Introduction to algorithms
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Matrix algorithms
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Acquiring Linear Subspaces for Face Recognition under Variable Lighting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Neighborhood Preserving Embedding
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Sparsity preserving projections with applications to face recognition
Pattern Recognition
Biased ISOMap projections for interactive reranking
ICME'09 Proceedings of the 2009 IEEE international conference on Multimedia and Expo
Bidirectional visible neighborhood preserving embedding
Proceedings of the First International Conference on Internet Multimedia Computing and Service
Distance approximating dimension reduction of Riemannian manifolds
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Biased discriminant euclidean embedding for content-based image retrieval
IEEE Transactions on Image Processing
Biologically inspired feature manifold for scene classification
IEEE Transactions on Image Processing
Two-dimensional supervised local similarity and diversity projection
Pattern Recognition
Artificial Intelligence Review
Supervised manifold learning for image and video classification
Proceedings of the international conference on Multimedia
Decision fusion for urine particle classification in multispectral images
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Adaptively weighted subpattern-based isometric projection for face recognition
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
Structured sparse linear graph embedding
Neural Networks
Face recognition using discriminant sparsity neighborhood preserving embedding
Knowledge-Based Systems
Expert Systems with Applications: An International Journal
Joint geometry and variability for image recognition
Neurocomputing
A minimax probabilistic approach to feature transformation for multi-class data
Applied Soft Computing
Learning orthogonal projections for Isomap
Neurocomputing
Feature extraction using two-dimensional neighborhood margin and variation embedding
Computer Vision and Image Understanding
Manifold alignment preserving global geometry
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embedding, ISOMAP, and Laplacian Eigenmap. However, these algorithms are nonlinear and only provide the embedding results of training samples. In this paper, we propose a novel linear dimensionality reduction algorithm, called Isometric Projection. Isometric Projection constructs a weighted data graph where the weights are discrete approximations of the geodesic distances on the data manifold. A linear subspace is then obtained by preserving the pairwise distances. In this way, Isometric Projection can be defined everywhere. Comparing to Principal Component Analysis (PCA) which is widely used in data processing, our algorithm is more capable of discovering the intrinsic geometrical structure. Specially, PCA is optimal only when the data space is linear, while our algorithm has no such assumption and therefore can handle more complex data space. Experimental results on two real life data sets illustrate the effectiveness of the proposed method.