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Metric learning for text documents.

¹Department of Statistics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA. lebanon@stat.purdue.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence

|March 29, 2006

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This study introduces a novel method for learning data-driven distance metrics, outperforming standard measures in text classification by optimizing Riemannian geometry for machine learning algorithms.

Area of Science:

Machine Learning
Differential Geometry
Statistical Inference

Background:

Machine learning algorithms often require effective distance metrics for optimal performance.
Default metrics like Euclidean may not capture the underlying data structure.
Learning data-specific metrics is crucial for improving algorithm accuracy.

Purpose of the Study:

To develop a method for learning Riemannian metrics from data.
To apply this method to the multinomial simplex for text classification.
To compare the learned metric against existing measures like tfidf cosine similarity.

Main Methods:

Learning a parametric family of Riemannian metrics by maximizing the inverse data volume.
Utilizing maximum likelihood estimation under a specific probability model.

Related Experiment Videos

Applying pull-back metrics of Fisher information under Lie group transformations.

Main Results:

The proposed method successfully learns a Riemannian metric tailored to the data.
The learned geodesic distance measure demonstrated superior performance compared to tfidf cosine similarity in text document classification.
The approach provides a statistically grounded method for metric learning.

Conclusions:

Data-driven Riemannian metric learning offers significant advantages over default metrics.
The developed technique enhances machine learning model performance, particularly in text analysis.
This work bridges differential geometry and machine learning for improved data representation.