A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1

A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors. The behavior of several of these estimators is investigated by a simulation study. Finally, the use of empirical influence functions is illustrated by a real data example.

We propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes. The system employs higher order autocorrelation features of scale space data which permit linear classification. An optimal linear classification method is presented, which is able to cope with a large number of classes represented by many, as well as very few samples. In the course of the analysis of our system, we examine which numerical methods for feature transformation and classification show sufficient stability to fulfill these demands. The implementation has been extensively tested. We present the results of our own application and several classification benchmarks. Image recognition Face recognition Scale invariancy Scale space Higher order autocorrelation Optimal linear classification 1. INTRODUCTION The task of visual recognition which was defined by Marr (1) with the question: "What objects are where in the environment?" is still ...

An efficient method for increasing the generalization capacity of neural character recognition is presented. The network uses a biologically inspired architecture for feature extraction and character classification. The numerical methods used are, however, optimized for use on massively parallel array processors. The method for training set construction, when applied to handwritten digit recognition, yielded a writer-independent recognition rate of 92%. The activation strength produced by network recognition is an effective statistical confidence measure of the accuracy of recognition. A method of using the activation strength for reclassification is described which when applied to handwritten digit recognition reduced substitutional errors to 2.2%. 1.0 Introduction This paper uses a three part method for writer-independent digit recognition. First, character images are used to calculate least squares optimized Gabor components. For the digit recognition problem, 32 Gabor basis funct...

this paper draw heavily on materials in chapters 3 and 4 of Sargent's Bounded Rationality in Macroeconomics, Oxford University Press, 1993. 2 Neural Networks for Encoding and Adapting in Dynamic Economies Neural Networks for Encoding and Adapting in Dynamic Economies Introduction

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis, The plot of structure correlations is shown to be optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biptots may be interpreted. Key words: biplot, canonical correlation analysis, canonical weight, interbattery factor analy-sis, partial analysis, redundancy analysis, regression coefficient, reduced rank regression, struc-ture correlations.

In the Bayesian factor analysis model (Press & Shigemasu, 1989), the sample size was assumed to be large enough to estimate the overall population mean by the sample mean. In this paper, the procedure of estimating the population mean by the sample mean is compared to estimating it along with the other parameters both by Gibbs sampling and Iterated Conditional Modes. Results show that even in small samples, the Gibbs sampling and iterated conditional modes estimates of the mean are for practical purposes iden- tical to the sample mean. Thus, the population mean is adequately estimated by its sample value.

Creating long animation sequences with non-trivial repetitions is a time consuming and often difficult task. This is true for 2D images and even more true for 3D sequences. Based upon the idea of video textures we propose a simple algorithm to create new user controlled animation sequences based only on a few key frames by the analysis of velocity and position coherence. The simplicity of the method is achieved by carrying out the calculations on the main principal components of the reference animation, hence reducing the dimensionality of the input data. This also leads to significant compression. Smooth animations are ensured, using one of the proposed blending schemes. 1

In the Bayesian factor analysis model (Press & Shigemasu, 1989), available knowledge regarding the model parameters is incorporated in the form of prior distributions. This has the added consequence of eliminating the ambiguity of rotation found in the traditional factor analysis model. In the model presented by Press and Shigemasu, a vague prior distribution was implicitly specified for the population mean. The sample size was assumed to be large enough to estimate the overall population mean by the sample mean. In this paper, available prior knowledge regarding the population mean is incorporated into the inferences in the form of a prior distribution. The population mean is estimated along with the other parameters by both Gibbs sampling and Iterated Conditional Modes. 1 Introduction A factor analysis is performed to explain the relationship among a set of observed variables in terms of a smaller number of unobserved variables or latent factors which underlie the observations. This...

We propose a new method for analyzing factor analysis models using a Bayesian approach. Normal theory is used for the sampling distribution, and we adopt a model with a full disturbance covariance matrix. Using vague and natural conjugate priors for the parameters, we find that the marginal posterior distribution of the factor scores is approximately a matrix T-distribution, in large samples. This explicit result permits simple interval estimation and hypothesis testing of the factor scores. Explicit point and interval estimators of the factor score elements, in large samples, are obtained as means as means of the respective marginal posterior distributions. Factor loadings are estimated as joint modes (with factor scores), or alternatively as means or modes of the distribution of the factor loadings conditional upon the estimated factor scores. Disturbance variances and covariances are estimated conditional upon the estimated factor scores and factor loadings. This revision includes the correction of some typographical errors and some revised computations, plus an appendix that provides some intermediate results. 1