Assessing the stability of principal components using regression

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.The authors would like to thank the four anonymous reviewers and the two editors for their valuable comments. Atanu R. Sinha gratefully acknowledges the research support received from the Marketing Studies Center, AGSM, UCLA. Send requests for reprints to Atanu R. Sinha, B418 Gold Hall, 110 Westwood Plaza, Los Angeles, CA 90095.     

Applying matrix factorization techniques to compare experts’ categorization process during case formulation task performed by concept maps

The aim of this paper was to present a method to enable the analysis of the process of categorization of patients’ testimonials and the comparison of individual categories created by professionals. A complex diagnostic task (case conceptualization) was employed to study the categorization function in professional thinking. Two groups of psychotherapists (30 people in each group) served as subjects of the research. The main objective of the study was to find an appropriate representation of concept maps enabling a comparison of both the categories and the structures between experts. In the comparison process, only the information about the premises justifying each given category was taken into account and represented by a concept-testimonials matrix. Three different elements weighting schemes and matrix factorization-based unsupervised clustering methods were analyzed in the context of consistency and ability to establish main semantic groups of concepts common to the majority of experts. Moreover, special attention was paid to determining the number of main semantic classes. The study showed that even the used representation was similar to the task of documents indexing there was some discrepancy. The highest accuracy in generating main semantic groups was achieved using the PCA and K-Means (nKM) (the average false positive rate in clusters was 32%). This method outperformed Tempered PLSA (the average false positive rate per cluster was 52%). It was demonstrated that in analyzed task the nKM method allowed comparing the similarity of concepts even when they were created by various experts using different conceptual apparatus.     

No strong evidence for lateralisation of word reading and face recognition deficits following posterior brain injury

Face recognition and word reading are thought to be mediated by relatively independent cognitive systems lateralised to the right and left hemispheres, respectively. In this case, we should expect a higher incidence of face recognition problems in patients with right hemisphere injury and a higher incidence of reading problems in patients with left hemisphere injury. We tested this hypothesis in a group of 31 patients with unilateral right or left hemisphere infarcts in the territory of the posterior cerebral arteries. In most domains tested (e.g., visual attention, object recognition, visuo-construction, motion perception), we found that both patient groups performed significantly worse than a matched control group. In particular, we found a significant number of face recognition deficits in patients with left hemisphere injury and a significant number of patients with word reading deficits following right hemisphere injury. This suggests that face recognition and word reading may be mediated by more bilaterally distributed neural systems than is commonly assumed.     

Uniqueness of N-way N-mode hierarchical classes models

This paper presents two uniqueness theorems for the family of hierarchical classes models, a collection of order preserving Boolean decomposition models for binary N-way N-mode data. The theorems are compared with uniqueness results for the closely related family of N-way N-mode principal component models. It is concluded that the two-way two-mode PCA and N-way N-mode TuckerN models suffer more from a lack of identifiability than their hierarchical classes analogues, whereas the uniqueness conditions for N-way N-mode PARAFAC/CANDECOMP models are less restrictive than the ones derived for their N-way N-mode hierarchical classes counterparts.     

Social learning under the labeling effect: Exploring travellers’ behavior in social dilemmas

This paper presents results of a laboratory experiment, in which subjects made choices between public and private transportation when managing Personal Carbon Allowances (PCAs). The objectives of this study were twofold. Firstly, it was aimed at investigating the labeling effect under the social dilemma context. Secondly, it showed insights into the decision-making process when feedback about others’ choices was provided. A combination of the labeling effect and feedback helped individuals change their commuting pattern and increase the number of trips by public transportation under the PCAs regime. Feedback on others’ choices resulted in social learning and incentivized choice of public transportation more frequently in social dilemma situations.     

An electro-physiological temporal principal component analysis of processing stages of number comparison in developmental dyscalculia

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltész et al., 2007) here our objective was to identify and compare cognitive processes in adolescents with DD and in matched control participants in one-digit number comparison. To this end we used temporal principal component analysis (PCA) on ERP data. First, PCA has identified four major components explaining the 85.8% of the variance in number comparison. Second, the ERP correlate of the most frequently used marker of the so-called magnitude representation, the numerical distance effect, was intact in DD during all processing stages identified by PCA. Third, hemispheric differences in the first temporal component and group differences in the second temporal component suggest executive control differences between DD and controls.     

Skill level constrains the coordination of posture and upper-limb movement in a pistol-aiming task

The purpose of the experiment was to investigate whether skill level differentially organizes the coordination of the postural system and upper limb kinematics in a pistol-aiming task. Participants aimed an air-pistol at a target center in 30 s trials as accurately as possible while standing on a force platform with shooting arm joint kinematics recorded. The novice group had greater motion of the pistol end point, arm joints and the center of pressure than the skilled group. Principal components analysis (PCA) showed that the skilled group required 2 components as opposed to the 3 components of the novice group to accommodate the variance. Coherence analysis in the 0–1 Hz bandwidth revealed that the coupling between posture and upper-limb movement was stronger in the skilled than the novice group. The findings are consistent with the view that skill acquisition reduces the kinematic variables into a lower dimensional functional unit that in pistol-aiming is defined over the collective posture and upper-limb system.     

Higher-order activity beyond the word level: cortical dynamics of simple transitive sentence comprehension

Slow electrophysiological effects, which fluctuate throughout the course of a sentence, independent of transient responses to individual words, have been reported. However, this type of activity has scarcely been studied, and with only limited use of electrophysiological information, so that the brain areas in which these variations originate have not been clearly identified. To improve this state of affairs, a principal component analysis and a modern source analysis algorithm (LORETA) were applied to the slow activity underlying transitive sentence reading. Four components explained 97.3% of the variance. Of key interest was a slow variation that occurred throughout the entire sentence but peaked with the appearance of the verb. The main solution for this component was localized in prefrontal and temporal regions presumably involved in semantic sentence processing. This constitutes empirical evidence for cortical activity--related to semantic processes thought to be involved in thematic role assignment--developing throughout the sentence but presenting a conspicuous maximum with the appearance of the verb. This finding also highlights the central role of verb information in the understanding of transitive sentences.     

Multi-segmental movement patterns reflect juggling complexity and skill level

The juggling action of six experts and six intermediates jugglers was recorded with a motion capture system and decomposed into its fundamental components through Principal Component Analysis. The aim was to quantify trends in movement dimensionality, multi-segmental patterns and rhythmicity as a function of proficiency level and task complexity. Dimensionality was quantified in terms of Residual Variance, while the Relative Amplitude was introduced to account for individual differences in movement components. We observed that: experience-related modifications in multi-segmental actions exist, such as the progressive reduction of error-correction movements, especially in complex task condition. The systematic identification of motor patterns sensitive to the acquisition of specific experience could accelerate the learning process.