Deep learning is the state-of-art technology in pattern recognition, especially in face recognition. The robustness of the deep network leads a better performance when the size of the training set becomes larger and larger. Convolutional Neural Network (CNN) is one of the most popular deep learning technologies in the modern world. It helps obtain various features from multiple filters in the convolutional layer and performs well in the hand written digits classification. Unlike the unique structure of each hand written digit, face features are more complex, and many difficulties are existed for face recognition in current research field, such as the variations of lighting conditions, poses, ages, etc. So the limitation of the nonlinear feature fitting of the regular CNN appears in the face recognition application. In order to create a better fitting curve for face features, we introduce a polynomial structure to the regular CNN to increase the non-linearity of the obtained features. The modified architecture is named as Convolutional Polynomial Neural Network (CPNN). CPNN creates a polynomial input for each convolutional layer and captures the nonlinear features for better classification. We firstly prove the proposed concept with MNIST handwritten database and compare the proposed CPNN with regular CNN. Then, different parameters in CPNN are tested by CMU AMP face recognition database. After that, the performance of the proposed CPNN is evaluated on three different face databases: CMU AMP, Yale and JAFFE as well as the images captured in real world environment. The proposed CPNN obtains the best recognition rates (CMU AMP: 99.95%, Yale: 90.89%, JAFFE: 98.33%, Real World: 97.22%) when compared to other different machine learning technologies. We are planning to apply the state-of-art structures, such as inception and residual, to the current CPNN to increase the depth and stability as our future research work.
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