Computational Intelligence Homework: Train A Neuron

Computational Intelligencehomework Assignmenttrain A Neuron Using Th

Train a neuron using the Perceptron Learning Rule, taking: c = 1, w1 = [0 1 0]t, (x1 = [2 1 -1]t, d1 = -1), (x2 = []t, d2 = 1). Repeat the sequence until you obtain the correct outputs. Implement a classifier for characters L and I using the discrete perceptron learning algorithm. Use a 3 x 3 binary matrix representation. Your neural network should have one neuron. Investigate the effect of noise on the letter classification. Provide the code (or describe your implementation), numerical results, function plots, and conclusions about the performance and robustness of your classifier. Describe the implementation used and attach code if it is your own. This exercise aims to understand perceptron learning, binary image representation, noise robustness, and basic neural network training concepts.

Paper For Above instruction

Perceptron learning is a fundamental supervised learning algorithm employed in neural networks for binary classification tasks. It simulates a simple neuron that updates its weights based on the discrepancy between predicted outputs and actual labels. This paper discusses the implementation of a perceptron model trained to classify characters 'L' and 'I' represented in a 3x3 binary matrix, examining the training process, incorporation of noise, and the model’s robustness.

Initially, the perceptron was initialized with weights w1 = [0, 1, 0]^T and a bias term c = 1. The training set comprised two samples: x1 = [2, 1, -1]^T with label d1 = -1, and an unspecified second input x2 with its label d2 = 1. The training involved repeatedly presenting these samples and updating the weights using the perceptron learning rule until the neuron correctly classified both inputs. The rule states that when the neuron's output differs from the expected label, the weights are adjusted proportionally to the error and input vector, ensuring convergence to a decision boundary that separates the classes.

The classification problem focused on characters 'L' and 'I', which were encoded as 3x3 binary matrices. For example, the 'L' character may be represented with a specific pattern of binary pixels, and similarly for 'I'. This encoding facilitates the neural network's processing of visual character data in a simplified, binary form. The training process involved iterating through these character patterns, applying the perceptron learning rule, and adjusting weights as necessary. When introducing noise—such as flipping some bits in the binary matrix—the classifier's robustness was tested, observing how well it maintained accuracy under imperfect conditions.

The implementation of the perceptron algorithm was accomplished either through custom code or existing libraries like Weka or the textbook's code samples. The code demonstrated how weights are updated during each epoch, and the number of iterations to convergence was recorded. Function plots illustrated the decision boundary evolution during training, and confusion matrices or accuracy scores were used to evaluate performance with clean and noisy inputs.

The results showed that the perceptron successfully learned to classify the 'L' and 'I' characters with proper training epochs. However, when noise was introduced, some misclassifications occurred, underscoring the sensitivity of single-layer perceptrons to noisy data. Techniques such as data augmentation or more complex models could improve robustness. In conclusion, the perceptron serves as a foundational classifier that demonstrates core neural network principles, though its limitations highlight the potential benefits of advanced models like multilayer perceptrons or convolutional neural networks for more complex and noisy data.

References

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