### Abstract

In many real applications, the input data are naturally expressed as tensors, such as virtual metrology in semiconductor manufacturing, face recognition and gait recognition in computer vision, etc. In this paper, we propose a general optimization framework for dealing with tensor inputs. Most existing methods for supervised tensor learning use only rank-one weight tensors in the linear model and cannot readily incorporate domain knowledge. In our framework, we obtain the weight tensor in a hierarchical way - we first approximate it by a low-rank tensor, and then estimate the low-rank approximation using the prior knowledge from various sources, e.g., different domain experts. This is motivated by wafer quality prediction in semiconductor manufacturing. Furthermore, we propose an effective algorithm named H-MOTE for solving this framework, which is guaranteed to converge. The time complexity of H-MOTE is linear with respect to the number of examples as well as the size of the weight tensor. Experimental results show the superiority of H-MOTE over state-of-the-art techniques on both synthetic and real data sets.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the National Conference on Artificial Intelligence |

Pages | 1233-1239 |

Number of pages | 7 |

Volume | 2 |

State | Published - 2012 |

Externally published | Yes |

Event | 26th AAAI Conference on Artificial Intelligence and the 24th Innovative Applications of Artificial Intelligence Conference, AAAI-12 / IAAI-12 - Toronto, ON, Canada Duration: Jul 22 2012 → Jul 26 2012 |

### Other

Other | 26th AAAI Conference on Artificial Intelligence and the 24th Innovative Applications of Artificial Intelligence Conference, AAAI-12 / IAAI-12 |
---|---|

Country | Canada |

City | Toronto, ON |

Period | 7/22/12 → 7/26/12 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Artificial Intelligence

### Cite this

*Proceedings of the National Conference on Artificial Intelligence*(Vol. 2, pp. 1233-1239)

**Hierarchical modeling with tensor inputs.** / Zhu, Yada; He, Jingrui; Lawrence, Rick.

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

*Proceedings of the National Conference on Artificial Intelligence.*vol. 2, pp. 1233-1239, 26th AAAI Conference on Artificial Intelligence and the 24th Innovative Applications of Artificial Intelligence Conference, AAAI-12 / IAAI-12, Toronto, ON, Canada, 7/22/12.

}

TY - GEN

T1 - Hierarchical modeling with tensor inputs

AU - Zhu, Yada

AU - He, Jingrui

AU - Lawrence, Rick

PY - 2012

Y1 - 2012

N2 - In many real applications, the input data are naturally expressed as tensors, such as virtual metrology in semiconductor manufacturing, face recognition and gait recognition in computer vision, etc. In this paper, we propose a general optimization framework for dealing with tensor inputs. Most existing methods for supervised tensor learning use only rank-one weight tensors in the linear model and cannot readily incorporate domain knowledge. In our framework, we obtain the weight tensor in a hierarchical way - we first approximate it by a low-rank tensor, and then estimate the low-rank approximation using the prior knowledge from various sources, e.g., different domain experts. This is motivated by wafer quality prediction in semiconductor manufacturing. Furthermore, we propose an effective algorithm named H-MOTE for solving this framework, which is guaranteed to converge. The time complexity of H-MOTE is linear with respect to the number of examples as well as the size of the weight tensor. Experimental results show the superiority of H-MOTE over state-of-the-art techniques on both synthetic and real data sets.

AB - In many real applications, the input data are naturally expressed as tensors, such as virtual metrology in semiconductor manufacturing, face recognition and gait recognition in computer vision, etc. In this paper, we propose a general optimization framework for dealing with tensor inputs. Most existing methods for supervised tensor learning use only rank-one weight tensors in the linear model and cannot readily incorporate domain knowledge. In our framework, we obtain the weight tensor in a hierarchical way - we first approximate it by a low-rank tensor, and then estimate the low-rank approximation using the prior knowledge from various sources, e.g., different domain experts. This is motivated by wafer quality prediction in semiconductor manufacturing. Furthermore, we propose an effective algorithm named H-MOTE for solving this framework, which is guaranteed to converge. The time complexity of H-MOTE is linear with respect to the number of examples as well as the size of the weight tensor. Experimental results show the superiority of H-MOTE over state-of-the-art techniques on both synthetic and real data sets.

UR - http://www.scopus.com/inward/record.url?scp=84868282525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868282525&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84868282525

SN - 9781577355687

VL - 2

SP - 1233

EP - 1239

BT - Proceedings of the National Conference on Artificial Intelligence

ER -