Modeling Mental Qualities

Conscious experiences are characterized by mental qualities, such as those involved in seeing red, feeling pain, or smelling cinnamon. The standard framework for modeling mental qualities represents them via points in geometrical spaces, where distances between points inversely correspond to degrees of phenomenal similarity. This paper argues that the standard framework is structurally inadequate and develops a new framework that is more powerful and flexible. The core problem for the standard framework is that it cannot capture precision structure: for example, consider the phenomenal contrast between seeing an object as crimson in foveal vision versus merely as red in peripheral vision. The solution I favor is to model mental qualities using regions, rather than points. I explain how this seemingly simple formal innovation not only provides a natural way of modeling precision, but also yields a variety of further theoretical fruits: it enables us to formulate novel hypotheses about the space and structures of mental qualities, formally differentiate two dimensions of phenomenal similarity, generate a quantitative model of the phenomenal sorites, and define a measure of discriminatory grain. A noteworthy consequence is that the structure of the mental qualities of conscious experiences is fundamentally different from the structure of the perceptible qualities of external objects

Generalization of form in visual pattern classification.

Human observers were trained to criterion in classifying compound Gabor signals with sym- metry relationships, and were then tested with each of 18 blob-only versions of the learning set. General- ization to dark-only and light-only blob versions of the learning signals, as well as to dark-and-light blob versions was found to be excellent, thus implying virtually perfect generalization of the ability to classify mirror-image signals. The hypothesis that the learning signals are internally represented in terms of a 'blob code' with explicit labelling of contrast polarities was tested by predicting observed generalization behaviour in terms of various types of signal representations (pixelwise, Laplacian pyramid, curvature pyramid, ON/OFF, local maxima of Laplacian and curvature operators) and a minimum-distance rule. Most representations could explain generalization for dark-only and light-only blob patterns but not for the high-thresholded versions thereof. This led to the proposal of a structure-oriented blob-code. Whether such a code could be used in conjunction with simple classifiers or should be transformed into a propo- sitional scheme of representation operated upon by a rule-based classification process remains an open question

On the adequacy of current empirical evaluations of formal models of categorization

Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts. Progress in assessing the relative adequacy of formal categorization models has, to date, been limited because (a) formal model comparisons are narrow in the number of models and phenomena considered and (b) models do not often clearly define their explanatory scope. Progress is further hampered by the practice of fitting models with arbitrarily variable parameters to each data set independently. Reviewing examples of good practice in the literature, we conclude that model comparisons are most fruitful when relative adequacy is assessed by comparing well-defined models on the basis of the number and proportion of irreversible, ordinal, penetrable successes (principles of minimal flexibility, breadth, good-enough precision, maximal simplicity, and psychological focus)

Measuring category intuitiveness in unconstrained categorization tasks

What makes a category seem natural or intuitive? In this paper, an unsupervised categorization task was employed to examine observer agreement concerning the categorization of nine different stimulus sets. The stimulus sets were designed to capture different intuitions about classification structure. The main empirical index of category intuitiveness was the frequency of the preferred classification, for different stimulus sets. With 169 participants, and a within participants design, with some stimulus sets the most frequent classification was produced over 50 times and with others not more than two or three times. The main empirical finding was that cluster tightness was more important in determining category intuitiveness, than cluster separation. The results were considered in relation to the following models of unsupervised categorization: DIVA, the rational model, the simplicity model, SUSTAIN, an Unsupervised version of the Generalized Context Model (UGCM), and a simple geometric model based on similarity. DIVA, the geometric approach, SUSTAIN, and the UGCM provided good, though not perfect, fits. Overall, the present work highlights several theoretical and practical issues regarding unsupervised categorization and reveals weaknesses in some of the corresponding formal models

Nonmetric Unfolding of Marketing Data: Degeneracy and Stability

Nonmetric unfolding is a powerful (nonparametric) analytical tool generating a preference-based joint display of subjects (e.g., customers) and objects (e.g., brands or products). Systematic patterns in customers’ preferences can be directly inferred from this display, and may provide valuable input for making important marketing decisions such as deciding what new product to launch. Unfortunately, nonmetric unfolding frequently produces degenerate unfolding solutions (i.e., unfolding solutions showing close-to-perfect model fit irrespective of the data analyzed). As a degenerated display shows ill-positioned customers and brands/products, the chance of making an incorrect marketing decision (e.g., launching the wrong product) is very high. To solve this problem adequately, we combine bootstrapping with penalized nonmetric unfolding (Prefscal) to obtain an accurate, nondegenerate and stable unfolding solution