Constrained multidimensional scaling inN spaces

A gradient method is used to obtain least squares estimates of parameters of them-dimensional euclidean model simultaneously inN spaces, given the observation of all pairwise distances ofn stimuli for each space. The procedure can estimate an additive constant as well as stimulus projections and the metric of the reference axes of the configuration in each space. Each parameter in the model can be fixed to equal some a priori value, constrained to be equal to any other parameter, or free to take on any value in the parameter space. Two applications of the procedure are described.     

Perceiving the centroid of configurations on a rolling wheel

Undergraduates observed configurations of point-lights undergoing wheel-generated motions and judged how wheel-like the movement of each stimulus appeared on a 7-point scale. Viewer judgments were predicted by a metric defining the variable parameters for the motion path of each configuration’s geometric center—the centroid. The effects on judgments of eye movement and the stimulus characteristics of rotation, translation, and configuration were explored in six experiments. First, a strain operation on the dynamic stimuli did not affect the ability of the metric to predict perceptual judgments. Second, the predictive strength of the metric did not interact with the type of eye movements used in viewing the stimuli, though judged wheel-likeness was greater under pursuit vision than under static fixation. Third, variations in the extent of translation yielded little, if any, effect on observers’ judgments, nor did translation in a circular path. Finally, for stimuli having two lights extremely close together in the configuration, the metric’s predictive value was slightly lessened but only at the limits of visual acuity. Thus, within a wide range of presentation conditions, and for a wide variety of configurations, a metric that defined the variable parameters for the motion path of the centroid was an accurate predictor of observers’ judgments of goodness of perceived rotary motion.     

Dissimilarity, Quasimetric, Metric

Dissimilarity is a function that assigns to every pair of stimuli a nonnegative number vanishing if and only if two stimuli are identical, and that satisfies the following two conditions called the intrinsic uniform continuity and the chain property, respectively: it is uniformly continuous with respect to the uniformity it induces, and, given a set of stimulus chains (finite sequences of stimuli), the dissimilarity between their initial and terminal elements converges to zero if the chains’ length (the sum of the dissimilarities between their successive elements) converges to zero. The four properties axiomatizing this notion are shown to be mutually independent. Any conventional, symmetric metric is a dissimilarity function. A quasimetric (satisfying all metric axioms except for symmetry) is a dissimilarity function if and only if it is symmetric in the small. It is proposed to reserve the term metric (not necessarily symmetric) for such quasimetrics. A real-valued binary function satisfies the chain property if and only if whenever its value is sufficiently small it majorates some quasimetric and converges to zero whenever this quasimetric does. The function is a dissimilarity function if, in addition, this quasimetric is a metric with respect to which the function is uniformly continuous.     

Infants avoid 'labouring in vain' by attending more to learnable than unlearnable linguistic patterns

Every environment contains infinite potential features and correlations among features, or patterns. Detecting valid and learnable patterns in one environment is beneficial for learners because doing so lends predictability to new environments where the same or analogous patterns recur. However, some apparent correlations among features reflect spurious patterns, and attempting to learn the latter costs time and resources with no advantage to the learner. Thus, an efficient learner in a complex environment needs to devote more attention to input that reflects a real and learnable pattern than to input that reflects a spurious or ultimately unlearnable pattern. However, in order to achieve such efficiency in the absence of external feedback, learners need to have an implicit metric of their own learning progress. Do human infants have such a metric? Data from two experiments demonstrate that 17‐month‐olds attend longer to learnable vs. unlearnable linguistic grammars, taking more trials to habituate and more overall time to habituate for grammars in which a valid generalization over input stimuli can be made. These data provide the first evidence that infants have an implicit metric of their own learning progress and preferentially direct their attention to learnable aspects of their environment.     

