### Abstract

The vanishing ideal of a set of points, S ⊂ ℝ^{n}, is the set of all polynomials that attain the value of zero on all the points in S. Such ideals can be compactly represented using a small set of polynomials known as generators of the ideal. Here we describe and analyze an efficient procedure that constructs a set of generators of a vanishing ideal. Our procedure is numerically stable, and can be used to find approximately vanishing polynomials. The resulting polynomials capture nonlinear structure in data, and can for example be used within supervised learning. Empirical comparison with kernel methods show that our method constructs more compact classifiers with comparable accuracy.

Original language | English (US) |
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Pages | 597-605 |

Number of pages | 9 |

State | Published - Jan 1 2013 |

Event | 30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA, United States Duration: Jun 16 2013 → Jun 21 2013 |

### Other

Other | 30th International Conference on Machine Learning, ICML 2013 |
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Country | United States |

City | Atlanta, GA |

Period | 6/16/13 → 6/21/13 |

### All Science Journal Classification (ASJC) codes

- Human-Computer Interaction
- Sociology and Political Science

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## Cite this

*Vanishing component analysis*. 597-605. Paper presented at 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, United States.