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Metric Learning for Text Documents
April 2006 (vol. 28 no. 4)
pp. 497-508
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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Index Terms:
Distance learning, text analysis, machine learning.
Citation:
Guy Lebanon, "Metric Learning for Text Documents," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 497-508, April 2006, doi:10.1109/TPAMI.2006.77
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