In image set classification, dual linear regression classification (DLRC) has shown the excellent performance on face image data without the interference of the complex background. However, DLRC could not well identify the data set with the complex background. The complex background means that the background is cluttered and the viewpoint is unusual or the object is partially occluded. This paper proposes a new model, kernelized dual regression (KDR), based on DLRC and the kernel trick which is a useful technique in image classification. Different from DLRC, KDR adopts a block partitioning strategy to extract the local information, which is able to conquer the shortcoming of DLRC. To capture the nonlinear relationship between the training set and test set, KDR tactfully maps these image sets into a high-dimensional feature space by adopting the nonlinear mapping associated with the Gaussian kernel function. In the reproducing kernel Hilbert space (RKHS), KDR can find the joint coefficients by minimizing the distance between training set and test set, and has a closed-form solution. Extensive experiments on four datasets show that KDR could achieve better classification performance than that of DLRC and other existing methods.

在图像集分类中，双重线性回归分类（DLRC）在人脸图像数据上显示了出色的性能，而没有复杂背景的干扰。但是，DLRC无法很好地识别具有复杂背景的数据集。复杂的背景意味着背景杂乱，视点不正常或对象被部分遮挡。本文提出了一种基于DLRC和核技巧的核化对偶回归（KDR）模型，该模型是图像分类中的一种有用技术。与DLRC不同，KDR采用块划分策略提取本地信息，从而可以克服DLRC的缺点。为了捕获训练集和测试集之间的非线性关系，KDR通过采用与高斯核函数关联的非线性映射，将这些图像集巧妙地映射到高维特征空间。在再现内核希尔伯特空间（RKHS）中，KDR可以通过最小化训练集和测试集之间的距离来找到联合系数，并且具有封闭形式的解决方案。在四个数据集上的大量实验表明，与DLRC和其他现有方法相比，KDR可以实现更好的分类性能。