislocations carried by PSBs cannot transfer through the GB continuously even though the bicrystal has a common primary slip plane and its surface slip bands are continuous across the GB.     

Inconsistency as an interactional problem: a lesson from political rhetoric

The classical theory of cognitive dissonance suggests that when two related cognitions are mutually inconsistent, one of them will change to restore consistency. However, Billig suggests that inconsistency is primarily an interactional problem between subjects and not a cognitive problem within a subject. In the current paper, we adopt Billig's rhetorical approach to inconsistency and study inconsistency as an interactional problem in the context of political rhetoric. More specifically, we use Action-Implicative Discourse Analysis to identify the discursive strategies the former Israeli Prime Minister Benjamin Netanyahu, used to cope with the inconsistency between his national ideology and his contradictory behavior during his short term in office.     

Categorization and individuation in the cross-race recognition deficit: Toward a solution to an insidious problem

Recent theory and evidence suggest that the Cross-Race Effect (better recognition for same-race (SR) faces than for cross-race (CR) faces) is due to social-cognitive processes of categorization of out-group members, causing perceivers to attend to category-specifying information of CR faces at the expense of individuating information. Three experiments seek to extend this social-cognitive explanation of the CRE by investigating the extent to which the Cross-Race Effect can be reduced by inducing perceivers to individuate rather than categorize CR faces. In all three experiments, participants who received warning of the Cross-Race Effect prior to encoding, and instructions to individuate out-group members, showed no CRE. Experiment 2 suggests that this elimination of the CRE was not due merely to increased motivation to process all stimuli. This is one of few empirical displays of an elimination of the CRE outside of visual training. Moreover, these results are congenial with Levin’s (2000) feature-selection model, which suggests that the CRE is due to differential social cognitions about in-group and out-group members, rather than to differences in perceptual expertise. By eliciting individuation of out-group members at encoding, the CRE can be eliminated.     

几何模块论的局限性——来自梯形实验的证据

以往研究表明幼儿主要依赖几何信息进行再定向,但这些研究大多使用矩形空间。在本研究中,幼儿所处的空间为几何信息更丰富,目标物体所在位置确定的梯形。结果发现,幼儿并不会利用新增的几何信息确定目标物体,仍然去正确位置的对角寻找,表现出的寻找模式与矩形空间一样,这说明幼儿在空间再定向任务中对几何信息的利用很有限。此外,录像分析的结果发现,幼儿在面向梯形两底边时会更多地且径直地走向正确位置或对角,这种寻找过程上的特点表明他们可能基于空间轴朝向结合左右方位感表征物体位置     

The verbalization of multiple strategies in a variant of the traveling salesperson problem

What kinds of strategies do humans employ when confronted with a complex spatial task, and how do they verbalize these strategies? Previous research concerned with the well-known traveling salesperson problem (TSP) typically aimed at the identification of a generally applicable heuristics that adequately represents human behavior in relation to the abstract task of combining points. This paper adopts a novel perspective in two respects. On the one hand, it addresses the strategies people employ when confronted with a more complex task, involving distractors and feature information rather than identical points. On the other hand, retrospective linguistic representations of the strategies used are analyzed in relation to the behavioral data, using discourse analytic methods. Results show that both the behavioral results and the verbalizations point to a range of strategies related to those proposed for solving abstract TSPs. However, in contrast to earlier accounts in the literature, the participants employ a repertory of multi-faceted strategies and planning processes, simplifying and structuring the problem space across subtasks and processes in flexible ways. These findings provide further insight into the nature of human strategies in spatial problem solving tasks and their retrospective verbalization, highlighting how procedures generally known in the literature may be adapted to more complex tasks, and how they may be verbalized spontaneously.