SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Matrix computations (3rd ed.)
Dimensionality reduction for similarity searching in dynamic databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
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
Generalized low rank approximations of matrices
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Generalized low rank approximations of matrices
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A non-linear dimensionality-reduction technique for fast similarity search in large databases
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps
Proceedings of the 24th international conference on Machine learning
A Tensor Approximation Approach to Dimensionality Reduction
International Journal of Computer Vision
Motion segmentation using GPCA techniques and optical flow
EATIS '07 Proceedings of the 2007 Euro American conference on Telematics and information systems
Uncorrelated multilinear principal component analysis through successive variance maximization
Proceedings of the 25th international conference on Machine learning
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Pattern Recognition
Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning
IEEE Transactions on Neural Networks
Distinguishing variance embedding
Image and Vision Computing
A prediction error compression method with tensor-PCA in video coding
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Incremental Tensor Subspace Learning and Its Applications to Foreground Segmentation and Tracking
International Journal of Computer Vision
A survey of multilinear subspace learning for tensor data
Pattern Recognition
Identification and tracking of robots in an intelligent space using static cameras and an XPFCP
Robotics and Autonomous 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
Who is repinning?: predicting a brand's user interactions using social media retrieval
Proceedings of the Thirteenth International Workshop on Multimedia Data Mining
Learning canonical correlations of paired tensor sets via tensor-to-vector projection
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Multi-linear neighborhood preserving projection for face recognition
Pattern Recognition
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Recent years have witnessed a dramatic increase in the quantity of image data collected, due to advances in fields such as medical imaging, reconnaissance, surveillance, astronomy, multimedia etc. With this increase has come the need to be able to store, transmit, and query large volumes of image data efficiently. A common operation on image databases is the retrieval of all images that are similar to a query image. For this, the images in the database are often represented as vectors in a high-dimensional space and a query is answered by retrieving all image vectors that are proximal to the query image in this space, under a suitable similarity metric. To overcome problems associated with high dimensionality, such as high storage and retrieval times, a dimension reduction step is usually applied to the vectors to concentrate relevant information in a small number of dimensions. Principal Component Analysis (PCA) is a well-known dimension reduction scheme. However, since it works with vectorized representations of images, PCA does not take into account the spatial locality of pixels in images. In this paper, a new dimension reduction scheme, called Generalized Principal Component Analysis (GPCA), is presented. This scheme works directly with images in their native state, as two-dimensional matrices, by projecting the images to a vector space that is the tensor product of two lower-dimensional vector spaces. Experiments on databases of face images show that, for the same amount of storage, GPCA is superior to PCA in terms of quality of the compressed images, query precision, and computational cost.