# American Institute of Mathematical Sciences

February  2020, 3(1): 51-64. doi: 10.3934/mfc.2020005

## An improved deep convolutional neural network model with kernel loss function in image classification

 1 Key Laboratory of Education Informatization for Nationalities, Ministry of Education, Yunnan Normal University, Kunming 650500, China 2 School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China

* Corresponding author: Tianwei Xu

Received  December 2019 Revised  December 2019 Published  February 2020

Fund Project: This work is supported by National Natural Science Foundation of China (No. 61862068)

To further enhance the performance of the current convolutional neural network, an improved deep convolutional neural network model is shown in this paper. Different from the traditional network structure, in our proposed method the pooling layer is replaced by two continuous convolutional layers with $3 \times 3$ convolution kernel between which a dropout layer is added to reduce overfitting, and cross entropy kernel is used as loss function. Experimental results on Mnist and Cifar-10 data sets for image classification show that, compared to several classical neural networks such as Alexnet, VGGNet and GoogleNet, the improved network achieve better performance in learning efficiency and recognition accuracy at relatively shallow network depths.

Citation: Yuantian Xia, Juxiang Zhou, Tianwei Xu, Wei Gao. An improved deep convolutional neural network model with kernel loss function in image classification. Mathematical Foundations of Computing, 2020, 3 (1) : 51-64. doi: 10.3934/mfc.2020005
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Mini-network replacing the $3 \times 3$ convolutions
kernel size: $3 \times 3$, stride: 2
Max pooling operation, kernel size: $4\times 4$, stride: 2
Dropout workflow
The improved network structure
The curve of recognition accuracy of Alexnet network and improved network with the training times on cifar-10
The curve of recognition accuracy of VGGNet and improved network with the training times on cifar-10
The curve of recognition accuracy of Google network and improved network with the training times on cifar-10
The curve of recognition accuracy of Alexnet network and improved network with the training times on Minist
The curve of recognition accuracy of VGGNet and improved network with the training times on Minist
The curve of recognition accuracy of GoogleNet network and improved network with the training times on Mnist
 Parameters Value CPU: Intel core i9-9900k GPU: NVIDIA GeForce RTX 2080ti RAM: 16.0 GB OS: WIN10 64-bit Develop software: Python3.7 + TensorFlow framework (GPU mode)
 Parameters Value CPU: Intel core i9-9900k GPU: NVIDIA GeForce RTX 2080ti RAM: 16.0 GB OS: WIN10 64-bit Develop software: Python3.7 + TensorFlow framework (GPU mode)
 Network Cifar Mnist Alexnet: train acc:0.95, test acc:0.78 train acc:0.98, test acc:0.97 VGGNet: train acc:0.98, test acc:0.83 train acc:0.99, test acc:0.98 Google network: train acc:1.0, test acc:0.90 train acc:1.0, test acc:1.0 Improve network: train acc:1.0, test acc:0.94 train acc:1.0, test acc:1.0
 Network Cifar Mnist Alexnet: train acc:0.95, test acc:0.78 train acc:0.98, test acc:0.97 VGGNet: train acc:0.98, test acc:0.83 train acc:0.99, test acc:0.98 Google network: train acc:1.0, test acc:0.90 train acc:1.0, test acc:1.0 Improve network: train acc:1.0, test acc:0.94 train acc:1.0, test acc:1.0
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