Abstract We study projectional properties of Poisson cut-out sets E in non-Euclidean spaces. In the first Heisenbeg group \[\mathbb{H} = \mathbb{C} \times \mathbb{R}\] , endowed with Korányi metric, we show that Hausdorff dimension vertical projection \[\pi (E)\] (projection along center \[\mathbb{H}\] ) almost surely equals \[\min \{ 2,{\dim _\operatorname{H} }(E)\} \] and has non-empty interi...

We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are m...

We consider variants of Metric Temporal Logic (MTL) with the past operators S and SI . We show that these operators can be “eliminated” in the sense that for any formula in these logics containing the S and SI modalities, we can give a formula over an extended set of propositions which does not contain these past operators, and which is equivalent to the original formula modulo a projection ont...

Existing penalty-based haptic rendering approaches are based on the penetration depth estimation in strictly translational sense and cannot properly take object rotation into account. We propose a new six-degree-of-freedom (6-DOF) haptic rendering algorithm which is based on determining the closest-point projection of the inadmissible configuration onto the set of admissible configurations. Ene...

In this paper a proximal point algorithm for convex function is considered in complete CAT(0) spaces. We introduce necessary and sufficient condition the set of minimizers to be nonempty, by showing that case, iterative sequence converges strongly metric projection some onto function.

Pan-tilt cameras are widely used in surveillance networks. These cameras are often equipped with telephoto lenses to capture objects at a distance. Such a camera makes full-metric calibration more difficult since the projection with a telephoto lens is close to orthographic. This paper discusses the problems caused by pan-tilt cameras with long focal length and presents a method to improve the ...

In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic regression and the estimation of additive models. A geometrical interpretation enables us to link this iterative method with Von Neumann’s algorithm. Moreover, making...

In this paper we are proposed a novel approach to extracting the features from a hand-written off-line signature. The experiments are carried out on a user created data base. We are extracting the geometrical distance-metric features and pruned projection features. The extracted pruned projection features are huge in dimensions, it's difficult to process and analysis. To reduce the feature...

Matrices are a common form of data encountered in a wide range of real applications. How to efficiently classify this kind of data is an important research topic. In this paper, we propose a novel distance metric learning method named two dimensional large margin nearest neighbor (2DLMNN), for improving the performance of k-nearest neighbor (KNN) classifier in matrix classification. Different f...