Fitting a graph to vector data

Authors:
Samuel I. Daitch;Jonathan A. Kelner;Daniel A. Spielman
Affiliations:
Yale University, New Haven, CT;Massachusetts Institute of Technology, Cambridge, MA;Yale University, New Haven, CT
Venue:
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Year:
2009

Citing 9
Cited 4

C4.5: programs for machine learning

C4.5: programs for machine learning
Laplacian Eigenmaps for dimensionality reduction and data representation

Neural Computation
Spectral Partitioning of Random Graphs

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Not So Naive Bayes: Aggregating One-Dependence Estimators

Machine Learning
Beyond the point cloud: from transductive to semi-supervised learning

ICML '05 Proceedings of the 22nd international conference on Machine learning
Full Bayesian network classifiers

ICML '06 Proceedings of the 23rd international conference on Machine learning
Machine learning: a review of classification and combining techniques

Artificial Intelligence Review
Graph transduction via alternating minimization

Proceedings of the 25th international conference on Machine learning

Locality preserving discriminant projections for face and palmprint recognition

Neurocomputing
Sample-dependent graph construction with application to dimensionality reduction

Neurocomputing
GANC: Greedy agglomerative normalized cut for graph clustering

Pattern Recognition
Constrained large Margin Local Projection algorithms and extensions for multimodal dimensionality reduction

Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a measure of how well a combinatorial graph fits a collection of vectors. The optimal graphs under this measure may be computed by solving convex quadratic programs and have many interesting properties. For vectors in d dimensional space, the graphs always have average degree at most 2(d + 1), and for vectors in 2 dimensions they are always planar. We compute these graphs for many standard data sets and show that they can be used to obtain good solutions to classification, regression and clustering problems.