The Gaussian kernel function is widely used to encode the nonlinear correlations of the face images. However, some issues greatly limit its superiority, for example, it is sensitive to the parameter setting because of its definition based on the exponential operation, on the other hand, the Gaussian kernel needs costly computational time. Besides, the hidden information such as the distance information of the samples is conducive to improving the performance of face recognition. To overcome the above problems, we propose a reciprocal kernel-based weighted collaborative–competitive representation for face recognition. Different from other methods, a new reciprocal kernel is designed to realize the nonlinear representation of the samples. Moreover, a new weight based on the reciprocal kernel is imposed on coding coefficients to disclose the hidden information of the samples in the nonlinear space. With the help of the collaborative–competitive method, the proposed method can well achieve the trade-off between collaborative and competitive representation to promote the performance of face recognition. These factors explicitly encourage the proposed method to be a better representation-type classifier. Finally, extensive experiments are conducted on five benchmark datasets, and the experimental results show that the proposed approach outperforms many state-of-the-art approaches.

高斯核函数被广泛用于编码人脸图像的非线性相关性。但是，某些问题极大地限制了它的优越性，例如，由于其基于指数运算的定义，因此对参数设置很敏感，另一方面，高斯内核需要耗费大量的计算时间。此外，样本的距离信息等隐藏信息有利于提高人脸识别性能。为了克服上述问题，我们提出了一种基于核的倒数加权协作竞争表示法来进行人脸识别。与其他方法不同，设计了一个新的倒数核来实现样本的非线性表示。此外，在编码系数上施加了基于倒数核的新权重，以揭示非线性空间中样本的隐藏信息。借助于协作-竞争方法，所提出的方法可以很好地实现协作和竞争表示之间的权衡，从而提高人脸识别的性能。这些因素明确地鼓励所提出的方法成为更好的表示类型分类器。最后，在五个基准数据集上进行了广泛的实验，实验结果表明，所提出的方法优于许多最新方法。所提出的方法可以很好地实现协作和竞争表示之间的权衡，从而提高人脸识别的性能。这些因素明确地鼓励所提出的方法成为更好的表示类型分类器。最后，在五个基准数据集上进行了广泛的实验，实验结果表明，所提出的方法优于许多最新方法。所提出的方法可以很好地实现协作和竞争表示之间的权衡，从而提高人脸识别的性能。这些因素明确地鼓励所提出的方法成为更好的表示类型分类器。最后，在五个基准数据集上进行了广泛的实验，实验结果表明，所提出的方法优于许多最新方法。