Frontiers of Computer Science

, Volume 13, Issue 6, pp 1243–1254 | Cite as

Non-negative matrix factorization based modeling and training algorithm for multi-label learning

  • Liang Sun
  • Hongwei GeEmail author
  • Wenjing Kang
Research Article


Multi-label learning is more complicated than single-label learning since the semantics of the instances are usually overlapped and not identical. The effectiveness of many algorithms often fails when the correlations in the feature and label space are not fully exploited. To this end, we propose a novel non-negative matrix factorization (NMF) based modeling and training algorithm that learns from both the adjacencies of the instances and the labels of the training set. In the modeling process, a set of generators are constructed, and the associations among generators, instances, and labels are set up, with which the label prediction is conducted. In the training process, the parameters involved in the process of modeling are determined. Specifically, an NMF based algorithm is proposed to determine the associations between generators and instances, and a non-negative least square optimization algorithm is applied to determine the associations between generators and labels. The proposed algorithm fully takes the advantage of smoothness assumption, so that the labels are properly propagated. The experiments were carried out on six set of benchmarks. The results demonstrate the effectiveness of the proposed algorithms.


multi-label learning non-negative least square optimization non-negative matrix factorization smoothness assumption 


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The authors are grateful to the support of the National Natural Science Foundation of China (Grant Nos. 61402076, 61572104, 61103146), the Fundamental Research Funds for the Central Universities (DUT17JC04), and the Project of the Key Laboratory of Symbolic Computation and Knowledge Engineering ofMinistry of Education, Jilin University (93K172017K03).

