Semi-supervised support vector machines (S3VMs) are a kind of popular approaches which try to improve learning performance by exploiting unlabeled data. Though S3VMs have been found helpful in many situations, they may degenerate performance and the resultant generalization ability may be even worse than using the labeled data only. In this paper, we try to reduce the chance of performance degeneration of S3VMs. Our basic idea is that, rather than exploiting all unlabeled data, the unlabeled instances should be selected such that only the ones which are very likely to be helpful are exploited, while some highly risky unlabeled instances are avoided. We propose the S3VM- method by using hierarchical clustering to select the unlabeled instances. Experiments on a broad range of data sets over eighty-eight different settings show that the chance of performance degeneration of S3VM- is much smaller than that of existing S3VMs.
Roughly speaking, existing semi-supervised learning approaches mainly fall into four categories. The first category is generative methods, e.g., @cite_21 @cite_24 , which extend supervised generative models by exploiting unlabeled data in parameter estimation and label estimation using techniques such as the EM method. The second category is graph-based methods, e.g., @cite_0 @cite_20 @cite_15 , which encode both the labeled and unlabeled instances in a graph and then perform label propagation on the graph. The third category is disagreement-based methods, e.g., @cite_26 @cite_25 , which employ multiple learners and improve the learners through labeling the unlabeled data based on the exploitation of disagreement among the learners. The fourth category is S3VMs, e.g., @cite_16 @cite_4 , which use unlabeled data to regularize the decision boundary to go through low density regions @cite_8 .
@cite_26 @cite_4 @cite_8 @cite_21 @cite_24 @cite_0 @cite_15 @cite_16 @cite_25 @cite_20
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In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks. It is usually expected that, when labeled data are limited, the learning performance can be improved by exploiting unlabeled data. In many cases, however, the performances of current semi-supervised learning approaches may be even worse than purely using the limited labeled data. It is desired to have safe semi-supervised learning approaches which never degenerate learning performance by using unlabeled data. In this paper, we focus on semi-supervised support vector machines (S3VMs) and propose S4VMs, i.e., safe S3VMs. Unlike S3VMs which typically aim at approaching an optimal low-density separator, S4VMs try to exploit the candidate low-density separators simultaneously to reduce the risk of identifying a poor separator with unlabeled data. We describe two implementations of S4VMs, and our comprehensive experiments show that the overall performance of S4VMs are highly competitive to S3VMs, while in contrast to S3VMs which degenerate performance in many cases, S4VMs are never significantly inferior to inductive SVMs. In classification, semi-supervised learning occurs when a large amount of unlabeled data is available with only a small number of labeled data. In such a situation, how to enhance predictability of classification through unlabeled data is the focus. In this article, we introduce a novel large margin semi-supervised learning methodology, using grouping information from unlabeled data, together with the concept of margins, in a form of regularization controlling the interplay between labeled and unlabeled data. Based on this methodology, we develop two specific machines involving support vector machines and ψ-learning, denoted as SSVM and SPSI, through difference convex programming. In addition, we estimate the generalization error using both labeled and unlabeled data, for tuning regularizers. Finally, our theoretical and numerical analyses indicate that the proposed methodology achieves the desired objective of delivering high performance in generalization, particularly against some strong performers. Semi-supervised learning, which uses unlabeled data to help learn a discriminative model, is especially important for structured output problems, as considerably more effort is needed to label its multi-dimensional outputs versus standard single output problems. We propose a new max-margin framework for semi-supervised structured output learning, that allows the use of powerful discrete optimization algorithms and high order regularizers defined directly on model predictions for the unlabeled examples. We show that our framework is closely related to Posterior Regularization, and the two frameworks optimize special cases of the same objective. The new framework is instantiated on two image segmentation tasks, using both a graph regularizer and a cardinality regularizer. Experiments also demonstrate that this framework can utilize unlabeled data from a different source than the labeled data to significantly improve performance while saving labeling effort.