In this chapter we discuss how to learn an optimal manifold presentation to regularize nonegative matrix factorization (NMF) for data representation problems. NMF, which tries to represent a nonnegative data matrix as a product of two low rank nonnegative matrices, has been a popular method for data representation due to its ability to explore the latent part-based structure of data. Recent stu...

A new manifold learning method, called nearest feature line (NFL) embedding, for face hallucination is proposed. While many manifold learning based face hallucination algorithms have been proposed in recent years, most of them apply the conventional nearest neighbour metric to derive the subspace and may not effectively characterise the geometrical information of the samples, especially when th...

Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in order to calculate similarities between image samples. But the computation cost of these approaches is very high. These methods require many training samples...

Recently manifold learning has attracted extensive interest in machine learning and related communities. This paper investigates the noise manifold learning problem, which is a key issue in applying manifold learning algorithm to practical problems. We propose a robust version of LTSA algorithm called RLTSA. The proposed RLTSA algorithm makes LTSA more robust from three aspects: firstly robust ...

A new algorithm for manifold learning is presented. Given only samples of a finite-dimensional differentiable manifold and no a priori knowledge of the manifold’s geometry or topology except for its dimension, the goal is to find a description of the manifold. The learned manifold must approximate the true manifold well, both geometrically and topologically, when the sampling density is suffici...

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...

Manifold learning methods have widely used in ordinary image processing domain. It has many advantages, depending on the different formulation of the manifold. Hyperspectral images are kind of images acquired by air-borne or space-born platforms. This paper introduces a novel manifold learning based dimension reduction (DR) method for hyperspectral classification. The purpose is to fully utiliz...