Abstract:

To solve the problem of slow convergence after defining loss function as Cosine Margin Loss Function（Cosineface） in convolutional neural network and the defect of measuring feature similarity with L2 norm in practical use, a variable slope Cosine Margin Loss Function （Kcosine） and a multiple-norm method calculating feature similarity are proposed. By adding the cosine slope factor on the basis of cosine margin loss function, intra-class constraints increase with the increase of cosine value, and the intra-class distance is reduced explicitly. At the same time, the face feature similarity vector is constructed by using L2 norm and L∞ norm, and the classification is realized by Support Vector Machine（SVM） so that modifying instability of L2 norm space measurement. The 1∶1 validation experiments on LFW and Agedb databases show that the improved loss function not only accelerates the convergence speed of training, but also reduces the intra-class distance by more than 15%. At the same time, by using multiple-norm features instead of L2 norm, the average recognition rate can be increased by about 0.1%, and the standard deviation of recognition rate can also be reduced.

Key words: loss function, L2-norm, multiple-norm, face recognition

摘要：

针对在卷积神经网络中定义损失函数为余弦裕度损失函数（Cosineface）后导致收敛变慢以及在实际使用过程中使用L2范数衡量特征相似度存在缺陷的问题，提出了斜率可变的余弦裕度损失函数（Kcosine）和多重范数计算特征相似度的方法。该方法通过在余弦裕度损失函数的基础上添加余弦斜率因子，使得损失函数类内约束随着余弦值的增大而逐渐增强，显式地缩小类内距离，同时利用L2范数和L∞范数构建人脸特征相似度向量，并通过支撑向量机（SVM）实现分类，修正L2范数空间衡量的不稳定性。在LFW和Agedb的数据库上1∶1验证实验表明，改进的损失函数不仅加快了训练的收敛速度，并且将类内距离减少15%以上，同时通过使用多重范数特征代替L2范数，可以将识别率均值提升0.1%左右，标准差也有所降低。

关键词: 损失函数, L2范数, 多重范数, 人脸识别