Geert De Soete

A least squares algorithm for fitting additive trees to proximity data

A least squares algorithm for fitting additive trees to proximity data is described. The algorithm uses a penalty function to enforce the four point condition on the estimated path length distances. The algorithm is evaluated in a small Monte Carlo study. Finally, an illustrative application is presented.

Perceptual scaling of synthesized musical timbres: common dimensions, specificities, and latent subject classes.

To study the perceptual structure of musical timbre and the effects of musical training, timbral dissimilarities of synthesized instrument sounds were rated by professional musicians, amateur musicians, and nonmusicians. The data were analyzed with an extended version of the multidimensional scaling algorithm CLASCAL (Winsberg & De Soete, 1993), which estimates the number of latent classes of subjects, the coordinates of each timbre on common Euclidean dimensions, a specificity value of unique attributes for each timbre, and a separate weight for each latent class on each of the common dimensions and the set of specificities. Five latent classes were found for a three-dimensional spatial model with specificities. Common dimensions were quantified psychophysically in terms of log-rise time, spectral centroid, and degree of spectral variation. The results further suggest that musical timbres possess specific attributes not accounted for by these shared perceptual dimensions. Weight patterns indicate that perceptual salience of dimensions and specificities varied across classes. A comparison of class structure with biographical factors associated with degree of musical training and activity was not clearly related to the class structure, though musicians gave more precise and coherent judgments than did nonmusicians or amateurs. The model with latent classes and specificities gave a better fit to the data and made the acoustic correlates of the common dimensions more interpretable.

A Maximum Likelihood Method for Fitting the Wandering Vector Model.

After introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data, an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed. The possibility of testing various hypotheses by means of likelihood ratio tests is discussed. Finally, the algorithm is applied to some existing data sets for illustrative purposes.

Optimal variable weighting for ultrametric and additive tree clustering

A method is developed which for a given objects by variables data matrix estimates weighted inter-object distances that are optimally suited for either an ultrametric or an additive tree representation. The effectiveness of the method is demonstrated on two synthetic data sets having a known tree structure and on one real data set. In the final section, some possible extensions of the present method are discussed.

A latent class approach to fitting the weighted euclidean model, clascal

A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.

The Estimation of Ultrametric and Path Length Trees from Rectangular Proximity Data

A least-squares algorithm for fitting ultrametric and path length or additive trees to two-way, two-mode proximity data is presented. The algorithm utilizes a penalty function to enforce the ultrametric inequality generalized for asymmetric, and generally rectangular (rather than square) proximity matrices in estimating an ultrametric tree. This stage is used in an alternating least-squares fashion with closed-form formulas for estimating path length constants for deriving path length trees. The algorithm is evaluated via two Monte Carlo studies. Examples of fitting ultrametric and path length trees are presented.

Optimal variable weighting for hierarchical clustering: An alternating least-squares algorithm

This paper presents the development of a new methodology which simultaneously estimates in a least-squares fashion both an ultrametric tree and respective variable weightings for profile data that have been converted into (weighted) Euclidean distances. We first review the relevant classification literature on this topic. The new methodology is presented including the alternating least-squares algorithm used to estimate the parameters. The method is applied to a synthetic data set with known structure as a test of its operation. An application of this new methodology to ethnic group rating data is also discussed. Finally, extensions of the procedure to model additive, multiple, and three-way trees are mentioned.

Subjective complaints versus neuropsychological test performance after cardiopulmonary bypass.

The study by Newman et al. (Journal of Psychosomatic Research, 1989) compared subjective reports of cognition with assessed cognitive performance in patients one year after coronary artery bypass surgery. The current study reinvestigated this relation in a larger and more heterogeneous group--90 cardiac patients six months after cardiopulmonary bypass--using a more extensive checklist of subjective complaints and different neuropsychological tests. In agreement with previous research, the patients who reported complaints in specific cognitive areas were not found to have impaired cognitive functions as assessed with appropriate neuropsychological tests. The patients who reported deterioration in cognition after surgery were found to have higher levels of depression and state anxiety. These differences were significant for almost all evaluated cognitive functions. An alternative explanation of the relationship between mood and cognitive complaints based on personality traits, i.e., neuroticism, is offered.

A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix

A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix is developed. The algorithm is evaluated in a Monte Carlo study in which error-perturbed randomly generated ultrametric distances were analyzed. Finally, an illustrative application is presented.

On the Use of Hierarchical Clustering for the Analysis of Nonsymmetric Proximities

Rao and Sabavala (1981) recently proposed a hierarchical clustering methodology applied to normalized brand switching matrices to assess competitive market structure. We introduce a recently developed clustering method that appears to be more suited to the analysis of such nonsymmetric data, and describe an application and comparison of the various approaches.