Applications and examples in image recognition and the principle of error back propagation algorithm

Error back propagation is a commonly used machine learning algorithm and is widely used in neural network training, especially in the field of image recognition. This article will introduce the application, principles and examples of this algorithm in image recognition.

1. Application of error back propagation algorithm

Image recognition is a method that uses computer programs to analyze, process and analyze numbers or images. Methods of understanding to identify information and features. In image recognition, the error back propagation algorithm is widely used. This algorithm achieves the recognition task by training a neural network. A neural network is a computational model that simulates the interactions between neurons in the human brain and is capable of efficiently processing and classifying complex input data. By continuously adjusting the weights and biases of the neural network, the error backpropagation algorithm allows the neural network to gradually learn and improve its recognition capabilities.

The error back propagation algorithm minimizes the error between the output results and the actual results by adjusting the weights and biases of the neural network. The training process consists of the following steps: calculating the output of the neural network, calculating the error, backpropagating the error to each neuron, and adjusting the weights and biases based on the error.

1. Randomly initialize the weights and biases of the neural network.

2. Calculate the output of the neural network by inputting a set of training data.

3. Calculate the error between the output result and the actual result.

4. Back propagate errors and adjust the weights and biases of the neural network.

5. Repeat steps 2-4 until the error reaches the minimum value or the preset training times are reached.

The training process of the error back propagation algorithm can be regarded as an optimization problem, that is, minimizing the error between the output result of the neural network and the actual result. During the training process, the algorithm will continuously adjust the weights and biases of the neural network, so that the error gradually decreases, and ultimately achieves a higher recognition accuracy.

The application of error back propagation algorithm is not only limited to image recognition, but can also be used in speech recognition, natural language processing and other fields. Its widespread application allows many artificial intelligence technologies to be implemented more efficiently.

2. Principle of error back propagation algorithm

The principle of error back propagation algorithm can be summarized in the following steps:

1. Forward propagation: Input a training sample and calculate the output result through forward propagation of the neural network.

2. Calculate the error: Compare the output result with the actual result and calculate the error.

3. Back propagation: Back propagate the error from the output layer to the input layer, adjusting the weight and bias of each neuron.

4. Update weights and biases: Based on the gradient information obtained by backpropagation, update the weights and biases of the neurons to make the error smaller in the next round of forward propagation.

In the error back propagation algorithm, the back propagation process is the key. It passes the error from the output layer to the input layer through the chain rule, calculates the contribution of each neuron to the error, and adjusts the weights and biases according to the degree of contribution. Specifically, the chain rule can be expressed by the following formula:

\frac{\partial E}{\partial w_{i,j}}=\frac{\partial E }{\partial y_j}\frac{\partial y_j}{\partial z_j}\frac{\partial z_j}{\partial w_{i,j}}

Where, E represents the error, w_{i,j} represents the weight connecting the i-th neuron and the j-th neuron, y_j represents the output of the j-th neuron, and z_j represents the weighted sum of the j-th neuron. This formula can be interpreted as that the impact of the error on the connection weight is composed of the product of the output y_j, the derivative of the activation function \frac{\partial y_j}{\partial z_j} and the input x_i.

Through the chain rule, the error can be back-propagated to each neuron and the contribution of each neuron to the error is calculated. Then, the weights and biases are adjusted according to the degree of contribution, so that the error in the next round of forward propagation is smaller.

3. Example of error back propagation algorithm

The following is a simple example to illustrate how the error back propagation algorithm is applied to pictures Identify.

Suppose we have a 28x28 picture of handwritten digits, and we want to use a neural network to recognize this number. We expand this image into a 784-dimensional vector and use each pixel as input to the neural network.

We use a neural network with two hidden layers for training. Each hidden layer has 64 neurons, and the output layer has 10 neurons, representing the numbers 0-9 respectively.

First, we randomly initialize the weights and biases of the neural network. We then input a set of training data and compute the output through forward propagation. Assume that the output result is [0.1,0.2,0.05,0.3,0.02,0.15,0.05,0.1,0.03,0.1], which means that the neural network believes that this picture is most likely to be the number 3.

Next, we calculate the error between the output result and the actual result. Suppose the actual result is [0,0,0,1,0,0,0,0,0,0], which means the actual number of this picture is 3. We can use the cross-entropy loss function to calculate the error, the formula is as follows:

E=-\sum_{i=1}^{10}y_i log(p_i)

Among them, y_i represents the i-th element of the actual result, and p_i represents the i-th element of the output result of the neural network. Substituting the actual results and the output of the neural network into the formula, the error is 0.356.

Next, we backpropagate the error into the neural network, calculate each neuron's contribution to the error, and adjust the weights and biases based on the degree of contribution. We can use the gradient descent algorithm to update the weights and biases as follows:

w_{i,j}=w_{i,j}-\alpha\frac{\partial E }{\partial w_{i,j}}

Among them, \alpha represents the learning rate, which is used to adjust the step size of each update. By continuously adjusting the weights and biases, we can make the output results of the neural network closer to the actual results, thereby improving the recognition accuracy.

The above is the application, principle and example of the error back propagation algorithm in image recognition. The error back propagation algorithm continuously adjusts the weights and biases of the neural network so that the neural network can identify images more accurately and has broad application prospects.

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