Manifold learning is a novel approach in non-linear dimensionality reduction that has shown great potential in numerous applications and has gained ground compared to linear techniques. In addition, sparse representations have been recently applied on computer vision problems with success, demonstrating promising results with respect to robustness in challenging scenarios. A key concept shared ...

Due to the physiological constraints of articulatory motion the speech apparatus has limited degrees of freedom. As a result, the range of speech sounds a human is capable of producing may lie on a low dimensional submanifold of the high dimensional space of all possible sounds. In this study a number of manifold learning algorithms are applied to speech data in an effort to extract useful low ...

Traditional manifold learning algorithms often bear an assumption that the local neighborhood of any point on embedded manifold is roughly equal to the tangent space at that point without considering the curvature. The curvature indifferent way of manifold processing often makes traditional dimension reduction poorly neighborhood preserving. To overcome this drawback we propose a new algorithm ...

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.

The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning perspective, the resulting structure, an atlas of a manifold, may be viewed as a combination of dimensionality reduction and “fuzzy” clustering.

High-dimensional datasets are well-approximated by low-dimensional structures. Over the past decade, this empirical observation motivated the investigation of detection, measurement, and modeling techniques to exploit these low-dimensional intrinsic structures, yielding numerous implications for high-dimensional statistics, machine learning, and signal processing. Manifold learning (where the l...

Modeling training data is a fundamental problem in machine learning. In this thesis, we put together the two most powerful data modeling techniques, namely manifold learning and statistical modeling, so that the combined method will benefit from the advantages of both approaches. Based on our relevant previous works, this thesis proposed a theoretical framework in terms of backgrounds on Rieman...