Generalized approaches to the maxbet problem and the maxdiff problem,with applications to canonical correlations

Van de Geer has reviewed various criteria for transforming two or more matrices to maximal agreement, subject to orthogonality constraints. The criteria have applications in the context of matching factor or configuration matrices and in the context of canonical correlation analysis for two or more matrices. The present paper summarizes and gives a unified treatment of fully general computational solutions for two of these criteria, Maxbet and Maxdiff. These solutions will be shown to encompass various well-known methods as special cases. It will be argued that the Maxdiff solution should be preferred to the Maxbet solution whenever the two criteria coincide. Horst's Maxcor method will be shown to lack the property of monotone convergence. Finally, simultaneous and successive versions of the Maxbet and Maxdiff solutions will be treated as special cases of a fully flexible approach where the columns of the rotation matrices are obtained in successive blocks.The author is obliged to Henk Kiers for computational assistance and helpful comments.     

The effect of a non-informative cueing signal in a three-choice reaction-time task

Summary Many studies have shown that in a simple reaction-time (RT) task a non-informative leading cue decreases RT to a subsequent target presented in the same region as the cue. This facilitation lasts about 150 ms; it is then replaced by a sustained inhibition. Experiment 1 tests the hypothesis that the initial facilitation is due to motor, rather than perceptual, processes by using choice RT. Facilitation is greater and lasts longer in choice than in simple tasks, thus supporting the hypothesis. Experiment 2 shows that facilitation occurs even when the subject actively orients his or her attention away from the cue.     

Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.Financial support by the Netherlands organization for scientific research (NWO) is gratefully acknowledged.     

Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

Maps between some different kinds of contraction function: The finite case

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open.     

Concept learning,memory and transfer of dot pattern categories

In the first experiment, subjects rated the similarity of a sample of pairs of random dot patterns generated from 3 prototypes consisting of either 4, 6, or 9 dots. The results of the experiment tended to confirm the structure imposed on the patterns by the construction method. In the second experiment, subjects learned to classify random patterns generated from 2 prototypes with either short or long interprototype distance and consisting of either 4, 6, or 9 dots in a traditional concept identification task. After acquisition, memory for old and new distortions and the prototype, which was not presented during learning, was assessed. The tendency to call a pattern “new” increased with the distance between the pattern and its prototype. In a subsequent transfer test, all subjects saw patterns of either 4, 6, or 9 dots. Performance was above chance and the transfer from larger to smaller patterns tended to be greater than the transfer from smaller to larger patterns. This is consistent with a process of schema formation based on features common to most exemplars of the category. The results are discussed in relation to several theories of concept learning and schema abstraction.     

Bilinguals in a monolingual and a bilingual speech mode: The effect on lexical access

The time course of lexical access in fluent Portuguese-English bilinguals and in English speaking monolinguals was examined during the on-line processing of spoken sentences using the phoneme-triggered lexical decision task (Blank, 1980). The bilinguals were tested in two distinct speech modes: a monolingual, English or Portuguese, speech mode, and a bilingual, code-switching, speech mode. Although the bilingual’s lexical decision response times to word targets in the monolingual speech modes were identical to those of the monolingual subjects, their response times to code-switched word targets in the bilingual mode were significantly slower. In addition, the bilinguals took longer to detect nonwords in both the monolingual and bilingual modes. These results confirm that bilinguals cannot totally deactivate their other language when in a monolingual speech mode. It is hypothesized that bilinguals search both lexicons when confronted with nonwords, even when in a totally monolingual mode, and that they search the base-language lexicon before the other lexicon when in a bilingual, code-switching, speech mode.