Making large-scale support vector machine learning practical
Advances in kernel methods
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Diffusion Kernels on Statistical Manifolds
The Journal of Machine Learning Research
Beyond the point cloud: from transductive to semi-supervised learning
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning from labeled and unlabeled data on a directed graph
ICML '05 Proceedings of the 22nd international conference on Machine learning
Semi-supervised learning with graphs
Semi-supervised learning with graphs
Label propagation through linear neighborhoods
ICML '06 Proceedings of the 23rd international conference on Machine learning
The Journal of Machine Learning Research
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
Regression on manifolds using kernel dimension reduction
Proceedings of the 24th international conference on Machine learning
DiffusionRank: a possible penicillin for web spamming
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
Supervised nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Neighborhood detection using mutual information for the identification of cellular automata
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
A Kernel Approach for Semisupervised Metric Learning
IEEE Transactions on Neural Networks
Semisupervised Learning Based on Generalized Point Charge Models
IEEE Transactions on Neural Networks
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Heat-diffusion models have been successfully applied to various domains such as classification and dimensionality-reduction tasks in manifold learning. One critical local approximation technique is employed to weigh the edges in the graph constructed from data points. This approximation technique is based on an implicit assumption that the data are distributed evenly. However, this assumption is not valid in most cases, so the approximation is not accurate in these cases. To solve this challenging problem, we propose a volume-based heat-diffusion model (VHDM). In VHDM, the volume is theoretically justified by handling the input data that are unevenly distributed on an unknown manifold. We also propose a novel volume-based heat-diffusion classifier (VHDC) based on VHDM. One of the advantages of VHDC is that the computational complexity is linear on the number of edges given a constructed graph. Moreover, we give an analysis on the stability of VHDC with respect to its three free parameters, and we demonstrate the connection between VHDC and some other classifiers. Experiments show that VHDC performs better than Parzen window approach, K nearest neighbor, and the HDC without volumes in prediction accuracy and outperforms some recently proposed transductive-learning algorithms. The enhanced performance of VHDC shows the validity of introducing the volume. The experiments also confirm the stability of VHDC with respect to its three free parameters.