Multiway data analysis
The nature of statistical learning theory
The nature of statistical learning theory
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
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
Advances in Large Margin Classifiers
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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
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
Discriminant Analysis with Tensor Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
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ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
SVM-KNN: Discriminative Nearest Neighbor Classification for Visual Category Recognition
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
New Least Squares Support Vector Machines Based on Matrix Patterns
Neural Processing Letters
Knowledge and Information Systems
General Tensor Discriminant Analysis and Gabor Features for Gait Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Extracting the optimal dimensionality for local tensor discriminant analysis
Pattern Recognition
Unified discriminative subspace learning for multimodality image analysis
Unified discriminative subspace learning for multimodality image analysis
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Visual tracking and recognition using probabilistic appearance manifolds
Computer Vision and Image Understanding
IEEE Transactions on Neural Networks
Discriminant Locally Linear Embedding With High-Order Tensor Data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Nearest neighbor pattern classification
IEEE Transactions on Information Theory
Locality Versus Globality: Query-Driven Localized Linear Models for Facial Image Computing
IEEE Transactions on Circuits and Systems for Video Technology
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
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In the past decades, maximum margin classifiers have been recognized as a powerful tool for pattern classification problem. However, for image and video data, it is still hard to map the visual features to the semantic labels, although many maximum margin techniques have announced impressive classification results in their own datasets. The performance uncertainty of maximum margin classifiers in real world applications is mainly caused by the lack of theoretical ground for kernel projection, which unfortunately, is just the key of the performance improvement. Either the kernel space distorts the semantics of the visual space or the dataset is not linear separable in the kernel space, the classification performance cannot be guaranteed. Therefore, this paper proposes a novel Tensor-based Locally Maximum Margin Classifier (TLMMC), which avoids the kernel projection with unclear physical meaning. TLMMC employs the tensor techniques to represent the image and video data in high-order space directly, so the intrinsic structure of the data point is well preserved. To address the difficulty of seeking a linear discriminant hyperplane in the tensor space, TLMMC utilizes a set of local multilinear hyperplanes to construct a global nonlinear one. To find the optimal solution for each local hyperplane, maximum margin technique is used to minimize the generalization error in the smaller but more relevant subset of the training data. Integrating the attractive characters of tensor representation, local-based method, and maximum margin classifier, TLMMC shows impressive results in both theoretical analysis and empirical validation. Besides an effective image and video classifier, this paper also illustrates a new thought of semantics oriented classifier design, which emphasizes the model with clear physical explanation and solid theoretical support instead of performance improvement on individual learning tasks.