In this paper we introduce a new underlying probabilistic model for principal componentanalysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrainsthe mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions whichallow nonlinear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our nonlinear algorithm can be further kernelised leading to'twin kernel PCA' in which a mapping between feature spaces occurs.

While the mixture approach is intriguing, neither of [8, 9] compare their model to other methods.

Given a sentence, learning is first applied at word level to identify phrase candidates 0f the solution.

We consider situations where training data is abundant and computing resources are comparatively scarce. We argue that suitably designed online learningalgorithms asymptotically outperform any batch learning algorithm. Both theoretical and experimental evidences are presented.

The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data. The core idea of our method is to rank the data with respect to the intrinsic manifold structure collectively revealed by a great amount of data. Encouraging experimental results from synthetic, image, and text data illustrate the validity of our method.

Clustering aims at extracting hidden structure in dataset. While the problem offinding compact clusters has been widely studied in the literature, extractingarbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm whichtackles the problem by a two step procedure: first the data are transformed in such a way that elongated structures become compact ones. In a second step, these new objects are clustered by optimizing a compactness-based criterion. The advantages of the method over related approaches are threefold: (i) robustness properties of compactness-based criteria naturally transfer to the problem of extracting elongated structures, leadingto a model which is highly robust against outlier objects; (ii) the transformed distances induce a Mercer kernel which allows us to formulate a polynomial approximation scheme to the generally N P-hard clustering problem; (iii) the new method does not contain free kernel parameters in contrast to methods like spectral clustering or mean-shift clustering.

The 2-class transduction problem, as formulated by Vapnik [1], involves finding a separating hyperplane for a labelled data set that is also maximally distant from a given set of unlabelled test points. In this form, the problem has exponential computational complexity in the size of the working set. So far it has been attacked by means of integer programming techniques [2] that do not scale to reasonable problem sizes, or by local search procedures [3]. In this paper we present a relaxation of this task based on semidefinite programming(SDP), resulting in a convex optimization problem that has polynomial complexity in the size of the data set. The results are very encouraging for mid sized data sets, however the cost is still too high for large scale problems, due to the high dimensional searchspace. To this end, we restrict the feasible region by introducing an approximation based on solving an eigenproblem. With this approximation, the computational cost of the algorithm is such that problems with more than 1000 points can be treated.

A common way of image denoising is to project a noisy image to the subspace ofadmissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion.

Satellite domains are becoming a fashionable area of research within the AI community due to the complexity of the problems that satellite domains need to solve. With the current U.S. and European focus on launching satellites for communication, broadcasting, or localization tasks, among others, the automatic control of these machines becomes an important problem. Many new techniques in both the planning and scheduling fields have been applied successfully, but still much work is left to be done for reliable autonomous architectures. The purpose of this article is to present CONSAT, a real application that plans and schedules the performance of nominal operations in four satellites during the course of a year for a commercial Spanish satellite company, HISPASAT. For this task, we have used an AI domain-independent planner that solves the planning and scheduling problems in the HISPASAT domain thanks to its capability of representing and handling continuous variables, coding functions to obtain the operators' variable values, and the use of control rules to prune the search. We also abstract the approach in order to generalize it to other domains that need an integrated approach to planning and scheduling.

Cognition: The Mathematics of Mind. (CORES 2005). Stefanie Bruninghaus, University of Pittsburgh The ICCBR'05 Program Committee invites submissions of original theoretical research, Industry Day Chair: applied research and deployed application (MDAI 2005). Must have a Masters Degree in Data Mining.