Ranking is the major problem in variety of applications like information retrieval (IR), Data mining (DM) and natural language processing (NLP). To rank the objects according to their importance multiplicity has also been identified as a important criterion. Manifold Ranking with Sink Points (MRSP) is one of the novel approaches to conquer this problem. This approach uses a manifold ranking pro...

This article discusses the relationship between the inertial manifolds " with delay " introduced by Debussche & Temam, and the standard definition. In particular, the " multi-valued " manifold of the same paper is shown to arise naturally from the manifolds " with delay " when considering issues of convergence as the delay time tends to infinity. This leads to a new characterisation of the mult...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

Graph-oriented methods have been widely adopted in multi-view clustering because of their efficiency learning heterogeneous relationships and complex structures hidden data. However, existing are typically investigated based on a Euclidean structure instead more suitable manifold topological structure. Hence, it is expected that will be to carry out intrinsic similarity learning. In this paper,...

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to multi-manifolds learning. In this paper, we proposed a new multi-manifolds learning algorithm (M-Isomap) with the help of a general procedure. The new algorithm preserves...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

Manifold regularization is an approach which exploits the geometry of the marginal distribution. The main goal of this paper is to analyze the convergence issues of such regularization algorithms in learning theory. We propose a more general multi-penalty framework and establish the optimal convergence rates under the general smoothness assumption. We study a theoretical analysis of the perform...

Spectral Methods. The basic idea is to assume that the data lies on a manifold/surface in D-dimensional space, see figure (1) Perform multi-dimensional scaling, or other dimension reduction method, using distances calculated on the manifold, see figure (2). Figure 1. We assume that the data lies on a manifold. This is a surface which is locally flat.