We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning

Abstract Most current intrusion detection systems employ signature-based methods or data mining-based methods which rely on labeled training data. This training data is typically expensive to produce. We present a new geometric framework for unsupervised anomaly detection, which are algorithms

minimize f0(x)

A new context is introduced to give a formal geometric environment for the study of Impulsive Mechanics of systems with finite number of degrees of freedom. The new structures embody the usual ones of Analytical Mechanics such as tangent bundles for time independent systems and jet–bundles for time

In this paper we introduce public announcement logic in different geo-metric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the completeness of public announcement logic in those

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processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view

are difficult to analyze and visualize, and usually are converted to 0-1 memberships. In this paper, we propose a geometric framework to visualize fuzzy-clustered data. The scheme provides a geometric visualization by grouping the objects with similar cluster membership, and shows clear advantages over existing

We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate the theory of the classical r-matrix for integrable systems. In this picture the r-matrix is related to a fourth rank tensor, named the r-tensor, on the configuration space. The r-matrix itself carries one connection type

of real-scenes in the presence of noise. A statistical geometric framework is described that provides a unified approach to probabilistic scene reconstruction from sparse or even dense 3D scene structure. 1