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—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a two-dimensional (2-D) surface in three-dimensional (3-D) space for gray-level images

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)

Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, series-parallel digraphs, planar st-digraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straight-line, polyline, visibility), and update the drawing in a smooth way.

Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant

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

Dynamic binary instrumentation (DBI) frameworks make it easy to build dynamic binary analysis (DBA) tools such as checkers and profilers. Much of the focus on DBI frameworks has been on performance; little attention has been paid to their capabilities. As a result, we believe the potential of DBI

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