Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide lear...

We have investigated the role of geographical slant in simple navigation and spatial memory tasks, using a computer graphics town called \Hexatown" (Gillner & Mallot 1998). This environment was a hexagonal grid of streets with landmarks placed in each angle between two streets. The whole environment could be slanted by an angle of 4 . Three slant conditions were used: at: no slant; slanted NW: ...

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physic...

In the study of submanifolds in a homogeneous space X = G/P of a Lie group G, the method of moving frames is both a unifying concept and an effective tool, which is the version of the method of equivalence applied to submanifold geometry. Let φ be the left invariant, Lie algebra g-valued Maurer-Cartan form of G. The local equivalence problem for a submanifold f : M →֒ X is solved on a canonical ...

Many people’s handwriting exhibits various writing slant. This is one of factors greatly varying human handwriting and thus making it more difficult to recognize. This report describes experiments with slant counteraction. The writing slant is estimated on a per word basis and the way the handwriting data is “seen” by the recognizer is transformed in order to counteract the slant. This leaves t...

On an even-dimensional real submanifold of a Hermitian manifold, making use of the fundamental 2-form of the ambient manifold, we define a function. In this paper, we investigate the function in detail in some special submanifold.

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Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in several machine learning methods like semi-supervised learning, dimensionality reduction and clustering. In this paper we determine the pointwise limit of three d...

* Correspondence: meraj79@gmail. com Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia Full list of author information is available at the end of the article Abstract In this article, we have obtained necessary and sufficient conditions in terms of canonical structure F on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduced...