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Estimation of high-density regions using One-Class Neighbor Machines
Alberto Muñoz1, Javier M Moguerza
1Department of Statistics, University Carlos III, Getafe, Madrid, Spain. alberto.munoz@uc3m.es
Summary
We introduce the One-Class Neighbor Machine (OCNM) to estimate high-density regions in data. This new method accurately identifies density contour clusters, outperforming existing techniques.
Area of Science:
- Statistics
- Machine Learning
- Data Mining
Background:
- Estimating high-density regions is crucial for data analysis.
- Density contour clusters are minimum volume sets with specified probability.
- One-Class Support Vector Machines (OCSVM) are related but have limitations.
Purpose of the Study:
- To propose a novel method for estimating minimum volume sets (density contour clusters).
- To introduce the One-Class Neighbor Machine (OCNM) and analyze its properties.
- To demonstrate the advantages of OCNM over existing methods.
Main Methods:
- Developed the One-Class Neighbor Machine (OCNM) algorithm.
- Analyzed the asymptotic convergence properties of OCNM.
- Conducted numerical experiments to compare OCNM with other methods.
Main Results:
- OCNM provides an effective solution for estimating density contour clusters.
- The OCNM solution asymptotically converges to the true minimum volume set.
- Numerical results show OCNM offers advantages in accuracy and performance.
Conclusions:
- OCNM is a promising new method for identifying high-density regions in data.
- The method offers theoretical guarantees of convergence.
- OCNM demonstrates practical utility and superiority in empirical evaluations.
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