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A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classification. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast optimization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the origin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spline function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient. [ABSTRACT FROM AUTHOR]

Semantic smoothing, which incorporates synonym and sense information into the language models, is effective and potentially significant to improve retrieval performance. The implemented semantic smoothing models, such as the translation model which statistically maps document terms to query terms, and a number of works that have followed have shown good experimental results. However, these models are unable to incorporate contextual information. Thus, the resulting translation might be mixed and fairy general. To overcome this limitation, we propose a novel context sensitive semantic smoothing method that decomposes a document or a query into a set of weighted context-sensitive topic signatures and then translate those topic signatures into query terms. In detail, we solve this problem through (1) choosing concept pairs as topic signatures and adopting an ontology-based approach to extract concept pairs; (2) estimating the translation model for each topic signature using the EM algorithm; and (3) expanding document and query models based on topic signature translations. The new smoothing method is evaluated on TREC 2004/05 Genomics Track collections and significant improvements are obtained. The MAP (mean average precision) achieves a 33.6% maximal gain over the simple language model, as well as a 7.8% gain over the language model with context-insensitive semantic smoothing. [ABSTRACT FROM AUTHOR]