Diffusions for global optimizations
SIAM Journal on Control and Optimization
The cortex transform: rapid computation of simulated neural images
Computer Vision, Graphics, and Image Processing
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
What is the goal of sensory coding?
Neural Computation
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
The nature of statistical learning theory
The nature of statistical learning theory
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Natural gradient works efficiently in learning
Neural Computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Performance evaluation in content-based image retrieval: overview and proposals
Pattern Recognition Letters - Special issue on image/video indexing and retrieval
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
An Information-Theoretic Approach to Neural Computing
An Information-Theoretic Approach to Neural Computing
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Optimal Linear Representations of Images for Object Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
A Theory for Learning by Weight Flow on Stiefel-Grassman Manifold
Neural Computation
Journal of Cognitive Neuroscience
A Bayesian approach to geometric subspace estimation
IEEE Transactions on Signal Processing
Shiftable multiscale transforms
IEEE Transactions on Information Theory - Part 2
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
A theory for learning based on rigid bodies dynamics
IEEE Transactions on Neural Networks
Face recognition by independent component analysis
IEEE Transactions on Neural Networks
Two-stage optimal component analysis
Computer Vision and Image Understanding
Stochastic orthogonal and nonorthogonal subspace basis pursuit
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Statistical Methods and Models for Video-Based Tracking, Modeling, and Recognition
Foundations and Trends in Signal Processing
Optimal linear projections for enhancing desired data statistics
Statistics and Computing
Nearest-neighbor search algorithms on non-Euclidean manifolds for computer vision applications
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Kernel methods for nonlinear discriminative data analysis
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Image and Vision Computing
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Simplicity and efficiency of linear transformations make them a popular tool for extracting features and reducing dimension before or during statistical analysis of large datasets. Examples of their applications include image compression and reconstruction, discriminant analysis, pattern classification, and image or text retrieval. Linear transformations with natural orthogonality constraints can be represented as elements of Stiefel and Grassmann manifolds. We advocate that the choice of a transformation for dimension reduction is not standard; it is dictated by the application and the data set, and can be formulated as an optimization problem on these above-mentioned manifolds. We demonstrate this idea by deriving dimension-reducing transformations in several applications, including image-based recognition of objects and content-based retrieval of images.