基于Tucker分解的半监督支持张量机

Semi-supervised Support Tensor Based on Tucker Decomposition

传统的机器学习方法所使用的数据大多是基于向量空间的。支持向量机(Support Vector Machine,SVM)作为一种重要的机器学习方法,在解决小样本、非线性、高维数据等问题时具有较好的性能。但在实际应用中,图像和视频等数据都是用张量形式表示的,如果将这些张量数据直接转换成向量数据,往往会丢失一些原有的结构和相关性信息,有可能造成维度灾难和小样本问题。为了设法保持尽量多的张量结构信息,提出了一种采用Tucker分解的支持张量机(Support Tensor Machine,STM)算法。实验表明,该方法可以明显提高分类器性能;同时,支持张量机作为监督学习方式,存在无法利用未标记数据的缺点,往往受限于训练数据不足的情况。因此,将半监督学习方法与支持张量机相结合,进而提出了基于Tucker分解的半监督支持张量机算法(Semi-Supervised STM,S3TM)。该算法既可以保持较多的张量结构信息,又能充分利用未标记数据。实验表明,采用该算法的预测准确率达到90.26%,从而验证了所提算法的有效性。

Most data used by traditional machine learning methods belong to vector space.As an important machine learning method,support vector machine (SVM) has better performance in solving small samples,nonlinearity and high- dimensionality problems.However,in practical applications,some data like images and videos are both stored in tensor form.If tensor data are convert into vector data,some original structure and related information may be lost,which will cause dimensional disasters and small samples problems.Therefore,to maintain as much tensor structure information as possible,support tensor machine (STM) based on Tucker decomposition was proposed.Experiments show that this method can significantly improve the classification performance.Meanwhile,as a supervised learning method,support vector machine cannot use unlabeled data,which often encounter problems with insufficient training data.Therefore,semi- supervised support tensor machine based on Tucker decomposition was proposed.This algorithm can not only maintain more tensor structure information,but also make full use of the unlabeled data.Experiments show that the prediction accuracy rate is 90.26%,which validates the effectiveness of the proposed method.