# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 901-914. doi: 10.3934/dcdss.2019060

## An efficient face recognition algorithm using the improved convolutional neural network

 Qingdao Vocational and Technical College of Hotel Management, Qingdao 266100, China

* Corresponding author: Honggang Yu

Received  August 2017 Revised  December 2017 Published  November 2018

This paper concentrates on the problem of human face recognition problem, which is a crucial problem in computer vision. In this paper, the semi-supervised learning based convolutional neural network is used to implement the face recognition system with high efficiency. Convolutional neural networks denote a multi-layer neural network, in which each layer is made up of multiple two-dimension planes and each plane consists of a lot of independent neurons. To extract the rich and discriminative information of human face images, the sparse Laplacian filter learning is utilized to learn the filters of the network with a large scale unlabeled human face images. Afterwards, a softmax classifier layer is trained by multi-task learning using only a small number of labeled human face images as the output layer. In the end, a series of experiments are conducted to test the performance of our proposed algorithm. Experimental results show that face recognition accuracy of the proposed improved CNN method performs better than other methods.

Citation: Honggang Yu. An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 901-914. doi: 10.3934/dcdss.2019060
##### References:

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##### References:
Internal structure of the convolutional neural networks
Flowchart of the proposed CNN based human face recognition system
Rate of face recognition on the test dataset of ORL database
Rate of face recognition on the unlabeled training dataset of ORL database
Rate of face recognition on the test dataset of Yale database
Rate of face recognition on the unlabeled training dataset of Yale database
Rate of face recognition on the test dataset of Extended Yale B database
Rate of face recognition on the unlabeled training dataset of Extended Yale B database
Average face recognition accuracy for different methods
Description of the CNN baseline model
 Name Description Input layer $3\times 24\times 24$ color RGB in the range $[0,1]$ Convolution 1 $3\times 5\times 5$ kernels, 64 output maps of $20\times 20$ Convolution 2 $64\times 5\times 5$ kernels, 64 output maps of $6\times 6$ Convolution 3 $64\times 3\times 3$ kernels, 64 output maps of $1\times 1$ Pooling 1 $2\times 2$ non-overlapping subsampling, 64 output maps of $10\times 10$ Pooling 2 $2\times 2$ non-overlapping subsampling, 64 output maps of $3\times 3$ Fully connected 1 HalfRect Units with 64 output neurons Fully connected 2 10 output neurons
 Name Description Input layer $3\times 24\times 24$ color RGB in the range $[0,1]$ Convolution 1 $3\times 5\times 5$ kernels, 64 output maps of $20\times 20$ Convolution 2 $64\times 5\times 5$ kernels, 64 output maps of $6\times 6$ Convolution 3 $64\times 3\times 3$ kernels, 64 output maps of $1\times 1$ Pooling 1 $2\times 2$ non-overlapping subsampling, 64 output maps of $10\times 10$ Pooling 2 $2\times 2$ non-overlapping subsampling, 64 output maps of $3\times 3$ Fully connected 1 HalfRect Units with 64 output neurons Fully connected 2 10 output neurons
The face recognition accuracy using the CMU PIE database (mean $\pm$ std.dev%)
 Approach Unlabeled set Test set Fisherface 21.8$\pm$1.5 21.8$\pm$1.5 Laplacianface 35.9$\pm$1.6 34.8$\pm$1.4 SDA 41.8$\pm$1.9 43.8$\pm$1.8 LDA self-training 48.9$\pm$2.2 50.3$\pm$2.1 CNN 36.8$\pm$4.7 38.7$\pm$4.6 The improved CNN 91.8$\pm$1.1 92.1$\pm$1.2
 Approach Unlabeled set Test set Fisherface 21.8$\pm$1.5 21.8$\pm$1.5 Laplacianface 35.9$\pm$1.6 34.8$\pm$1.4 SDA 41.8$\pm$1.9 43.8$\pm$1.8 LDA self-training 48.9$\pm$2.2 50.3$\pm$2.1 CNN 36.8$\pm$4.7 38.7$\pm$4.6 The improved CNN 91.8$\pm$1.1 92.1$\pm$1.2
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