Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. algorithms can discover a much lower-dimensional representation (embedding) high-dimensional dataset through non-linear transformations that preserve the most important structure original data. State-of-the-art manifold directly optimise embedding without mapping between space and discovered embedde...

Knowledge transfer is computationally challenging, due in part to the curse of dimensionality, compounded by source and target domains expressed using different features (e.g., documents written in different languages). Recent work on manifold learning has shown that data collected in real-world settings often have high-dimensional representations, but lie on low-dimensional manifolds. Furtherm...

The faithful reconstruction of 3-D models from irregular and noisy point samples is a task central to many applications of computer vision and graphics. We present an approach to denoising that naturally handles intersections of manifolds, thus preserving high-frequency details without oversmoothing. This is accomplished through the use of a modified locally weighted regression algorithm that m...

It is well known that the sphere $S^6(1)$ admits an almost complex structure $J$ which nearly K\"{a}hler. A submanifold $M$ of Hermitian manifold called a CR if it differentiable distribution $\mathcal{D}_1$ such its orthogonal complement totally real distribution. In this case normal bundle also splits into two distributions $\mathcal{D}_3$, complex, and complement. proper three-dimensional si...

in this paper, we are going to study the g-natural metrics on the tangent bundle of finslermanifolds. we concentrate on the complex and kählerian and hermitian structures associated with finslermanifolds via g-natural metrics. we prove that the almost complex structure induced by this metric is acomplex structure on tangent bundle if and only if the finsler metric is of scalar flag curvature. t...

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎.