A Generic Scheme for Color Image Retrieval Based on the Multivariate Wald-Wolfowitz Test
IEEE Transactions on Knowledge and Data Engineering
Independent subspace analysis using geodesic spanning trees
ICML '05 Proceedings of the 22nd international conference on Machine learning
Estimating Entropy Rates with Bayesian Confidence Intervals
Neural Computation
A duality view of spectral methods for dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
Selection of the optimal parameter value for the Isomap algorithm
Pattern Recognition Letters
Texture retrieval based on a non-parametric measure for multivariate distributions
Proceedings of the 6th ACM international conference on Image and video retrieval
Finite Elements in Analysis and Design
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Journal of Computational Physics
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
Journal of Computational Physics
Dimension detection via slivers
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Intrinsic dimension estimation of manifolds by incising balls
Pattern Recognition
Continuous dimensionality characterization of image structures
Image and Vision Computing
A new approach to discover interlacing data structures in high-dimensional space
Journal of Intelligent Information Systems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Adapting indexing trees to data distribution in feature spaces
Computer Vision and Image Understanding
A template-based isomap algorithm for real-time removal of ocular artifacts from EEG signals
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
Batch linear manifold topographic map with regional dimensionality estimation
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
On local intrinsic dimension estimation and its applications
IEEE Transactions on Signal Processing
Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting
The Journal of Machine Learning Research
Robust automatic data decomposition using a modified sparse NMF
MIRAGE'07 Proceedings of the 3rd international conference on Computer vision/computer graphics collaboration techniques
Applications of average geodesic distance in manifold learning
RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
Automatic configuration of spectral dimensionality reduction methods
Pattern Recognition Letters
Joint manifolds for data fusion
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Estimating the indexability of multimedia descriptors for similarity searching
RIAO '10 Adaptivity, Personalization and Fusion of Heterogeneous Information
Large scale disk-based metric indexing structure for approximate information retrieval by content
Proceedings of the 1st Workshop on New Trends in Similarity Search
Mining interlacing manifolds in high dimensional spaces
Proceedings of the 2011 ACM Symposium on Applied Computing
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
Minimum neighbor distance estimators of intrinsic dimension
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
IDEA: intrinsic dimension estimation algorithm
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Local entropic graphs for globally-consistent graph matching
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Intrinsic dimension induced similarity measure for clustering
ADMA'11 Proceedings of the 7th international conference on Advanced Data Mining and Applications - Volume Part II
Manifold analysis of spectral munsell colors
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
Information-Theoretic dissimilarities for graphs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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In the manifold learning problem, one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper, we consider the closely related problem of estimating the manifold's intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sample points as realizations of an unknown multivariate density supported on an unknown smooth manifold. We introduce a novel geometric approach based on entropic graph methods. Although the theory presented applies to this general class of graphs, we focus on the geodesic-minimal-spanning-tree (GMST) to obtaining asymptotically consistent estimates of the manifold dimension and the Re´nyi α-entropy of the sample density on the manifold. The GMST approach is striking in its simplicity and does not require reconstruction of the manifold or estimation of the multivariate density of the samples. The GMST method simply constructs a minimal spanning tree (MST) sequence using a geodesic edge matrix and uses the overall lengths of the MSTs to simultaneously estimate manifold dimension and entropy. We illustrate the GMST approach on standard synthetic manifolds as well as on real data sets consisting of images of faces.