Metric learning for text documents

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...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 28; no. 4; pp. 497 - 508
Main Author: Lebanon, G.
Format: Journal Article
Language:English
Published: Los Alamitos, CA IEEE 01.04.2006
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Automatic Data Processing - methods
Classification
Computer Graphics
Computer science; control theory; systems
Distance learning
Documentation - methods
Euclidean distance
Exact sciences and technology
Geometry
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Information Storage and Retrieval - methods
Inverse
Joining processes
Kernel
Learning
Level measurement
Lie groups
Machine learning
Machine learning algorithms
Neural networks
Numerical Analysis, Computer-Assisted
Pattern analysis
Pattern Recognition, Automated - methods
Probability
Signal Processing, Computer-Assisted
Similarity
Speech and sound recognition and synthesis. Linguistics
Studies
Text analysis
Texts
Transformations
User-Computer Interface
Text analysis
Statistical analysis
Distance learning
Probabilistic approach
Metric space
Similarity
Euclidean theory
Riemann metric
Geodesic structure
Text
Transformation group
machine learning
Modeling
Remote teaching
Fisher information
Classification
Geodesic
Lie group
Maximum likelihood
Lie transformation
Learning algorithm
Pattern analysis
Artificial intelligence
ISSN:0162-8828, 1939-3539
Online Access:Get full text
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Description
Summary: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.
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ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2006.77