Set based image classification technology has been developed successfully in recent decades. Previous approaches dispose set based image classification by employing all the gallery sets to learn metrics or construct the model using a typical number of parameters. However, they are based on the assumption that the global structure is consistent with the local structure, which is rigid in real applications. Additionally, the participation of all gallery sets increases the influence of outliers. This paper conducts this task via sparse projection learning by employing ℓ_2,1 norm from the perspective of the query set. Instead of involving all the image sets, this work devotes to searching for a local region, which is centered with a query set and constructed by the candidates selected from different classes in the gallery sets. By maximizing the inter-class while minimizing the intra-class of the candidates from the gallery sets from the query set, this work can learn a discriminate and sparse projection for image set feature extraction. In order to learn the projection, an alternative updating algorithm to solve the optimization problem is proposed and the convergence and complexity are analyzed. Finally, the distance is measured in the discriminate low-dimensional space using Euclidean distance between the central data point of the query set and the central one of images from the same class. The proposed approach learns the projection in the local set centered with the query set with ℓ_2,1 norm, which contributes to more discriminative feature. Compared with the existing algorithms, the experiments on the challenging databases demonstrate that the proposed simple yet effective approach obtains the best classification accuracy with comparable time cost.

基于集合的图像分类技术在最近几十年中已经成功开发。先前的方法通过使用所有画廊集来学习度量或使用典型数量的参数来构建模型，从而对基于集合的图像分类进行处理。但是，它们基于这样的假设：全局结构与局部结构一致，这在实际应用中是严格的。此外，所有画廊集的参与都会增加离群值的影响。本文采用通过进行疏投影学习这个任务ℓ _2,1从查询集的角度看规范。这项工作不涉及所有图像集，而是致力于搜索局部区域，该区域以查询集为中心，并由从画廊集中不同类别中选择的候选项构成。通过最大化类间，同时最小化来自来自查询集的图库集中的候选者的类内，这项工作可以学习用于图像集特征提取的区分和稀疏投影。为了学习投影，提出了一种替代算法来解决优化问题，并分析了收敛性和复杂性。最后，使用查询集的中心数据点与同一类图像的中心之一之间的欧几里德距离，在可分辨的低维空间中测量距离。ℓ _2,1规范，这有助于更有辨别力的特征。与现有算法相比，在具有挑战性的数据库上进行的实验表明，所提出的简单而有效的方法以可比的时间成本获得了最佳的分类精度。