Multidimensional Fechnerian Scaling: Perceptual Separability

A new definition of the perceptual separability of stimulus dimensions is given in terms of discrimination probabilities. Omitting technical details, stimulus dimensions are considered separable if the following two conditions are met: (a) the probability of discriminating two sufficiently close stimuli is computable from the probabilities with which one discriminates the projections of these stimuli on the coordinate axes; (b) the psychometric differential for discriminating two sufficiently close stimuli that differ in one coordinate only does not depend on the value of their matched coordinates (the psychometric differential is the difference between the probability of discriminating a comparison stimulus from a reference stimulus and the probability with which the reference is discriminated from itself). Thus defined perceptual separability is analyzed within the framework of the regular variation version of multidimensional Fechnerian scaling. The result of this analysis is that the Fechnerian metric of a stimulus space with perceptually separable dimensions has the structure of a Minkowski power metric with respect to these dimensions. The exponent of this metric equals the psychometric order of the stimulus space, or 1, whichever is greater.     

Encoding Shape and Spatial Relations: The Role of Receptive Field Size in Coordinating Complementary Representations

An effective functional architecture facilitates interactions among subsystems that are often used together. Computer simulations showed that differences in receptive field sizes can promote such organization. When input was filtered through relatively small nonoverlapping receptive fields, artificial neural net-works learned to categorize shapes relatively quickly; in contrast, when input was filtered through relatively large overlapping receptive fields, networks learned to encode specific shape exemplars or metric spatial relations relatively quickly. Moreover, when the receptive field sizes were allowed to adapt during learning, networks developed smaller receptive fields when they were trained to categorize shapes or spatial relations, and developed larger receptive fields when they were trained to encode specific exemplars or metric distances. In addition, when pairs of networks were constrained to use input from the same type of receptive fields, networks learned a task faster when they were paired with networks that were trained to perform a compatible type of task. Finally, using a novel modular architecture, networks were not preassigned a task, but rather competed to perform the different tasks. Networks with small nonover-lapping receptive fields tended to win the competition for categorical tasks whereas networks with large overlapping receptive fields tended to win the competition for exemplar/metric tasks.     

Dynamic field theory of movement preparation

A theoretical framework for understanding movement preparation is proposed. Movement parameters are represented by activation fields, distributions of activation defined over metric spaces. The fields evolve under the influence of various sources of localized input, representing information about upcoming movements. Localized patterns of activation self-stabilize through cooperative and competitive interactions within the fields. The task environment is represented by a 2nd class of fields, which preshape the movement parameter representation. The model accounts for a sizable body of empirical findings on movement initiation (continuous and graded nature of movement preparation, dependence on the metrics of the task, stimulus uncertainty effect, stimulus-response compatibility effects, Simon effect, precuing paradigm, and others) and suggests new ways of exploring the structure of motor representations.     

Pupillary dilation as a measure of attention: a quantitative system analysis

It has long been known that the pupil dilates as a consequence of attentional effort. But the function that relates attentional input to pupillary output has never been the subject of quantitative analysis. We present a system analysis of the pupillary response to attentional input. Attentional input is modeled as a string ofattentional pulses. We show that the system is linear; the effects of input pulses on the pupillary response are additive. The impulse response has essentially a gamma distribution with two free parameters. These parameters are estimated; they are fairly constant over tasks and subjects. The paper presents a method of estimating the string of attentional input pulses, given some average pupillary output. The method involves the technique of deconvolution; it can be implemented with a public-domain software package, Pupil.     

Numerical vs Cardinal Measurements in Multiattribute Decision Making: How Exact Is Enough?

Multiattribute decision making can involve consideration of both quantitative and qualitative measures of criteria attaintment. Some decision support systems (decision aids) to help multiattribute decision making quantify value functions. One of the most popular of these systems, multiattribute utility theory (MAUT), requires two types of input. Decision makers need to express the relative value of different attainment levels on each criterion, as well as express the relative importance of these criteria. Some systems (such as DECAID) require simple direct graphical input of value and criterion importance. Other systems (such as LOGICAL DECISION) use more complex means of expressing relative value. Either way, MAUT converts expressions of criterion importance into quantitative form. This study compares the relative stability of numerical results obtained through two decision support systems, DECAID and LOGICAL DECISION (LD), used in the task of evaluation of multiattribute alternatives. Additionally the relative stability of results was measured by comparison with results obtained using an ordinal method, ZAPROS. ZAPROS is a decision support system for construction of a partial order over the set of alternatives. It does not require conversion of qualitative measures into quantitative form. The relations among alternatives are close to those based on ordinal dominance. The results of experiments show that ordinal relationships between task parameters are much more stable than those obtained from quantitative measures. Results from DECAID and LD are much less coincident with each other than with results obtained through ZAPROS. Many inconsistencies were found in subject responses. It is concluded that more attention should be given to the means of testing judgment consistency, and that in some cases, attempts to solve decision tasks through more "exact" judgments of value function parameters may lead to erroneous results.     

