For manifold learning, it is assumed that high-dimensional sample/data points are on an embedded low-dimensional manifold. Usually, distances among samples are computed to represent the underlying data structure, for a specified distance measure such as the Euclidean distance or geodesic distance. For manifold learning, here we propose a metric according to the angular change along a geodesic l...

Recently, there has been much interest in spectral approaches to learning manifolds— so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the...

Several manifold learning techniques have been developed to learn, given a data, a single lower dimensional manifold providing a compact representation of the original data. However, for complex data sets containing multiple manifolds of possibly of different dimensionalities, it is unlikely that the existing manifold learning approaches can discover all the interesting lower-dimensional struct...

Multi-view representation learning attempts to learn a from multiple views and most existing methods are unsupervised. However, learned only unlabeled data may not be discriminative enough for further applications (e.g., clustering classification). For this reason, semi-supervised which could use along with the labeled multi-view need developed. Manifold information plays an important role in l...

In recent years manifold methods have attracted a considerable amount of attention in machine learning. However most algorithms in that class may be termed “manifold-motivated” as they lack any explicit theoretical guarantees. In this paper we take a step towards closing the gap between theory and practice for a class of Laplacian-based manifold methods. These methods utilize the graph Laplacia...

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in mo...

This paper investigates approaches for low dimensional speech feature transformation using manifold learning. It has recently been shown that speech sounds may exist on a low dimensional manifold nonlinearly embedded in high dimensional space. A number of techniques have been developed in recent years that attempt to discover the geometric structure of the underlying low dimensional manifold. T...