Ewa Skubalska-Rafajłowicz

Random Projection RBF Nets for Multidimensional Density Estimation

Random Projection RBF Nets for Multidimensional Density Estimation The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random projections as the first (additional) layer, we are able to reduce the dimensionality of input data. Bounds on the accuracy of RBF nets equipped with a random projection layer in comparison to RBF nets without dimensionality reduction are established. Finally, the results of simulations concerning multidimensional density estimation are briefly reported.

Fast k-NN classification rule using metric on space-filling curves

A fast nearest neighbor algorithm for pattern classification is proposed and tested on real data. The patterns (points in d-dimensional Euclidean space) are sorted along a space-filling curve. This way the multi-dimensional problem is compressed to the simplest case of the nearest neighbor search in one dimension. Instead of Euclidean distance a metric on space-filling curve is used. The method may be inferior or superior to the k-NN rule in multidimensional Euclidean space.

Combining Space-Filling Curves and Radial Basis Function Networks

We propose here to use a space-filling curve (SFC) as a tool to introduce a new metric in I d defined as a distance along the space-filling curve. This metric is to be used inside radial functions instead of the Euclidean or the Mahalanobis distance. This approach is equivalent to using SFC to pre-process the input data before training the RBF net. All the network tuning operations are performed in one dimension. Furthermore, we introduce a new method of computing the weights of linear output neuron, which is based on connection between RBF net and Nadaraya-Watson kernel regression estimators.

Local Correlation and Entropy Maps as Tools for Detecting Defects in Industrial Images

Local Correlation and Entropy Maps as Tools for Detecting Defects in Industrial Images The aim of this paper is to propose two methods of detecting defects in industrial products by an analysis of gray level images with low contrast between the defects and their background. An additional difficulty is the high nonuniformity of the background in different parts of the same image. The first method is based on correlating subimages with a nondefective reference subimage and searching for pixels with low correlation. To speed up calculations, correlations are replaced by a map of locally computed inner products. The second approach does not require a reference subimage and is based on estimating local entropies and searching for areas with maximum entropy. A nonparametric estimator of local entropy is also proposed, together with its realization as a bank of RBF neural networks. The performance of both methods is illustrated with an industrial image.

RBF neural network for probability density function estimation and detecting changes in multivariate processes

We propose a new radial basis function (RBF) neural network for probability density function estimation. This network is used for detecting changes in multivariate processes. The performance of the proposed model is tested in terms of the average run lengths (ARL), i.e., the average time delays of the change detection. The network allows the processing of large streams of data, memorizing only a small part of them. The advantage of the proposed approach is in the short and reliable net training phase.

Random projections and Hotelling's T2 statistics for change detection in high-dimensional data streams

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn. We examine the random projection method using artificial noisy image sequences as examples.

Clipped median and space-filling curves in image filtering

The aim of this paper is to introduce two new ingredients into the classical median filter. The first one is applicable both to smoothing signals or functions observed in random errors and its essence is in clipping of observations, which are outside a specified range. The second one is dedicated to smoothing images or multivariate functions and it is based on calculating the median from neighbours, which are placed along a space-filling curve. The reason for introducing this new tools to the median method is to make it more egde (or jump) preserving, what is confirmed by application to real images.

Clustering of data and nearest neighbors search for pattern recognition with dimensionality reduction using random projections

The dimensionality and the amount of data that need to be processed when intensive data streams are classified may occur prohibitively large. The aim of this paper is to analyze Johnson-Linden-strauss type random projections as an approach to dimensionality reduction in pattern classification based on K-nearest neighbors search. We show that in-class data clustering allows us to retain accuracy recognition rates obtained in the original high-dimensional space also after transformation to a lower dimension.

Detection and estimation translations of large images using random projections

This paper describes a technique of fast detection and estimation of translations in large image frames for image stabilization. Our approach is based on random projection methodology for reduction of image dimension which retain with prescribed accuracy and probability the squared Euclidean norm of projected vectors (images rows and columns). We formulate simple optimization problems for estimation of vertical and horizontal motions of the frame. The first one tries to find the best match between energies (squared norms) of rows (columns) of the actual projected image and the projected reference frame. The second one uses the squared Euclidean distance between the same objects. An iterative procedure based on the successive, alternate estimation of a vertical and a horizontal translation is proposed.

MAD Loss in Pattern Recognition and RBF Learning

We consider a multi-class pattern recognition problem with linearly ordered labels and a loss function, which measures absolute deviations of decisions from true classes. In the bayesian setting the optimal decision rule is shown to be the median of a posteriori class probabilities. Then, we propose three approaches to constructing an empirical decision rule, based on a learning sequence. Our starting point is the Parzen-Rosenblatt kernel density estimator. The second and the third approach are based on radial bases functions (RBF) nets estimators of class densities.