MEASUREMENT OF THE INTENSITY OF AN UNDERLYING FIGURAL PROCESS: A methodological study

K ünnapas , T. M. Measurement of the intensity of an underlying figural process. A methodological study. Scand. J. Psychol ., 1961, 2 , 174–184.—A method is proposed for studying the intensity of the figural process underlying the well-known phenomenon of figural fluctuations. A metric model is presented according to which a measure of the intensity of the underlying process is obtained in units of dispersion. The model is illustrated by an experimental example. An equation is given which is analogous to that of the damped harmonic vibration. Four parameters are involved in this equation. A technique for determining the parameters is developed. Very good agreement between theoretical and empirical scale values demonstrates the applicability of the proposed method.     

The impossibility of incommensurable values

Many recent attacks on consequentialism and several defenses of pluralism have relied on arguments for the incommensurability of value. Such arguments have, generally, turned on empirical appeals to aspects of our everyday experience of value conflict. My intention, largely, is to bypass these arguments and turn instead to a discussion of the conceptual apparatus needed to make the claim that values are incommensurable. After delineating what it would mean for values to be incommensurable, I give an a priori argument that such is impossible. It is widely accepted that value is conceptually tied to desire. I argue that, more specifically, it is proportional to merited desire strength. This connection gives one a metric of all value if there is any such thing. This metric entails that value is a complete ordering over all states of affairs, or, in other words, that value is commensurable.     

Using dynamic field theory to rethink infant habituation

Much of what psychologists know about infant perception and cognition is based on habituation, but the process itself is still poorly understood. Here the authors offer a dynamic field model of infant visual habituation, which simulates the known features of habituation, including familiarity and novelty effects, stimulus intensity effects, and age and individual differences. The model is based on a general class of dynamic (time-based) models that integrate environmental input in varying metric dimensions to reach a single decision. Here the authors provide simulated visual input of varying strengths, distances, and durations to 2 coupled and interacting fields. The 1st represents the activation that drives "looking," and the 2nd, the inhibition that leads to "looking away," or habituation. By varying the parameters of the field, the authors simulate the time course of habituation trials and show how these dynamics can lead to different depths of habituation, which then determine how the system dishabituates. The authors use the model to simulate a set of influential experiments by R. Baillargeon (1986, 1987a, 1987b) using the well-known "drawbridge" paradigm. The dynamic field model provides a coherent explanation without invoking infant object knowledge. The authors show that small changes in model parameters can lead to qualitatively different outcomes. Because in typical infant cognition experiments, critical parameters are unknown, effects attributed to conceptual knowledge may be explained by the dynamics of habituation.     

Serial pattern complexity: irregularity and hierarchy.

In perception research, various models have been designed for the encoding of, for example, visual patterns, in order to predict the human interpretation of such patterns. Each of these encoding models provides a few coding rules to obtain codes for a pattern, each code expressing regularity and hierarchy in that pattern. Some of these models employ the minimum principle which states that the human interpretation of a pattern is reflected by the simplest code for that pattern, ie the simplest code according to a given complexity metric. In this paper a new complexity metric is proposed. This metric is based on a formal analysis of the concept of regularity. Some conclusions of this analysis are sketched. The new metric does not depend on artifacts of the coding rules. It accounts for the amounts of irregularity and hierarchy as represented in a code of a pattern, such that these two amounts can be added to determine the complexity of a code. An experiment is discussed that shows that the new metric performs significantly better than the metrics used previously. In particular, the new metric predicts more local pattern organizations than the old metrics. This implies that various local pattern organizations do not falsify the minimum principle anymore.     

