Research on geometric figure classification algorithm based on Deep Learning

Abstract: In recent years, with the rapid development of computer information technology, the development of artificial intelligence has been accelerating. The traditional geometry recognition technology is relatively backward and the recognition rate is low. In the face of massive information database, the traditional algorithm model inevitably has the problems of low recognition accuracy and poor performance. Deep learning theory has gradually become a very important part of machine learning. The implementation of convolutional neural network (CNN) reduces the difficulty of graphics generation algorithm. In this paper, using the advantages of lenet-5 architecture sharing weights and feature extraction and classification, the proposed geometric pattern recognition algorithm model is faster in the training data set. By constructing the shared feature parameters of the algorithm model, the cross-entropy loss function is used in the recognition process to improve the generalization of the model and improve the average recognition accuracy of the test data set.

• The paper proposes a geometric figure classification algorithm model based on a deep Convolutional Neural Network (CNN), specifically utilizing the LeNet-5 architecture.
• The methodology involves building a geometry database, training the LeNet-5 model with data augmentation, using a cross-entropy loss function, and adjusting parameters through back-propagation.
• The key result shows the CNN model achieves a 90% accuracy rate in classifying geometric figures, demonstrating improved intelligence and accuracy over traditional methods, though noting challenges in image processing time.

The paper "Research on geometric figure classification algorithm based on Deep Learning" addresses the problem of geometric figure recognition using a deep learning approach. The authors propose a geometric pattern recognition algorithm model based on a convolutional neural network (CNN) using the LeNet-5 architecture. The model leverages shared weights and feature extraction to achieve faster training on the dataset. The model uses a cross-entropy loss function to improve generalization and recognition accuracy.

The paper begins by discussing traditional geometric figure recognition techniques and their limitations, such as low recognition rates and the need for manual preprocessing. Deep learning, particularly CNNs, are presented as a solution to overcome these limitations. The authors emphasize the ability of deep learning to train data models and its success in areas like natural language processing and speech recognition.

The authors describe the CNN theory, detailing its structure as an artificial neural network composed of convolution and correlation sampling layers. The paper includes the forward and reverse training propagation processes. The formula for calculating the mapping feature graph and convolution kernel in the CNN is given as:

$$s(i, j) = \sum_{a=0}^{B} \sum_{b=0}^{B} (W_{a,b} * X_{i+a, j+b} + W_m)$$

where:

• $s(i, j)$ is the eigenvector matrix
• $W_{a,b}$ is the convolution kernel matrix
• $X_{i+a, j+b}$ is the two-dimensional input matrix
• $W_m$ is the offset
• $a$ and $b$ are indices for the summation over the convolution kernel
• $B$ is the size of the convolution kernel

The cross-entropy loss function, used for network model construction, is defined as:

$$L = \frac{1}{N} \sum_{n} [y \ln(a) + (1-y) \ln(1-a)]$$

where:

• $L$ is the loss function parameter
• $X$ is the input sample data
• $a$ is the calculation result
• $y$ is the label sheet
• $N$ is the total number of samples

The paper details the model design based on a deep CNN, utilizing the LeNet-5 framework. The process includes:

1. Building a geometry database from Kaggle, expanding the data to create a training set.
2. Setting up the LeNet-5 architecture, which combines feature extraction, image recognition, and self-learning. The architecture consists of one input layer, two convolution layers, two pooling layers, and two fully connected layers.
3. Setting the parameters for the convolution layer, including a step size of 2 and a 5x5 convolution kernel matrix.
4. Setting pooling layer parameters, where the feature map is converted using max pooling.
5. Training the model using 300 test set images, classifying them into triangles, circles, and squares to generate geometric pattern recognition results.

The experimental platform used was python38, PyCharm. The dataset consisted of 300 28x28 gray images of geometric figures. Data augmentation techniques such as turning, folding, and translating were applied to enhance data diversity, resulting in a training set of 2100 images.

The LeNet-5 network model was trained with 10 training times, a 0.001 learning rate, and 0.9 momentum test parameters. After training, the back-propagation parameters were adjusted. The final geometric graph classification result was obtained by importing geometric graphs into the test set.

The paper concludes that the deep learning CNN algorithm has made image classification and recognition more intelligent, significantly improving image recognition accuracy. A geometric figure classification model was established using the LeNet-5 model, which shares characteristic parameters. The model combines the advantages of CNNs, such as sharing weights, self-learning to extract classification features, and network training. The cross-entropy loss function was used to improve the generalization and accuracy of the model, achieving a final accuracy rate of 90%. The authors note existing problems such as complicated image processing and long preprocessing times, as well as challenges in data interface universality when introducing GPUs.