Supervised Spectral Space Classifier

Abstract

提出了一种非线性的监督式谱空间分类器(supervised spectral space classifier,简称S3C).S3C 首先将输入数据映射到融合了训练数据判别信息的低维监督式谱空间中,然后在该监督式谱空间中构造最大化间隔的最优分割超平面,并把测试数据以无监督的方式也映射到与训练数据相同的新特征空间中,最后,直接应用之前构建的分类超平面对映射后的测试数据进行分类.由于S3C 使研究者可以直观地观察到变化后的特征空间和映射后的数据,因此有利于对算法的评价和参数的选择.在S3C 的基础上,进一步提出了一种监督式谱空间分类器的改进算法(supervised spectral space transformation,简称S³T).S³T 通过采用线性子空间变换和强迫一致的方法,将映射到监督式谱空间内的数据再变换到指定的类别指示空间中去,从而获得关于测试数据的类别指示矩阵,并在此基础上对其进行分类.S³T 不仅保留了S3C 算法的各项优点,而且还可以用于直接处理多分类问题,抗噪声能力更强,性能更加鲁棒.在人工数据集和真实数据集上的大量实验结果显示,S3C 和S³T 与其他多种著名分类器相比,具有更加优越的分类性能.;This paper proposes a nonlinear classification algorithm S3C (supervised spectral space classifier), short for supervised spectral space classifier. S3C integrates the discriminative information into the construction of the low-dimensional supervised spectral space. The input training data is mapped into the supervised spectral space, followed by the optimization of the partitioning hyperplane with maximum margin. The test data is also transformed into the same feature space via an intermediate “bridge” between the original feature space and the target feature space. The classification result of S3C is obtained by applying the optimal partitioning hyperplane to the transformed test data, directly. S3C enables researchers to examine the transformed data in the supervised spectral space, which is beneficial to both algorithm evaluation and parameter selection. Moreover, the study presents a supervised spectral space transformation algorithm (S³T) on the basis of S3C. S³T (supervised spectral space transformation) estimates the class indicating matrix by projecting the data from the supervised spectral space to the class indicating space. S³T can directly deal with multi-class classification problems, and it is more robust on the data sets containing noise. Experimental results on both synthetic and real-world data sets demonstrate the superiority of S3C and S³T algorithms compared with other state-of-the-art classification algorithms.