A MEASUREMENT OF THE ADAPTATION OE COLOR VISION TO THE SPECTRAL ENVIRONMENT

Abstract —An exploratory factor analysis of the reflectance spectral distributions of a sample of natural and man-made objects yields a factor pattern remarkably similar to psychophysical color-matching curves. The goodness-of-fit indices from a maximum likelihood confirmatory factor model with fixed factor loadings specified by empirical trichromatic color-matching data indicate that the human visual system performs near to an optimum value for an ideal trichromatic system composed of three linear components. An unconstrained four-factor maximum likelihood model fits significantly better than a three-factor unconstrained model, suggesting that a color metric is better represented in four dimensions than in a three-dimensional space. This fourth factor can be calculated as a nonlinear interaction term between the first three factors: thus, a trichromatic input is sufficient to compute a color space of four dimensions. The visual system may exploit this nonlinear dependency in the spectral environment in order to obtain a four-dimensional color space without the biological cost of a fourth color receptor.     

MetrIntMeas a novel metric for measuring the intelligence of a swarm of cooperating agents

We propose a novel metric called MetrIntMeas (Metric for the Intelligence Measuring) for an accurate and robust measurement of the difficult problem-solving intelligence of a swarm system. The metric allows the classification if a swarm system belongs to the same class with the systems which have a specific reference intelligence value. For proving the efficiency of the proposed metric we realized a case study on a swarm system specialized in solving a NP-hard problem. As an application of the proposed metric, we present the measurement of the swarm systems’ evolution in intelligence. We gave a new definition to the intelligent evolving systems. The evolution of intelligent systems can be verified using the proposed MetrIntMeas metric.     

Apparent Distortions in Photography and the Geometry of Visual Space

In this paper I contrast the geometric structure of phenomenal visual space with that of photographic images. I argue that topologically both are two-dimensional and that both involve central projections of scenes being depicted. However, I also argue that the metric structures of the spaces differ inasmuch as two types of “apparent distortions”—marginal distortion in wide-angle photography and close-up distortions—which occur in photography do not occur in the corresponding visual experiences. In particular, I argue that the absence of marginal distortions in vision is evidence for a holistic metric of visual space that is spherical, and that the absence of close-up distortions shows that the local metric structure possesses a dynamic variable curvature which is dependent upon the distance away of objects being viewed at a given time.     

A method for obtaining an ordered metric scale

A method is presented for collecting data which will yield a scale on which the entities are ranked in preference (ordinality), the distances between the entities on the scale are ranked (ordered metric), and all combinations of the distances are ranked (higher-ordered metric). The sources drawn upon are von Neumann and Morgenstern (9), and lattice theory. An empirical example is given in which a higher-ordered metric scale is derived.I am grateful to Professor William L. Lepley (Department of Psychology) and Professor Jack R. Tessman (Department of Physics) for their critical reading of this paper. Paul Hurst and Robert Radlow participated in many discussions on the form of measurement discussed in this paper, and assisted in collecting data. I am also grateful to Professor T. C. Benton (Department of Mathematics) for certain source materials.     

多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。     

The orthogonal approximation of an oblique structure in factor analysis

A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique vectors by orthogonal vectors.Part of this research was carried out while the author was a psychometric fellow at the Educational Testing Service, Princeton, New Jersey.     

Serial position effects for tonal stimuli

Serial position effects for tones were studied in a recognition memory experiment The S was given a stimulus list consisting of several tone bursts followed by a number of test tones. Accuracy of recognition of stimulus items as a function of input position followed the classical bowed serial position curve. Memory strength was a monotonically decreasing function of position in the test list. The data were fitted with a strength theory model of memory. The fit yielded decay parameters corresponding to stimulus- and response-induced interference, which were comparable to the parameters reported for meaningful verbal material.