A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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SIAM Journal on Matrix Analysis and Applications
A Database for Handwritten Text Recognition Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
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On the Euclidean Distance of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neighborhood Preserving Embedding
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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General Tensor Discriminant Analysis and Gabor Features for Gait Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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Tensor distance based multilinear multidimensional scaling for image and video analysis
MM '09 Proceedings of the 17th ACM international conference on Multimedia
Visual tracking and recognition using probabilistic appearance manifolds
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IEEE Transactions on Audio, Speech, and Language Processing
A new implementation of common matrix approach using third-order tensors for face recognition
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A visualization metric for dimensionality reduction
Expert Systems with Applications: An International Journal
On image matrix based feature extraction algorithms
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Considerations of sample and feature size
IEEE Transactions on Information Theory
Multilinear Discriminant Analysis for Face Recognition
IEEE Transactions on Image Processing
Image Classification Using Correlation Tensor Analysis
IEEE Transactions on Image Processing
Reconstruction and Recognition of Tensor-Based Objects With Concurrent Subspaces Analysis
IEEE Transactions on Circuits and Systems for Video Technology
Face Image Modeling by Multilinear Subspace Analysis With Missing Values
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Image and video classification tasks often suffer from the problem of high-dimensional feature space. How to discover the meaningful, low-dimensional representations of such high-order, high-dimensional observations remains a fundamental challenge. In this paper, we present a unified framework for tensor based dimensionality reduction including a new tensor distance (TD) metric and a novel multilinear globality preserving embedding (MGPE) strategy. Different with the traditional Euclidean distance, which is constrained by orthogonality assumption, TD measures the distance between data points by considering the relationships among different coordinates of high-order data. To preserve the natural tensor structure in low-dimensional space, MGPE directly works on the high-order form of input data and employs an iterative strategy to learn the transformation matrices. To provide faithful global representation for datasets, MGPE intends to preserve the distances between all pairs of data points. According to the proposed TD metric and MGPE strategy, we further derive two algorithms dubbed tensor distance based multilinear multidimensional scaling (TD-MMDS) and tensor distance based multilinear isometric embedding (TD-MIE). TD-MMDS finds the transformation matrices by keeping the TDs between all pairs of input data in the embedded space, while TD-MIE intends to preserve all pairwise distances calculated according to TDs along shortest paths in the neighborhood graph. By integrating tensor distance into tensor based embedding, TD-MMDS and TD-MIE perform tensor based dimensionality reduction through the whole learning procedure and achieve obvious performance improvement on various standard datasets.