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Open AccessArticle

A Fast Algorithm for Multi-Class Learning from Label Proportions

by Fan Zhang 1,†, Jiabin Liu 2,†, Bo Wang 3, Zhiquan Qi 4,5,6,* and Yong Shi 4,5,6,7
1
School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
2
School of Computer Science and Technology, University of Chinese Academy Sciences, Beijing 100190, China
3
School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China
4
School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
5
Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190, China
6
Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing 100190, China
7
College of Information Science and Technology, University of Nebraska at Omaha, NE 68182, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Electronics 2019, 8(6), 609; https://doi.org/10.3390/electronics8060609
Received: 17 April 2019 / Revised: 24 May 2019 / Accepted: 27 May 2019 / Published: 30 May 2019
(This article belongs to the Section Artificial Intelligence)
Learning from label proportions (LLP) is a new kind of learning problem which has attracted wide interest in machine learning. Different from the well-known supervised learning, the training data of LLP is in the form of bags and only the proportion of each class in each bag is available. Actually, many modern applications can be successfully abstracted to this problem such as modeling voting behaviors and spam filtering. However, time-consuming training is still a challenge for LLP, which becomes a bottleneck especially when addressing large bags and bag sizes. In this paper, we propose a fast algorithm called multi-class learning from label proportions by extreme learning machine (LLP-ELM), which takes advantage of an extreme learning machine with fast learning speed to solve multi-class learning from label proportions. Firstly, we reshape the hidden layer output matrix and the training data target matrix of an extreme learning machine to adapt to the proportion information instead of the real labels. Secondly, a robust loss function with a regularization term is formulated and two efficient solutions are provided to different cases. Finally, various experiments demonstrate the significant speed-up of the proposed model with better accuracies on different datasets compared with several state-of-the-art methods. View Full-Text
Keywords: multi-class learning; learning from label proportions (LLP); extreme learning machine; fast learning speed multi-class learning; learning from label proportions (LLP); extreme learning machine; fast learning speed
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Zhang, F.; Liu, J.; Wang, B.; Qi, Z.; Shi, Y. A Fast Algorithm for Multi-Class Learning from Label Proportions. Electronics 2019, 8, 609.

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