Spectral methods have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (i.e., item-item similarity) matrix to reveal low dimensional structure in high dimensional data. The most popular manifold learning algorithms include Locally Linear Embedding, Isomap, and Laplacian Eigenmap...

Spectral methods have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (i.e., item-item similarity) matrix to reveal low dimensional structure in high dimensional data. The most popular manifold learning algorithms include Locally Linear Embedding, Isomap, and Laplacian Eigenmap...

This paper describes a novel appearance based scheme for extraction and representation of video objects. The tracking algorithm used for video object extraction is based upon a new eigen-space update scheme. We propose a scheme for organisation of video objects in an appearance based hierarchy. Appearance based hierarchy is constructed using a new SVD based eigen-space merging algorithm. The hi...

In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages. Ke...

A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of du-ality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians coincide with the eigen-functions of Hamiltonians of the original model. We explain that this duality can be considered as duality bet...