Weight-and-Universum-based semi-supervised multi-view learning machine


Semi-supervised multi-view learning machine is developed to process the corresponding semi-supervised multi-view data sets which consist of labeled and unlabeled instances. But in real-world applications, for a multi-view data set, only few instances are labeled with the limitation of manpower and cost. As a result, few prior knowledge which is necessary for the designing of a learning machine is provided. Moreover, in practice, different views and features play diverse discriminant roles while traditional learning machines treat these roles equally and assign the same weight just for convenience. In order to solve these problems, we introduce Universum learning to obtain more prior knowledge and assign different weights for views and features to reflect their diverse discriminant roles. The proposed learning machine is named as weight-and-Universum-based semi-supervised multi-view learning machine (WUSM). In WUSM, we first obtain weights of views and features. Then, we construct Universum set to obtain more prior knowledge on the basis of these weights. Different from traditional construction ways, the used construction way makes full use of the information of all labeled and unlabeled instances rather than only a pair of positive and negative training instances. Finally, we design the machine with the usage of the Universum set along with original data set. Our contributions are given as follows. (1) With the usage of all (labeled, unlabeled) instances of the data set, the Universum set provides more useful prior knowledge. (2) WUSM considers the diversities of views and features. (3) WUSM advances the development of semi-supervised multi-view learning machines. Experiments on bipartite ranking, feature selection, dimensionality reduction, classification, clustering, etc. validate the advantages of WUSM and draw a conclusion that with the introduction of Universum learning, view weights, and feature weights, the performance of a semi-supervised multi-view learning machine is boosted.

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    Example in this figure is also given in Liu et al. (2016).

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    For multiple classes, it can be divided into several binary class problems and the solution is the combination of optimal results of those binary class problems.

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    For example, a training data set consists of three classes, one has 100 instances, another has 120 instances, and the third has 140 instances, then \(N_\mathrm{e-max}=220\).

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    ROC: receiver operating characteristic.

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    For these evaluation metrics, \(\hbox {precision}=\frac{\hbox {TP}}{\hbox {TP}+\hbox {FP}}\), \(\hbox {recall}=\frac{\hbox {TP}}{\hbox {TP}+\hbox {FN}}\), \(\hbox {specificity}=\frac{\hbox {TN}}{\hbox {TN}+\hbox {FP}}\), \(\hbox {accuracy}=\frac{\hbox {TP}+\hbox {TN}}{\hbox {TP}+\hbox {FP}+\hbox {TN}+\hbox {FN}}\), and \(\hbox {F-measure}=\frac{2\hbox {recall}\times \hbox {precision}}{\hbox {recall}+\hbox {precision}}\). Here, TN: true negative, TP: true positive, FP: false positive, FN: false negative.

  9. 9.

    Limited by the length of this paper, we only show the results about accuracy rather than precision, recall, specificity, and F-measure. But the results on other evaluation metrics won’t change our conclusions.


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This work is supported by Project funded by China Postdoctoral Science Foundation under Grant Number 2019M651576, National Natural Science Foundation of China (Grant Nos. 61602296, 61673301), Natural Science Foundation of Shanghai (Grant Nos. 16ZR1414500), National Key R&D Program of China (Grant No. 213), Major Project of Ministry of Public Security (Grant No. 20170004). Furthermore, this work is also sponsored by ‘Chenguang Program’ supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission under Grant Number 18CG54. The authors would like to thank their supports.

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Zhu, C., Miao, D., Zhou, R. et al. Weight-and-Universum-based semi-supervised multi-view learning machine. Soft Comput 24, 10657–10679 (2020). https://doi.org/10.1007/s00500-019-04572-5

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  • Semi-supervised learning
  • Multi-view learning
  • View weights
  • Feature weights
  • Universum learning