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Nuclear norm regularized convolutional Max Pos@Top machine

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Abstract

In this paper, we propose a novel classification model for the multiple instance data, which aims to maximize the number of positive instances ranked before the top-ranked negative instances. This method belongs to a recently emerged performance, named as Pos@Top. Our proposed classification model has a convolutional structure that is composed by four layers, i.e., the convolutional layer, the activation layer, the max-pooling layer and the full connection layer. In this paper, we propose an algorithm to learn the convolutional filters and the full connection weights to maximize the Pos@Top measure over the training set. Also, we try to minimize the rank of the filter matrix to explore the low-dimensional space of the instances in conjunction with the classification results. The rank minimization is conducted by the nuclear norm minimization of the filter matrix. In addition, we develop an iterative algorithm to solve the corresponding problem. We test our method on several benchmark datasets. The experimental results show the superiority of our method compared with other state-of-the-art Pos@Top maximization methods.

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Acknowledgements

The Foundation of modern educational technology research of Jiangsu Province (No. 2015-R-42631) and The University Natural Science Foundation of Jiangsu Province (14KJD520003).

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Authors and Affiliations

  1. College of Computer and Information, Hohai University, Nanjing, China

    Qinfeng Li, Xiaofeng Zhou, Aihua Gu & Zonghua Li

  2. Department of Basic, Jinling Institute of Technology, Nanjing, China

    Qinfeng Li

  3. King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Ru-Ze Liang

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  1. Qinfeng Li
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  2. Xiaofeng Zhou
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  4. Zonghua Li
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Correspondence to Qinfeng Li.

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Li, Q., Zhou, X., Gu, A. et al. Nuclear norm regularized convolutional Max Pos@Top machine. Neural Comput & Applic 30, 463–472 (2018). https://doi.org/10.1007/s00521-016-2680-2

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