The mortality related to cervical cancer can be substantially reduced through early detection and treatment. However, current detection techniques, such as Pap smear and colposcopy, fail to achieve a concurrently high sensitivity and specificity. In vivo fluorescence spectroscopy is a technique which quickly, noninvasively and quantitatively probes the biochemical and morphological changes that occur in precancerous tissue. RBF ensemble algorithms based on such spectra provide automated, and near realtime implementation of pre-cancer detection in the hands of nonexperts. The results are more reliable, direct and accurate than those achieved by either human experts or multivariate statistical algorithms. 1 Introduction Cervical carcinoma is the second most common cancer in women worldwide, exceeded only by breast cancer (Ramanujam et al., 1996). The mortality related to cervical cancer can be reduced if this disease is detected at the precancerous state, known as squamous intraepitheliallesion (SIL). Currently, a Pap smear is used to 982 K. Turner, N. Ramanujam, R. Richards-Kortum and J. Ghosh screen for cervical cancer {Kurman et al., 1994}. In a Pap test, a large number of cells obtained by scraping the cervical epithelium are smeared onto a slide which is then fixed and stained for cytologic examination.

Recognition of specific objects, such as recognition of a particular face, can be based on representations that are object centered, such as 3D structural models. Alternatively, a 3D object may be represented for the purpose of recognition in terms of a set of views. This latter class of models is biologically attractive because model acquisition - the learning phase - is simpler and more natural. A simple model for this strategy of object recognition was proposed by Poggio and Edelman (Poggio and Edelman, 1990). They showed that, with few views of an object used as training examples, a classification network, such as a Gaussian radial basis function network, can learn to recognize novel views of that object, in partic- 42 E. Bricolo, T. Poggio and N. Logothetis

We address statistical classifier design given a mixed training set consisting of a small labelled feature set and a (generally larger) set of unlabelled features. This situation arises, e.g., for medical images, where although training features may be plentiful, expensive expertise is required to extract their class labels. We propose a classifier structure and learning algorithm that make effective use of unlabelled data to improve performance. The learning is based on maximization of the total data likelihood, i.e. over both the labelled and unlabelled data subsets. Two distinct EM learning algorithms are proposed, differing in the EM formalism applied for unlabelled data. The classifier, based on a joint probability model for features and labels, is a "mixture of experts" structure that is equivalent to the radial basis function (RBF) classifier, but unlike RBFs, is amenable to likelihood-based training. The scope of application for the new method is greatly extended by the observation that test data, or any new data to classify, is in fact additional, unlabelled data - thus, a combined learning/classification operation - much akin to what is done in image segmentation - can be invoked whenever there is new data to classify. Experiments with data sets from the UC Irvine database demonstrate that the new learning algorithms and structure achieve substantial performance gains over alternative approaches.

Field (1994) has suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and Barlow (1989) has reasoned that such responses should emerge from an unsupervised learning algorithm that attempts to find a factorial code of independent visual features. We show here that nonlinear'infomax', when applied to an ensemble of natural scenes, produces sets of visual filters that are localised and oriented. Some of these filters are Gabor-like and resemble those produced by the sparseness-maximisation network of Olshausen & Field (1996). In addition, the outputs of these filters are as independent as possible, since the infomax network is able to perform Independent Components Analysis (ICA). We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zero-phase whitening filters (ZCA).

We present a mixture of experts (ME) approach to interpolate sparse, spatially correlated earth-science data. Kriging is an interpolation method which uses a global covariation model estimated from the data to take account of the spatial dependence in the data. Based on the close relationship between kriging and the radial basis function (RBF) network (Wan & Bone, 1996), we use a mixture of generalized RBF networks to partition the input space into statistically correlated regions and learn the local covariation model of the data in each region. Applying the ME approach to simulated and real-world data, we show that it is able to achieve good partitioning of the input space, learn the local covariation models and improve generalization.

This paper describes how the early visual process of contour organisation can be realised using the EM algorithm. The underlying computational representation is based on fine spline coverings. According to our EM approach the adjustment of spline parameters draws on an iterative weighted least-squares fitting process. The expectation step of our EM procedure computes the likelihood of the data using a mixture model defined over the set of spline coverings. These splines are limited in their spatial extent using Gaussian windowing functions.

When combining a set of learned models to form an improved estimator, the issue of redundancy or multicollinearity in the set of models must be addressed. A progression of existing approaches and their limitations with respect to the redundancy is discussed. A new approach, PCR *, based on principal components regression is proposed to address these limitations. An evaluation of the new approach on a collection of domains reveals that: 1) PCR* was the most robust combination method as the redundancy of the learned models increased, 2) redundancy could be handled without eliminating any of the learned models, and 3) the principal components of the learned models provided a continuum of "regularized" weights from which PCR * could choose.

Unsupervised learning algorithms based on convex and conic encoders are proposed. The encoders find the closest convex or conic combination of basis vectors to the input. The learning algorithms produce basis vectors that minimize the reconstruction error of the encoders. The convex algorithm develops locally linear models of the input, while the conic algorithm discovers features. Both algorithms are used to model handwritten digits and compared with vector quantization and principal component analysis.

A new regression technique based on Vapnik's concept of support vectors is introduced. We compare support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space. On the basis of these experiments, it is expected that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space.

Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion for ill-posed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs are of increasing interest. In this paper we combine two such techniques on a pattern recognition problem. The method for improving generalization performance (the "virtual support vector" method) does so by incorporating known invariances of the problem. This method achieves a drop in the error rate on 10,000 NIST test digit images of 1.4% to 1.0%.