An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
A Database for Handwritten Text Recognition Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Problems of learning on manifolds
Problems of learning on manifolds
Image Categorization by Learning and Reasoning with Regions
The Journal of Machine Learning Research
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
The lack of a priori distinctions between learning algorithms
Neural Computation
Graph construction and b-matching for semi-supervised learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Graph based semi-supervised learning with sharper edges
ECML'06 Proceedings of the 17th European conference on Machine Learning
Aggregation pheromone metaphor for semi-supervised classification
Pattern Recognition
A second order cone programming approach for semi-supervised learning
Pattern Recognition
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Graph based methods are among the most active and applicable approaches studied in semi-supervised learning. The problem of neighborhood graph construction for these methods is addressed in this paper. Neighborhood graph construction plays a key role in the quality of the classification in graph based methods. Several unsupervised graph construction methods have been proposed that have addressed issues such as data noise, geometrical properties of the underlying manifold and graph hyper-parameters selection. In contrast, in order to adapt the graph construction to the given classification task, many of the recent graph construction methods take advantage of the data labels. However, these methods are not efficient since the hypothesis space of their possible neighborhood graphs is limited. In this paper, we first prove that the optimal neighborhood graph is a subgraph of a k'-NN graph for a large enough k', which is much smaller than the total number of data points. Therefore, we propose to use all the subgraphs of k'-NNs graph as the hypothesis space. In addition, we show that most of the previous supervised graph construction methods are implicitly optimizing the smoothness functional with respect to the neighborhood graph parameters. Finally, we provide an algorithm to optimize the smoothness functional with respect to the neighborhood graph in the proposed hypothesis space. Experimental results on various data sets show that the proposed graph construction algorithm mostly outperforms the popular k-NN based construction and other state-of-the-art methods.