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Semi-supervised Unified Latent Factor learning with multi-view data

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Abstract

Explosive multimedia resources are generated on web, which can be typically considered as a kind of multi-view data in nature. In this paper, we present a Semi-supervised Unified Latent Factor learning approach (SULF) to learn a predictive unified latent representation by leveraging both complementary information among multiple views and the supervision from the partially label information. On one hand, SULF employs a collaborative Nonnegative Matrix Factorization formulation to discover a unified latent space shared across multiple views. On the other hand, SULF adopts a regularized regression model to minimize a prediction loss on partially labeled data with the latent representation. Consequently, the obtained parts-based representation can have more discriminating power. In addition, we also develop a mechanism to learn the weights of different views automatically. To solve the proposed optimization problem, we design an effective iterative algorithm. Extensive experiments are conducted for both classification and clustering tasks on three real-world datasets and the compared results demonstrate the superiority of our approach.

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Notes

  1. \(\mathbf {w}_k\) is the \(k\)th row of \(\mathbf {W}\). In practice, \(||\mathbf {w}_k||_2\) could be close to zero but not zero. Theoretically, it could be zeros. For this case, we can let \(\varepsilon \) is very small constant, and regularize \(e_{kk}=\frac{1}{2\sqrt{\mathbf {w}_k^T\mathbf {w}_k+\varepsilon }}\).

  2. For convenience, \(\mathbf {A}\) is approximately as constant matrix when requiring the derivatives of \(\frac{\partial {\mathcal {L}}}{\partial \mathbf {V}_l}\).

  3. http://cvxr.com/cvx/.

  4. http://koen.me/research/colordescriptors/.

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Acknowledgments

This work was supported by 973 Program (2012C B316304) and National Natural Science Foundation of China (61272329, 61202325, and 61070104).

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Authors and Affiliations

  1. National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Yu Jiang, Jing Liu & Hanqing Lu

  2. School of Computer Science, Nanjing University of Science and Technology, Nanjing, China

    Zechao Li

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  1. Yu Jiang
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  2. Jing Liu
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  3. Zechao Li
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  4. Hanqing Lu
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Correspondence to Jing Liu.

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Jiang, Y., Liu, J., Li, Z. et al. Semi-supervised Unified Latent Factor learning with multi-view data. Machine Vision and Applications 25, 1635–1645 (2014). https://doi.org/10.1007/s00138-013-0556-3

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  • DOI: https://doi.org/10.1007/s00138-013-0556-3

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