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  1. 1.
    Zhang M L, Zhou Z H. A review on multi-label learning algorithms. IEEE Transactions on Knowledge and Data Engineering, 2014, 26(8): 1819–1837CrossRefGoogle Scholar
  2. 2.
    Zhang M L, Zhou Z H. Milti-label neural networks with applications to functional genomics and text categorization. IEEE Transactions on Knowledge and Data Engineering, 2006, 18(10): 1338–1351CrossRefGoogle Scholar
  3. 3.
    Lo H, Wang J, Wang H, Lin S. Cost sensitive multi-label learning for audio tag annotation and retrieval. IEEE Transactions on Multimedia, 2011, 13(3): 518–529CrossRefGoogle Scholar
  4. 4.
    Sanden C, Zhang J. Enhancing multi-label music genre classification through ensemble techniques. In: Proceedings of the 34th International ACMSIGIR Conference on Research and Development in Information Retrieval. 2011, 705–714Google Scholar
  5. 5.
    Tang L, Rajan S, Narayanan V. Large scale multi-label classification via metalabeler. In: Proceedings of the 19th International Conference on World Wide Web. 2009, 211–220CrossRefGoogle Scholar
  6. 6.
    Gopal S, Yang Y. Multi-label classification with meta-level features. In: Proceedings of the 33rd International ACM SIGIR Conference on Research & Development in Information Retrieval. 2010, 315–322Google Scholar
  7. 7.
    Zhu X, Ghahramani Z. Learning from labeled and unlabeled data with label propagation. Technical Report, 2002Google Scholar
  8. 8.
    Read J, Martino L, Olmos P M, Luengo D. Scalable multi-output label prediction: from classifier chains to classifier trellises. Pattern Recognition, 2015, 48(6): 2096–2109CrossRefzbMATHGoogle Scholar
  9. 9.
    Madjarov G, Gjorgjevikj D, Dzeroski S. Two stage architecture for multi-label learning. Pattern Recognition, 2012, 45(3): 1019–1034CrossRefGoogle Scholar
  10. 10.
    Teisseyre P. Feature ranking for multi-label classification usingMarkov networks. Neurocomputing, 2015, 205: 439–454CrossRefGoogle Scholar
  11. 11.
    Lee J, Kim D W. Memetic feature selection algorithm for multi-label classification. Information Sciences, 2015, 293: 80–96CrossRefGoogle Scholar
  12. 12.
    Zhu X, Lafferty J, Rosenfeld R. Semi-supervised learning with graphs. Carnegie Mellon University, Doctor Thesis, 2005Google Scholar
  13. 13.
    Chapelle O, Schlkopf B, Zien A. Semi-Supervised Learning. MA: The MIT Press, 2006CrossRefGoogle Scholar
  14. 14.
    Hou P, Geng X, Zhang M L. Multi-label manifold learning. In: Proceedings of the 30th AAAI Conference on Artificial Intelligence. 2016, 1680–1686Google Scholar
  15. 15.
    Gao N N, Huang S J, Chen S C. Multi-label active learning by model guided distribution matching. Frontiers of Computer Science, 2016, 10(5): 845–855CrossRefGoogle Scholar
  16. 16.
    Kong X, Ng M K, Zhou Z H. Transductive multi-label learning via label set propagation. IEEE Transactions on Knowledge and Data Engineering, 2013, 25(3): 704–719CrossRefGoogle Scholar
  17. 17.
    Huang S J, Yu Y, Zhou Z H. Multi-label hypothesis reuse. In: Proceedings of the 18th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2012, 525–533Google Scholar
  18. 18.
    Huang S J, Zhou Z H. Multi-label learning by exploiting label correlations locally. In: Proceedings of the 26th AAAI Conference on Artificial Intelligence. 2012, 949–955Google Scholar
  19. 19.
    Lo H, Lin S,Wang H. Generalized k-label sets ensemble for multi-label and cost-sensitive classification. IEEE Transactions on Knowledge and Data Engineering, 2014, 26(7): 1679–1691CrossRefGoogle Scholar
  20. 20.
    Lee J, Kim K, Kim N, Lee J H. An approach for multi-label classification by directed acyclic graph with label correlation maximization. Information Sciences, 2016, 351: 101–114CrossRefGoogle Scholar
  21. 21.
    Li P, Li H, Wu M. Multi-label ensemble based on variable pairwise constraint projection. Information Sciences, 2013, 222: 269–281CrossRefMathSciNetGoogle Scholar
  22. 22.
    Wang B, Tsotsos J. Dynamic label propagation for semi-supervised multi-class multi-label classification. Pattern Recognition, 2016, 52: 75–84CrossRefGoogle Scholar
  23. 23.
    Wang S, Wang J, Wang Z, Ji Q. Enhancing multi-label classification by modeling dependencies among labels. Pattern Recognition, 2014, 47(10): 3405–3413CrossRefGoogle Scholar
  24. 24.
    Pillai I, Fumera G, Roli F. Multi-label classification with a reject option. Pattern Recognition, 2013, 46(8): 2256–2266CrossRefGoogle Scholar
  25. 25.
    Sun F, Tang J, Li H, Qi G, Huang T S. Multi-label image categorization with sparse factor representation. IEEE Transactions on Image Processing, 2014, 23(3): 1028–1037CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Zhang Y, Zhou Z H. Multi-label dimensionality reduction via dependence maximization. ACM Transactions on Knowledge Discovery from Data, 2010, 4(3): 14CrossRefGoogle Scholar
  27. 27.
    Zhang M L, Zhang K. Multi-label learning by exploiting label dependency. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2010, 999–1007CrossRefGoogle Scholar
  28. 28.
    Zhang M L, Wu L. Lift: multi-label learning with label specific features. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(1): 107–120CrossRefGoogle Scholar
  29. 29.
    Triguero I, Vens C. Labelling strategies for hierarchical multi-label classification techniques. Pattern Recognition, 2016, 56: 170–183CrossRefGoogle Scholar
  30. 30.
    Quevedo J R, Luaces O, Bahamonde A. Multilabel classifiers with a probabilistic thresholding strategy. Pattern Recognition, 2012, 45(2): 876–883zbMATHGoogle Scholar
  31. 31.
    Zhang N, Ding S, Zhang J. Multi layer ELM-RBF for multi-label learning. Applied Soft Computing, 2016, 43: 535–545CrossRefGoogle Scholar
  32. 32.
    Huang Y, Wang W, Wang L. Unconstrained multimodal multi-label learning. IEEE Transactions on Multimedia, 2015, 17(11): 1923–1935CrossRefGoogle Scholar
  33. 33.
    Xu J, Jagadeesh V, Manjunath B S. Multi-label learning with fused multimodal Bi-relational graph. IEEE Transactions on Multimedia, 2014, 16(2): 403–412CrossRefGoogle Scholar
  34. 34.
    Gao W, Zhou Z. On the consistency of multi-label learning. Artificial Intelligence, 2013, 199(1): 22–44CrossRefzbMATHMathSciNetGoogle Scholar
  35. 35.
    Madjarov G, Kocev D, Gjorgjevikj D, Dzeroski S. An extensive experimental comparison of methods for multi-label learning. Pattern Recognition, 2012, 45(9): 3084–3104CrossRefGoogle Scholar
  36. 36.
    Lee D D, Seung H S. Learning the parts of objects by non-negative matrix factorization. Nature, 1999, 401(6755): 788–791CrossRefzbMATHGoogle Scholar
  37. 37.
    Lawson C L, Hanson R J. Solving Least Squares Problems. New Jersey: Prentice-Hall, Inc., 1974zbMATHGoogle Scholar
  38. 38.
    Joachims T. Transductive inference for text classification using support vector machines. In: Proceedings of the 16th International Conference on Machine Learning. 1999, 200–209Google Scholar
  39. 39.
    Vapnik V N. Statistical Learning Theory. New York: Wiley, 1998zbMATHGoogle Scholar
  40. 40.
    Belkin M, Niyogi P, Sindhwani V. Manifold regularization: a geometric framework for learning from examples. Journal of Machine Learning Research, 2006, 7: 2399–2434zbMATHMathSciNetGoogle Scholar
  41. 41.
    Xu M, Jin R, Zhou Z H. Speedup matrix completion with side information: application to multi-label learning. In: Proceedings of the 27th Annual Conference on Neural Information Processing Systems. 2013, 2301–2309Google Scholar
  42. 42.
    Read J, Pfahringer B, Holmes G, Frank E. Classifier chains for multilabel classification. Machine Learning, 2011, 85(3): 333–359CrossRefMathSciNetGoogle Scholar
  43. 43.
    Wang J, Zhao Y, Wu X, Hua X S. A transductive multi-label learning approach for video concept detection. Pattern Recognition, 2011, 44(10–11): 2274–2286CrossRefzbMATHGoogle Scholar
  44. 44.
    Furnkranz J, Hullermeier E, Mencia E L, Brinker K. Multilabel classification via calibrated label ranking. Machine Learning, 2008, 73(2): 133–153CrossRefGoogle Scholar
  45. 45.
    Mencia E L, Park S H, Furnkranz J. Efficient voting prediction for pairwise multi-label classification. Neurocomputing, 2010, 73(7–9): 1164–1176CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Computer Science and TechnologyDalian University of TechnologyDalianChina

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