Abstract: Small sample size is one challenging problem for face recognition. In many practical applications such as ID card identification, e-passport, even there is only single sample per person. Many traditional methods fail to work in this scenario because there are not enough samples for learning. This paper proposes a novel method which is based on manifold learning to solve this problem. Firstly, this proposed method views local feature (eyes, nose, mouth) of a face as a manifold and uses self-organization mapping neural network to train a multi-manifold structure. Then it associates each manifold by connection operator on frame bundle and learns the directions of inter- manifold and intra-manifold which are not sensitive to the variations of the input. Finally, it adds this additional information to supervised training. The proposed method combines neural network and manifold learning, changing single sample problem to multi-manifold matching problem. Experiments on well-known face databases ORL, UMIST, FERET and AR show that the proposed method outperforms some renowned methods and gets a better performance when facing the problem of variation of expression and pose, etc.

Key words: connection learning, frame bundle, multi-manifold, horizontal space, vertical space, one training sample

摘要： 人脸识别问题中，经常会面临样本少的情况，在身份证识别、电子护照识别等系统中，甚至只有一个训练样本，很多传统人脸识别方法在处理单样本时将失效。从流形学习角度出发提出了一种有效解决单样本人脸识别的方法。以自组织映射神经网络为基础，将人脸局部特征（眼、鼻、嘴等）视为一个流形，训练出多流形结构。利用联络关联不同的流形，同时学习出局部特征流形间与流形内的方向变化信息，再进行有监督的训练。整个方法结合了神经网络学习和流形学习，将单样本人脸识别问题转换成多流形匹配问题。在著名人脸库ORL、UMIST、FERET、AR上的实验显示该算法在处理单样本问题时优于已有算法，在处理姿态、表情等变化问题时也表现出很好的效果。

关键词: 联络学习, 标架丛, 多流形, 横空间, 纵空间, 单样本训练