Geometric representation of association between categories

Categories can be counted, rated, or ranked, but they cannot be measured. Likewise, persons or individuals can be counted, rated, or ranked, but they cannot be measured either. Nevertheless, psychology has realized early on that it can take an indirect road to measurement: What can be measured is the strength of association between categories in samples or populations, and what can be quantitatively compared are counts, ratings, or rankings made under different circumstances, or originating from different persons. The strong demand for quantitative analysis of categorical data has thus created a variety of statistical methods, with substantial contributions from psychometrics and sociometrics. What is the common basis of these methods dealing with categories? The basic element they share is that the sample space has a special geometry, in which categories (or persons) are point masses forming a simplex, while distributions of counts or profiles of ratings are centers of gravity, which are also point masses. Rankings form a discrete subset in the interior of the simplex, known as the permutation polytope, and paired comparisons form another subset on the edges of the simplex. Distances between point masses form the basic tool of analysis. The paper gives some history of major concepts, which naturally leads to a new concept: the shadow point. It is then shown how loglinear models, Luce and Rasch models, unfolding models, correspondence analysis and homogeneity analysis, forced classification and classification trees, as well as other models and methods, fit into this particular geometrical framework.     

Définir ou détecter des pathologies ? Utilisation et interprétation des scores seuils à la lumière du débat dimensions/catégories

A number of psychometric tests are aimed at locating the performance of an individual along a continuous range that goes from normal to worrying. In a different paradigm, there are tests whose goal is to assess whether or not an individual is healthy with respect to a psychological, psychiatric or neurological pathology that is defined independently from the test itself. The former rely on a dimensional concept of psychopathologies; the latter imply a categorical concept. The former require to compare the performance of the individual to a standard sample that is representative of the general population; the latter involve a standard sample representative of the healthy population only. The former might imply the use of a cut-off score to indicate that a certain degree of rarity of the performance has been reached, while the latter must involve a cut-off score to make a decision (whether the individual belongs to the “healthy” or “pathological” category), a score that is most often set so as to control the false-positive rate in making this decision. In the former paradigm, the cut-off score defines or contributes to define the pathology. In the latter, it only helps detecting it. This article aims at making clear the difference between these two realms and highlight their practical as well as theoretical impact on psychological practice.     

Cue effects on memory for location when navigating spatial displays

Participants maneuvered a rat image through a circular region on the computer screen to find a hidden target platform, blending aspects of two well-known spatial tasks. Like the Morris water maze task, participants first experienced a series of learning trials before having to navigate to the hidden target platform from different locations and orientations. Like the dot-location task, they determined the location of a position within a two-dimensional circular region. This procedure provided a way to examine how the number of surrounding cues (1, 2, or 3) affects the memory for spatial location in navigation. Memory performance was better when there were more cues and when targets were close to cues, consistent with the idea that cues bolster fine-grain memory, especially in proximal regions. Early and late measures of bias in memory reflected biases in a direction toward the nearest cue, implicating a cue-based category structure of the navigational space. Collectively, results suggest cue-based spatial memory representations that have been inferred from the dot-location task generalize to a navigation task within a simple, computer-based environment, as demonstrated by the good fits of the spatial model developed for the dot-location task ( Fitting, Wedell, & Allen, 2005, 2007 ).     

Categorical invariance and structural complexity in human concept learning

An alternative account of human concept learning based on an invariance measure of the categorical stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or size. To do this we introduce a mathematical framework based on the notion of a Boolean differential operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the category in respect to its dimensions. Using this framework, we propose that the structural complexity of a Boolean category is indirectly proportional to its degree of categorical invariance and directly proportional to its cardinality or size. Consequently, complexity and invariance notions are formally unified to account for concept learning difficulty. Beyond developing the above unifying mathematical framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of the SHJ [Shepard, R. N., Hovland, C. L., & Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the degree of learning difficulty of a large class of categories (in particular, the 41 category types studied by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature, 407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g., cognitively tractable).     

