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Principal manifolds and nonlinear dimensionality reduction via tangent space alignment

by Zhenyue Zhang, Hongyuan Zha - SIAM JOURNAL ON SCIENTIFIC COMPUTING , 2004
"... Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized ..."
Abstract - Cited by 261 (15 self) - Add to MetaCart
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized

Sufficient dimensionality reduction - a novel analysis principle

by Amir Globerson, Naftali Tishby - Proceedings of ICML'02 , 2002
"... Dimensionality reduction of empirical cooccurrence data is a fundamental problem in unsupervised learning. One principled approach to this problem is to represent the data in low dimension with minimal loss of (mutual) information contained in the original data. In this paper we introduce a novel in ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
Dimensionality reduction of empirical cooccurrence data is a fundamental problem in unsupervised learning. One principled approach to this problem is to represent the data in low dimension with minimal loss of (mutual) information contained in the original data. In this paper we introduce a novel

Coil sensitivity encoding for fast MRI. In:

by Klaas P Pruessmann , Markus Weiger , Markus B Scheidegger , Peter Boesiger - Proceedings of the ISMRM 6th Annual Meeting, , 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
Abstract - Cited by 193 (3 self) - Add to MetaCart
complementary to Fourier preparation by linear field gradients. Thus, by using multiple receiver coils in parallel scan time in Fourier imaging can be considerably reduced. The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil

Generalized nonnegative matrix approximations with Bregman divergences

by Inderjit S. Dhillon, Suvrit Sra - In: Neural Information Proc. Systems , 2005
"... Nonnegative matrix approximation (NNMA) is a recent technique for dimensionality reduction and data analysis that yields a parts based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, document clustering, face/imag ..."
Abstract - Cited by 99 (5 self) - Add to MetaCart
Nonnegative matrix approximation (NNMA) is a recent technique for dimensionality reduction and data analysis that yields a parts based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, document clustering, face

Spectral regression for dimensionality reduction

by Deng Cai, Xiaofei He, Jiawei Han , 2007
"... Spectral methods have recently emerged as a powerful tool for dimensionality reduction and man-ifold 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 pop ..."
Abstract - Cited by 17 (6 self) - Add to MetaCart
Spectral methods have recently emerged as a powerful tool for dimensionality reduction and man-ifold 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

Semi-supervised dimensionality reduction for image retrieval

by unknown authors
"... This paper proposes a novel semi-supervised dimensionality reduction learning algorithm for the ranking problem. Generally, we do not make the assumption of existence of classes and do not want to find the classification boundaries. Instead, we only assume that the data point cloud can construct a g ..."
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This paper proposes a novel semi-supervised dimensionality reduction learning algorithm for the ranking problem. Generally, we do not make the assumption of existence of classes and do not want to find the classification boundaries. Instead, we only assume that the data point cloud can construct a

Diffusion maps, spectral clustering and eigenfunctions of fokker-planck operators

by Boaz Nadler, Stéphane Lafon, Ronald R. Coifman, Ioannis G. Kevrekidis - in Advances in Neural Information Processing Systems 18 , 2005
"... This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points ..."
Abstract - Cited by 110 (14 self) - Add to MetaCart
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data

Offline Signature Verification and Identification using Dimensionality Reduction

by Rashmi B. N
"... In this paper we are proposed a novel approach to extracting the features from a hand-written off-line signature. The experiments are carried out on a user created data base. We are extracting the geometrical distance-metric features and pruned projection features. The extracted pruned projection fe ..."
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In this paper we are proposed a novel approach to extracting the features from a hand-written off-line signature. The experiments are carried out on a user created data base. We are extracting the geometrical distance-metric features and pruned projection features. The extracted pruned projection

A NOVEL APPROACH FOR HIGH DIMENSIONAL DATA CLUSTERING

by B. A Tidke, R. G Mehta, D. P Rana
"... High dimensional data clustering is the analysis of data with few to hundreds of dimensions. Large dimensions are not easy to handle and impossible in certain cases to visualize. To improve the efficiency and accuracy of clustering on high dimensions, data reduction is required as pre-processing. A ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
High dimensional data clustering is the analysis of data with few to hundreds of dimensions. Large dimensions are not easy to handle and impossible in certain cases to visualize. To improve the efficiency and accuracy of clustering on high dimensions, data reduction is required as pre-processing. A

A Tensor Approximation Approach to Dimensionality Reduction

by Hongcheng Wang, Narendra Ahuja, H. Wang, N. Ahuja
"... Abstract Dimensionality reduction has recently been extensively studied for computer vision applications. We present a novel multilinear algebra based approach to reduced dimensionality representation of multidimensional data, such as image ensembles, video sequences and volume data. Before reducing ..."
Abstract - Cited by 14 (0 self) - Add to MetaCart
Abstract Dimensionality reduction has recently been extensively studied for computer vision applications. We present a novel multilinear algebra based approach to reduced dimensionality representation of multidimensional data, such as image ensembles, video sequences and volume data. Before
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