It is widely believed that a dimension reduction (DR) process drops information inevitably in most practical scenarios. Thus, methods try to preserve some essential of data after DR, as well manifold based DR methods. However, they usually fail yield satisfying results, especially high-dimensional cases. In the context learning, we think good low-dimensional representation should topological an...

Multi-atlas segmentation has been widely used to segment various anatomical structures. The success of this technique partly relies on the selection of atlases that are best mapped to a new target image after registration. Recently, manifold learning has been proposed as a method for atlas selection. Each manifold learning technique seeks to optimize a unique objective function. Therefore, diff...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

In this work we present two examples of how a manifold learning model can represent the complexity of shape variation in images. Manifold learning techniques for image manifolds can be used to model data in sparse manifold regions. Additionally, they can be used as generative models as they can often better represent or learn structure in the data. We propose a method of estimating the underlyi...

In this paper, we proposed a new semi-supervised multi-manifold learning method, called semisupervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturall...

the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...