Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Matrix computations (3rd ed.)
Latent semantic indexing: a probabilistic analysis
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Dimensionality reduction for similarity searching in dynamic databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Applications of linear algebra in information retrieval and hypertext analysis
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Concept decompositions for large sparse text data using clustering
Machine Learning
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the effects of dimensionality reduction on high dimensional similarity search
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
Incremental Singular Value Decomposition of Uncertain Data with Missing Values
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
IEEE Transactions on Knowledge and Data Engineering
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image compression using wavelet transform and multiresolution decomposition
IEEE Transactions on Image Processing
Tensor space model for document analysis
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Matrix-pattern-oriented Ho-Kashyap classifier with regularization learning
Pattern Recognition
Compression of magnetohydrodynamic simulation data using singular value decomposition
Journal of Computational Physics
A Tensor Approximation Approach to Dimensionality Reduction
International Journal of Computer Vision
Matrix-pattern-oriented least squares support vector classifier with AdaBoost
Pattern Recognition Letters
Uncorrelated multilinear principal component analysis through successive variance maximization
Proceedings of the 25th international conference on Machine learning
Heterogeneous data fusion for alzheimer's disease study
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Incremental tensor analysis: Theory and applications
ACM Transactions on Knowledge Discovery from Data (TKDD)
Probabilistic Tensor Analysis with Akaike and Bayesian Information Criteria
Neural Information Processing
Bound for the L2 Norm of Random Matrix and Succinct Matrix Approximation
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
A note on two-dimensional linear discriminant analysis
Pattern Recognition Letters
Robust Simultaneous Low Rank Approximation of Tensors
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
n-Mode Singular Vector Selection in Higher-Order Singular Value Decomposition
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Factored principal components analysis, with applications to face recognition
Statistics and Computing
A convergent solution to tensor subspace learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Two-dimensional maximum margin feature extraction for face recognition
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on cybernetics and cognitive informatics
Semi-supervised bilinear subspace learning
IEEE Transactions on Image Processing
Mode-kn factor analysis for image ensembles
IEEE Transactions on Image Processing
Independent components extraction from image matrix
Pattern Recognition Letters
Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning
IEEE Transactions on Neural Networks
IEEE Transactions on Image Processing
Generalized low-rank approximations of matrices revisited
IEEE Transactions on Neural Networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on gait analysis
Incremental Tensor Subspace Learning and Its Applications to Foreground Segmentation and Tracking
International Journal of Computer Vision
Two-dimensional random projection
Signal Processing
A survey of multilinear subspace learning for tensor data
Pattern Recognition
Matrix-variate and higher-order probabilistic projections
Data Mining and Knowledge Discovery
A new face database and evaluation of face recognition techniques
ICS'10 Proceedings of the 14th WSEAS international conference on Systems: part of the 14th WSEAS CSCC multiconference - Volume II
Common component analysis for multiple covariance matrices
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Face recognition using two-dimensional CCA and PLS
International Journal of Biometrics
Comparing and combining spatial dimension reduction methods in face verification
IDEAL'06 Proceedings of the 7th international conference on Intelligent Data Engineering and Automated Learning
Separable linear discriminant analysis
Computational Statistics & Data Analysis
Low-rank matrix decomposition in L1-norm by dynamic systems
Image and Vision Computing
Random projection ensemble learning with multiple empirical kernels
Knowledge-Based Systems
A unified view of two-dimensional principal component analyses
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Three-fold structured classifier design based on matrix pattern
Pattern Recognition
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust tensor clustering with non-greedy maximization
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The problem of computing low rank approximations of matrices is considered. The novel aspect of our approach is that the low rank approximations are on a collection of matrices. We formulate this as an optimization problem, which aims to minimize the reconstruction (approximation) error. To the best of our knowledge, the optimization problem proposed in this paper does not admit a closed form solution. We thus derive an iterative algorithm, namely GLRAM, which stands for the Generalized Low Rank Approximations of Matrices. GLRAM reduces the reconstruction error sequentially, and the resulting approximation is thus improved during successive iterations. Experimental results show that the algorithm converges rapidly.We have conducted extensive experiments on image data to evaluate the effectiveness of the proposed algorithm and compare the computed low rank approximations with those obtained from traditional Singular Value Decomposition (SVD) based methods. The comparison is based on the reconstruction error, misclassification error rate, and computation time. Results show that GLRAM is competitive with SVD for classification, while it has a much lower computation cost. However, GLRAM results in a larger reconstruction error than SVD. To further reduce the reconstruction error, we study the combination of GLRAM and SVD, namely GLRAM + SVD, where SVD is preceded by GLRAM. Results show that when using the same number of reduced dimensions, GLRAM + SVD achieves significant reduction of the reconstruction error as compared to GLRAM, while keeping the computation cost low.