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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Vydáno v:	IEEE transactions on pattern analysis and machine intelligence Ročník 28; číslo 4; s. 497 - 508
Hlavní autor:	Lebanon, G.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Los Alamitos, CA IEEE 01.04.2006 IEEE Computer Society The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 ObjectType-Article-2 ObjectType-Feature-1
ISSN:	0162-8828 1939-3539
DOI:	10.1109/TPAMI.2006.77