Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Neural Network Initialization by Combined Classifiers
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
Label Propagation through Linear Neighborhoods
IEEE Transactions on Knowledge and Data Engineering
VisualRank: Applying PageRank to Large-Scale Image Search
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph construction and b-matching for semi-supervised learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Introduction to Semi-Supervised Learning
Introduction to Semi-Supervised Learning
Kernel sparse representation for image classification and face recognition
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Efficient manifold ranking for image retrieval
Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval
Noise resistant graph ranking for improved web image search
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Decoding by linear programming
IEEE Transactions on Information Theory
Adaptive Forward-Backward Greedy Algorithm for Learning Sparse Representations
IEEE Transactions on Information Theory
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In this paper, we propose a locality-constrained and sparsity-encouraged manifold fitting approach, aiming at capturing the locally sparse manifold structure into neighborhood graph construction by exploiting a principled optimization model. The proposed model formulates neighborhood graph construction as a sparse coding problem with the locality constraint, therefore achieving simultaneous neighbor selection and edge weight optimization. The core idea underlying our model is to perform a sparse manifold fitting task for each data point so that close-by points lying on the same local manifold are automatically chosen to connect and meanwhile the connection weights are acquired by simple geometric reconstruction. We term the novel neighborhood graph generated by our proposed optimization model M-Fitted Graph since such a graph stems from sparse manifold fitting. To evaluate the robustness and effectiveness of M-fitted graphs, we leverage graph-based semi-supervised learning as the testbed. Extensive experiments carried out on six benchmark datasets validate that the proposed M-fitted graph is superior to state-of-the-art neighborhood graphs in terms of classification accuracy using popular graph-based semi-supervised learning methods.