Learning Curved Multinomial Subfamilies for Natural Language Processing and Information Retrieval
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
The Bayes Decision Rule Induced Similarity Measures
IEEE Transactions on Pattern Analysis and Machine Intelligence
Information-theoretic metric learning
Proceedings of the 24th international conference on Machine learning
A transductive framework of distance metric learning by spectral dimensionality reduction
Proceedings of the 24th international conference on Machine learning
Kernel-Based Text Classification on Statistical Manifold
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
Engineering Applications of Artificial Intelligence
Local Metric Learning on Manifolds with Application to Query---Based Operations
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Modeling adaptive kernels from probabilistic phylogenetic trees
Artificial Intelligence in Medicine
Permanents, transport polytopes and positive definite kernels on histograms
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Distance metric learning for content identification
IEEE Transactions on Information Forensics and Security
Dimensionality reduction for text using domain knowledge
COLING '10 Proceedings of the 23rd International Conference on Computational Linguistics: Posters
Fast neighborhood component analysis
Neurocomputing
Metric and kernel learning using a linear transformation
The Journal of Machine Learning Research
An efficient framework for constructing generalized locally-induced text metrics
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Advances in matrix manifolds for computer vision
Image and Vision Computing
Random forests for metric learning with implicit pairwise position dependence
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
A new distance for probability measures based on the estimation of level sets
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Linear reconstruction measure steered nearest neighbor classification framework
Pattern Recognition
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Many algorithms in machine learning rely on being given a good distance metric over the input space. Rather than using a default metric such as the Euclidean metric, it is desirable to obtain a metric based on the provided data. We consider the problem of learning a Riemannian metric associated with a given differentiable manifold and a set of points. Our approach to the problem involves choosing a metric from a parametric family that is based on maximizing the inverse volume of a given data set of points. From a statistical perspective, it is related to maximum likelihood under a model that assigns probabilities inversely proportional to the Riemannian volume element. We discuss in detail learning a metric on the multinomial simplex where the metric candidates are pull-back metrics of the Fisher information under a Lie group of transformations. When applied to text document classification the resulting geodesic distance resemble, but outperform, the tfidf cosine similarity measure.