A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
A Database for Handwritten Text Recognition Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Neighborhood Preserving Embedding
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Visual tracking and recognition using probabilistic appearance manifolds
Computer Vision and Image Understanding
Riemannian manifold learning for nonlinear dimensionality reduction
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
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In this paper, we propose a series of dimensionality reduction algorithms according to a novel neighborhood graph construction method. This paper begins with the presentation of a new manifold learning algorithm called bidirectional visible neighborhood preserving embedding (BVNPE). Similar with existing manifold techniques, BVNPE first links every data point with its k nearest neighbors (NNs). Then, we construct a reliable neighborhood graph by checking two criteria: bidirectional linkage and visible neighborhood preserving. Third, we assign the weights to each edge in this reliable graph based on the pairwise distance between data points. Finally, we compute the low-dimensional embedding, trying to preserve the manifold structure of input dataset by mapping nearby points on the manifold to nearby points in low-dimensional space. Moreover, this paper also proposes a linear BVNPE called BVNPE/L for straightforward embedding of new data, and a multilinear BVNPE called BVNPE/M, which represents the tensor structure of image and video data better. Experiments on various datasets validate the effectiveness of proposed algorithms.