## 1 Introduction
In [12], two consecutive convolution operations were appended to each layer of the CNN, thereby increasing the recognition rate of image classification by doubling the number of feature extracts. However, this procedure has high memory requirements from the system. Focusing on the convergence speed of CNNs, reference [13] introduced multivariable maximum product and interpolation operator theory into the CNN structure using operator theory as the activation function. This study provided a detailed mathematical formula derivation but no application test results. [PERSON] et al. [14] proposed deeply-supervised nets by introducing companion objective functions at all the hidden layers and an overall objective function at the output layer. The companion objective functions are usually an additional constraint/regularization within the learning process. Thus, the performance of this method relies on the design of a companion objective function, but, it is not easy to do that. The CNN technology provides a new method for image feature extraction. Although many scholars have attempted to improve the performance of the classic CNN [15], the following deficiencies in image feature extraction are still observed. * The input value, which is originally changed considerably in a wide range to output within the \((0,1)\) range, can be squeezed when the sigmoid function is used as an activation function. When the training dataset is large, the sigmoid function easily causes gradient saturation and convergence is slowed. * In the CNN, the early stop and regularization strategies are often used to mitigate the overfitting problem. The dataset in the early stop strategy is divided into the training and test sets. The training set calculates the gradient and updates the connection and threshold. The test set evaluates the error. The training stop sign reduces the training set error and increases the test set error. In the regularization strategy, the error objective function considers the factors that describe the complexity. When the number of learning layers in the CNN increases, the capability of these layers to solve the overfitting problem is reduced. * In the training and evaluation phases, the CNN adjusts the cumulative error of the minimum training set of the target gradient through the reverse propagation algorithm and the gradient descent strategy. Not every level of training evaluates the cumulative error but evaluates it after a given interval layer. Although the time lock decreases, the cumulative error increases. To address these problems, this study designs an improved activation function to increase the convergence rate by adding a dropout layer between the fully connected and output layers. This resolves the overfitting problem caused by the increasing number of iterations and introduces the stochastic gradient descent (SGD) optimizer to the gradient descent strategy to reduce the cumulative error and improve the training speed. Thus, a modified CNN algorithm based on dropout and the SGD optimizer (MCNN-DS) is proposed. The remainder of this paper is organized as follows. Section 2 presents some related works. Section 3 is devoted to the description of the fundamentals of our proposed algorithms, and details the proposed algorithms. Section 4 presents the test environment, comparison algorithm, comprehensive experiments, and analysis. Finally, Section 5 concludes this paper and suggests some future research issues.