A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.

As a benchmark task, the spiral problem is well known in neural networks. Unlike previous work that emphasizes learning, we approach the problem from a generic perspective that does not involve learning. We point out that the spiral problem is intrinsically connected to the inside/outside problem. A generic solution to both problems is proposed based on oscillatory correlation using a time delay network. Our simulation results are qualitatively consistent with human performance, and we interpret human limitations in terms of synchrony and time delays, both biologically plausible. As a special case, our network without time delays can always distinguish these figures regardless of shape, position, size, and orientation.

The hierarchical representation of data has various applications in domains such as data mining, machine vision, or information retrieval. In this paper we introduce an extension of the Expectation-Maximization (EM) algorithm that learns mixture hierarchies in a computationally efficient manner. Efficiency is achieved by progressing in a bottom-up fashion, i.e. by clustering the mixture components of a given level in the hierarchy to obtain those of the level above. This cl ustering requires onl y knowledge of the mixture parameters, there being no need to resort to intermediate samples. In addition to practical applications, the algorithm allows a new interpretation of EM that makes clear the relationship with nonparametric kernel-based estimation methods, provides explicit control over the tradeoff between the bias and variance of EM estimates, and offers new insights about the behavior of deterministic annealing methods commonly used with EM to escape local minima of the likelihood.

We present a split and merge EM (SMEM) algorithm to overcome the local maximum problem in parameter estimation of finite mixture models. In the case of mixture models, non-global maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations we repeatedly perform simultaneous split and merge operations using a new criterion for efficiently selecting the split and merge candidates. We apply the proposed algorithm to the training of Gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split and merge operations to improve the likelihood of both the training data and of held-out test data. 1 INTRODUCTION Mixture density models, in particular normal mixtures, have been extensively used in the field of statistical pattern recognition [1]. Recently, more sophisticated mixture density models such as mixtures of latent variable models (e.g., probabilistic PCA or factor analysis) have been proposed to approximate the underlying data manifold [2]-[4].

SVMs have empirically been shown to give good generalization performance on a wide variety of problems. However, the use of SVMs is stilI limited to a small group of researchers. One possible reason is that training algorithms for SVMs are slow, especially for large problems. Another explanation is that SVM training algorithms are complex, subtle, and sometimes difficult to implement. This paper describes a new SVM learning algorithm that is easy to implement, often faster, and has better scaling properties than the standard SVM training algorithm. The new SVM learning algorithm is called Sequential Minimal Optimization (or SMO).

We present a probabilistic method for fusion of images produced by multiple sensors. The approach is based on an image formation model in which the sensor images are noisy, locally linear functions of an underlying, true scene. A Bayesian framework then provides for maximum likelihood or maximum a posteriori estimates of the true scene from the sensor images. Maximum likelihood estimates of the parameters of the image formation model involve (local) second order image statistics, and thus are related to local principal component analysis. We demonstrate the efficacy of the method on images from visible-band and infrared sensors. 1 Introduction Advances in sensing devices have fueled the deployment of multiple sensors in several computational vision systems [1, for example]. Using multiple sensors can increase reliability with respect to single sensor systems.

Gaussian process (GP) prediction suffers from O(n3) scaling with the data set size n. By using a finite-dimensional basis to approximate the GP predictor, the computational complexity can be reduced. We derive optimal finite-dimensional predictors under a number of assumptions, and show the superiority of these predictors over the Projected Bayes Regression method (which is asymptotically optimal). We also show how to calculate the minimal model size for a given n. The calculations are backed up by numerical experiments.

This paper describes a simple and efficient method to make template-based object classification invariant to in-plane rotations. The task is divided into two parts: orientation discrimination and classification. The key idea is to perform the orientation discrimination before the classification. This can be accomplished by hypothesizing, in turn, that the input image belongs to each class of interest. The image can then be rotated to maximize its similarity to the training images in each class (these contain the prototype object in an upright orientation). This process yields a set of images, at least one of which will have the object in an upright position. The resulting images can then be classified by models which have been trained with only upright examples. This approach has been successfully applied to two real-world vision-based tasks: rotated handwritten digit recognition and rotated face detection in cluttered scenes.

Dyadzc data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This type of data arises naturally in many application ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework of learning from dyadic data by statistical mixture models. Our approach covers different models with fiat and hierarchical latent class structures. We propose an annealed version of the standard EM algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains. 1 Introduction Over the past decade learning from data has become a highly active field of research distributed over many disciplines like pattern recognition, neural computation, statistics, machine learning, and data mining.

Structure in a visual scene can be described at many levels of granularity. At a coarse level, the scene is composed of objects; at a finer level, each object is made up of parts, and the parts of subparts. In this work, I propose a simple principle by which such hierarchical structure can be extracted from visual scenes: Regularity in the relations among different parts of an object is weaker than in the internal structure of a part. This principle can be applied recursively to define part-whole relationships among elements in a scene. The principle does not make use of object models, categories, or other sorts of higher-level knowledge; rather, part-whole relationships can be established based on the statistics of a set of sample visual scenes. I illustrate with a model that performs unsupervised decomposition of simple scenes. The model can account for the results from a human learning experiment on the ontogeny of partwhole relationships.