Compared with the traditional classification task based on a single image, an image set contains more complementary information, which is of great benefit to correctly classify a query subject. Thus, image set classification has attracted much attention from researchers. However, the main challenge is how to effectively represent an image set to fully exploit the latent discriminative feature. Unlike in previous works where an image set was represented by a single or a hybrid mode, in this paper, we propose a novel multi-model fusion method across the Euclidean space to the Riemannian manifold to jointly accomplish dimensionality reduction and metric learning. To achieve the goal of our framework, we first introduce three distance metric learning models, namely, Euclidean-Euclidean, Riemannian-Riemannian and Euclidean-Riemannian to better exploit the complementary information of an image set. Then, we aim to simultaneously learn two mappings performing dimensionality reduction and a metric matrix by integrating the two heterogeneous spaces (i.e., the Euclidean space and the Riemannian manifold space) into the common induced Mahalanobis space in which the within-class data sets are close and the between-class data sets are separated. This strategy can effectively handle the severe drawback of not considering the distance metric learning when performing dimensionality reduction in the existing set based methods. Furthermore, to learn a complete Mahalanobis metric, we adopt the L_2,1 regularized metric matrix for optimal feature selection and classification. The results of extensive experiments on face recognition, object classification, gesture recognition and handwritten classification demonstrated well the effectiveness of the proposed method compared with other image set based algorithms.

与基于单个图像的传统分类任务相比，图像集包含更多的补充信息，这对于正确地对查询主题进行分类非常有帮助。因此，图像集分类引起了研究人员的广泛关注。然而，主要的挑战是如何有效地表示图像集以充分利用潜在的区分特征。与以前的图像集以单一或混合模式表示的作品不同，本文提出了一种跨欧氏空间到黎曼流形的新型多模型融合方法，以共同完成降维和度量学习。为了实现我们框架的目标，我们首先介绍三种距离度量学习模型，即欧几里得-欧几里得，黎曼-黎曼和欧几里得-黎曼更好地利用图像集的互补信息。然后，我们的目标是通过将两个异构空间（即欧几里得空间和黎曼流形空间）整合到内部类数据集接近的公共感应马哈拉诺比斯空间中，同时学习两个执行降维和度量矩阵的映射类之间的数据集是分开的。该策略可以有效地解决严重的缺点，即在现有的基于集合的方法中执行降维时不考虑距离度量学习。此外，要了解完整的Mahalanobis指标，我们采用 我们的目标是通过将两个异质空间（即欧几里得空间和黎曼流形空间）整合到公共诱导的Mahalanobis空间中，同时学习两个执行降维和度量矩阵的映射，其中类内数据集接近，类之间的数据集是分开的。该策略可以有效地解决严重的缺点，即在现有的基于集合的方法中执行降维时不考虑距离度量学习。此外，要了解完整的Mahalanobis指标，我们采用 我们的目标是通过将两个异质空间（即欧几里得空间和黎曼流形空间）整合到公共诱导的Mahalanobis空间中，同时学习两个执行降维和度量矩阵的映射，其中类内数据集接近，类之间的数据集是分开的。该策略可以有效地解决严重的缺点，即在现有的基于集合的方法中执行降维时不考虑距离度量学习。此外，要了解完整的Mahalanobis指标，我们采用 该策略可以有效地解决严重的缺点，即在现有的基于集合的方法中执行降维时不考虑距离度量学习。此外，要了解完整的Mahalanobis指标，我们采用 该策略可以有效地解决严重的缺点，即在现有的基于集合的方法中执行降维时不考虑距离度量学习。此外，要了解完整的Mahalanobis指标，我们采用L _2,1正则化度量矩阵，用于最佳特征选择和分类。与其他基于图像集的算法相比，在面部识别，对象分类，手势识别和手写分类方面的大量实验结果很好地证明了该方法的有效性。