## Abstract

Many real-world applications call for learning predictive relationships from multi-modal data. In particular, in multi-media and web applications, given a dataset of images and their associated captions, one might want to construct a predictive model that not only predicts a caption for the image but also labels the individual objects in the image. We address this problem using a multi-modal hierarchical Dirichlet Process model (MoM-HDP) - a stochastic process for modeling multi-modal data. MoM-HDP is an analog of a multi-modal Latent Dirichlet Allocation (MoM-LDA) with an infinite number of mixture components. Thus MoM-HDP allows circumventing the need for a priori choice of the number of mixture components or the computational expense of model selection. During training, the model has access to an un-segmented image and its caption, but not the labels for each object in the image. The trained model is used to predict the label for each region of interest in a segmented image. The model parameters are estimated efficiently using variational inference. We use two large benchmark datasets to compare the performance of the proposed MoM-HDP model with that of MoM-LDA model as well as some simple alternatives: Naive Bayes and Logistic Regression classifiers based on the formulation of the image annotation and image-label correspondence problems as one-against-all classification. Our experimental results show that unlike MoM-LDA, the performance of MoM-HDP is invariant to the number of mixture components. Furthermore, our experimental evaluation shows that the generalization performance of MoM-HDP is superior to that of MoM-HDP as well as the one-against-all Naive Bayes and Logistic Regression classifiers.

Original language | English (US) |
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Title of host publication | Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133 |

Pages | 280-290 |

Number of pages | 11 |

State | Published - Dec 1 2009 |

Event | 9th SIAM International Conference on Data Mining 2009, SDM 2009 - Sparks, NV, United States Duration: Apr 30 2009 → May 2 2009 |

### Publication series

Name | Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics |
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Volume | 1 |

### Other

Other | 9th SIAM International Conference on Data Mining 2009, SDM 2009 |
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Country | United States |

City | Sparks, NV |

Period | 4/30/09 → 5/2/09 |

## All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Software
- Applied Mathematics