Speech perception deficits by Chinese children with phonological dyslexia

Findings concerning the relation between dyslexia and speech perception deficits are inconsistent in the literature. This study examined the relation in Chinese children using a more homogeneous sample—children with phonological dyslexia. Two experimental tasks were administered to a group of Chinese children with phonological dyslexia, a group of age-matched control children, and a group of adults. In addition to a categorical perception task, a selective adaptation task was carried out. The results indicated that Chinese children with phonological dyslexia were less consistent than both the child and adult control groups in identifying stimuli within a given phonetic category. Furthermore, they did not show any significant adaptation effects in the selective adaptation task even when the adapting stimulus was identical to an endpoint stimulus in the test continuum. It seems that children with phonological dyslexia have a general deficiency in representing and processing speech stimuli.     

Nature versus nurture: The simple contrast

We respond to the commentary of Franklin, Wright, and Davies (Journal of Experimental Child Psychology,102, 239-245 [2009]) by returning to the simple contrast between nature and nurture. We find no evidence from the toddler data that makes us revise our ideas that color categories are learned and never innate.     

Macaque monkeys discriminate pitch relationships

This study demonstrates that non-human primates can categorize the direction of the pitch change of tones in a sequence. Two Macaca fascicularis were trained in a positive-reinforcement behavioral paradigm in which they listened to sequences of a variable number of different acoustic items. The training of discriminating pitch direction was divided into three phases with increasing task complexity. In the first two phases, subjects learned to employ a same/different rule. In phase 1, they discriminated acoustic items of different sound quality. Subjects had to respond when there was a change from repeating noise bursts to repeating click trains or vice versa. In phase II, acoustic items differed along one physical dimension only. Subjects had to respond to a change of the frequency of a repeating series of pure tones. In phase III, sequences consisted of three series of repeating tones of different frequency. Subjects were required to respond when the frequency of the tones changed in a downward direction and to refrain from responding when the frequency remained constant or increased. After several ten thousand trials, subjects categorized pitch direction well above chance level. The discrimination was performed over a 4.5-octave range of frequencies and was largely independent of the temporal and ordinal position of the downward pitch direction within the sequence. These results demonstrate that monkeys can recognize pitch relationships and thus that monkeys have the concept of ordinal relations between acoustic items.     

The nature of infant color categorization: evidence from eye movements on a target detection task

Infants respond categorically to color. However, the nature of infants' categorical responding to color is unclear. The current study investigated two issues. First, is infants' categorical responding more absolute than adults' categorical responding? That is, can infants discriminate two stimuli from the same color category? Second, is color categorization in infants truly perceptual? Color categorization was tested by recording adults' and infants' eye movements on a target detection task. In Experiment 1, adults were faster at fixating a colored target when it was presented on a colored background from a different color category (between-category) than when it was presented on a colored background from the same color category (within-category), even when within- and between-category chromatic differences were equated in CIE (Committee International d'Eclairage) color space. This category effect was found for two chromatic separation sizes. In Experiment 2, 4-month-olds also responded categorically on the task. Infants were able to fixate the target when the background color was from the same category. However, as with adults, infants were faster at fixating the target when the target background chromatic difference was between-category than when it was within-category. This implies that infant color categorization, like adult color categorization, is truly perceptual.     

Categorical perception of familiar objects

We report three experiments where the categorical perception of familiar, three-dimensional objects was investigated. A continuum of shape change between 15 pairs of objects was created and the images along the continuum were used as stimuli. In Experiment 1 participants were first required to discriminate pairs of images of objects that lay along the shape continuum. Then participants were asked to classify each morph-image into one of two pre-specified classes. We found evidence for categorical perception in some but not all of our object pairs. In Experiment 2 we varied the viewpoint of the objects in the discrimination task and found that effects of categorical perception generalized across changes in view. In Experiment 3 similarity ratings for each object pair were collected. These similarity scores correlated with the degree of perceptual categorization found for the object pairs. Our findings suggest that some familiar objects are perceived categorically and that categorical perception is closely tied to inter-object perceptual similarity.