Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk

The purpose of this paper is to describe the R package {PTAk and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk() is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition), as well as some other well known methods included in the R package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i)~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging) study, (ii)~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic) data for a central nervous system (CNS) drug, and (iii)~geographical information system (GIS) with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the R package PTAk also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, PTAk constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.

On the Procrustean analogue of individual differences scaling (INDSCAL)

In this paper, individual differences scaling (INDSCAL) is revisited, considering INDSCAL as being embedded within a hierarchy of individual difference scaling models. We explore the members of this family, distinguishing (i) models, (ii) the role of identification and substantive constraints, (iii) criteria for fitting models and (iv) algorithms to optimise the criteria. Model formulations may be based either on data that are in the form of proximities or on configurational matrices. In its configurational version, individual difference scaling may be formulated as a form of generalized Procrustes analysis. Algorithms are introduced for fitting the new models. An application from sensory evaluation illustrates the performance of the methods and their solutions

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

EMPATH: A Neural Network that Categorizes Facial Expressions

There are two competing theories of facial expression recognition. Some researchers have suggested that it is an example of "categorical perception." In this view, expression categories are considered to be discrete entities with sharp boundaries, and discrimination of nearby pairs of expressive faces is enhanced near those boundaries. Other researchers, however, suggest that facial expression perception is more graded and that facial expressions are best thought of as points in a continuous, low-dimensional space, where, for instance, "surprise" expressions lie between "happiness" and "fear" expressions due to their perceptual similarity. In this article, we show that a simple yet biologically plausible neural network model, trained to classify facial expressions into six basic emotions, predicts data used to support both of these theories. Without any parameter tuning, the model matches a variety of psychological data on categorization, similarity, reaction times, discrimination, and recognition difficulty, both qualitatively and quantitatively. We thus explain many of the seemingly complex psychological phenomena related to facial expression perception as natural consequences of the tasks' implementations in the brain

Optimal Scaling of Interaction Effects in Generalized Linear Models

Multiplicative interaction models, such as Goodman's RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are only suitable for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of interaction effects in generalized linear models with any number of categorical predictor variables. This model, which we call the optimal scaling of interactions (OSI) model, is a parsimonious, one-dimensional multiplicative interaction model. We discuss how the model can be used to visually interpret the interaction effects. Two empirical data sets are used to show how the results of the model can be applied and interpreted. Finally, several multidimensional extensions of the one-dimensional model are explored.