Trace Inference, Curvature Consistency, and Curve Detection
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The nature of statistical learning theory
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Inferring global perceptual contours from local features
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Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data
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Intrinsic Dimensionality Estimation With Optimally Topology Preserving Maps
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A neural model of contour integration in the primary visual cortex
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An optimal algorithm for approximate nearest neighbor searching fixed dimensions
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Nonlinear component analysis as a kernel eigenvalue problem
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Inference of Integrated Surface, Curve, and Junction Descriptions From Sparse 3D Data
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N-Dimensional Tensor Voting and Application to Epipolar Geometry Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
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Sparse on-line Gaussian processes
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Locally Weighted Projection Regression: Incremental Real Time Learning in High Dimensional Space
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Laplacian Eigenmaps for dimensionality reduction and data representation
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SVMTorch: support vector machines for large-scale regression problems
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Sparse bayesian learning and the relevance vector machine
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Think globally, fit locally: unsupervised learning of low dimensional manifolds
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Learning a kernel matrix for nonlinear dimensionality reduction
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Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
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Unsupervised Learning of Image Manifolds by Semidefinite Programming
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Bayesian regression with input noise for high dimensional data
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Non-isometric manifold learning: analysis and an algorithm
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IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Unsupervised learning of image manifolds by semidefinite programming
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Nonrigid embeddings for dimensionality reduction
ECML'05 Proceedings of the 16th European conference on Machine Learning
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
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The shape of fuzzy sets in adaptive function approximation
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Bayesian support vector regression using a unified loss function
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On global-local artificial neural networks for function approximation
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Minimum neighbor distance estimators of intrinsic dimension
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IDEA: intrinsic dimension estimation algorithm
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Computers and Graphics
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We address instance-based learning from a perceptual organization standpoint and present methods for dimensionality estimation, manifold learning and function approximation. Under our approach, manifolds in high-dimensional spaces are inferred by estimating geometric relationships among the input instances. Unlike conventional manifold learning, we do not perform dimensionality reduction, but instead perform all operations in the original input space. For this purpose we employ a novel formulation of tensor voting, which allows an N-D implementation. Tensor voting is a perceptual organization framework that has mostly been applied to computer vision problems. Analyzing the estimated local structure at the inputs, we are able to obtain reliable dimensionality estimates at each instance, instead of a global estimate for the entire data set. Moreover, these local dimensionality and structure estimates enable us to measure geodesic distances and perform nonlinear interpolation for data sets with varying density, outliers, perturbation and intersections, that cannot be handled by state-of-the-art methods. Quantitative results on the estimation of local manifold structure using ground truth data are presented. In addition, we compare our approach with several leading methods for manifold learning at the task of measuring geodesic distances. Finally, we show competitive function approximation results on real data.