### Abstract

In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. In this chapter, we introduce the concept of tangent vectors, which compactly represent the essence of these transformation invariances, and two classes of algorithms, "tangent distance" and "tangent propagation", which make use of these invariances to improve performance.

Original language | English (US) |
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Title of host publication | Neural Networks: Tricks of the Trade |

Pages | 235-269 |

Number of pages | 35 |

Volume | 7700 LECTURE NO |

DOIs | |

State | Published - 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7700 LECTURE NO |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Neural Networks: Tricks of the Trade*(Vol. 7700 LECTURE NO, pp. 235-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7700 LECTURE NO). https://doi.org/10.1007/978-3-642-35289-8-17

**Transformation invariance in pattern recognition - Tangent distance and tangent propagation.** / Simard, Patrice Y.; LeCun, Yann; Denker, John S.; Victorri, Bernard.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Neural Networks: Tricks of the Trade.*vol. 7700 LECTURE NO, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7700 LECTURE NO, pp. 235-269. https://doi.org/10.1007/978-3-642-35289-8-17

}

TY - CHAP

T1 - Transformation invariance in pattern recognition - Tangent distance and tangent propagation

AU - Simard, Patrice Y.

AU - LeCun, Yann

AU - Denker, John S.

AU - Victorri, Bernard

PY - 2012

Y1 - 2012

N2 - In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. In this chapter, we introduce the concept of tangent vectors, which compactly represent the essence of these transformation invariances, and two classes of algorithms, "tangent distance" and "tangent propagation", which make use of these invariances to improve performance.

AB - In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. In this chapter, we introduce the concept of tangent vectors, which compactly represent the essence of these transformation invariances, and two classes of algorithms, "tangent distance" and "tangent propagation", which make use of these invariances to improve performance.

UR - http://www.scopus.com/inward/record.url?scp=84872577241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872577241&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-35289-8-17

DO - 10.1007/978-3-642-35289-8-17

M3 - Chapter

SN - 9783642352881

VL - 7700 LECTURE NO

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 235

EP - 269

BT - Neural Networks: Tricks of the Trade

ER -