Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Reflectance and texture of real-world surfaces
ACM Transactions on Graphics (TOG)
The FERET Evaluation Methodology for Face-Recognition Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
M-tree: An Efficient Access Method for Similarity Search in Metric Spaces
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Similarity Search in High Dimensions via Hashing
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
On Approximate Nearest Neighbors in Non-Euclidean Spaces
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Gabor-Based Kernel PCA with Fractional Power Polynomial Models for Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Covariance Tracking using Model Update Based on Lie Algebra
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
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
Online dictionary learning for sparse coding
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Scalable large-margin Mahalanobis distance metric learning
IEEE Transactions on Neural Networks
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Tensor sparse coding for region covariances
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
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
Human action recognition under log-euclidean riemannian metric
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Gabor-Based Region Covariance Matrices for Face Recognition
IEEE Transactions on Circuits and Systems for Video Technology
Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Unsupervised learning of functional network dynamics in resting state fMRI
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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We introduce Generalized Dictionary Learning (GDL), a simple but practical framework for learning dictionaries over the manifold of positive definite matrices. We illustrate GDL by applying it to Nearest Neighbor (NN) retrieval, a task of fundamental importance in disciplines such as machine learning and computer vision. GDL distinguishes itself from traditional dictionary learning approaches by explicitly taking into account the manifold structure of the data. In particular, GDL allows performing "sparse coding" of positive definite matrices, which enables better NN retrieval. Experiments on several covariance matrix datasets show that GDL achieves performance rivaling state-of-the-art techniques.