Assignment #$4$: Understanding and Implementing Backpropagation Networks in MATLAB

Objective:

The objective of this assignment is to understand the principles of backpropagation, implement a neural network with backpropagation from scratch in MATLAB, and analyze its performance on a given dataset.

Implementation

Neural Network Initialization

Initialize a neural network with one hidden layer.

Choose appropriate activation functions for the hidden and output layers.

Forward Propagation

Implement the forward propagation process in MATLAB.

Compute the output of the network for a given input.

Backpropagation Algorithm

Implement the backpropagation algorithm to update the weights.

Include the calculation of gradients for each layer.

Implement gradient descent to minimize the loss function.

Training the Network

Train the network on a simple dataset $($e$.$g$.,$ XOR problem$).$

Plot the loss function over iterations to visualize the training process.

Experimentation

Dataset for Comparison

Use a more complex dataset $($e$.$g$.,$ Iris dataset or MNIST dataset$).$

Split the dataset into training and testing sets.

Performance Evaluation

Train the network on the training set.

Evaluate its performance on the testing set using appropriate metrics $($accuracy$,$ precision, recall, etc.$).$

Experiment with different network architectures $($e$.$g$.,$ varying the number of neurons in the hidden layer$)$ and learning rates.

Compare and discuss the results.

Analysis and Reporting

Analysis

Discuss the convergence behavior of the network.

Analyze the impact of different activation functions and learning rates on the network's performance.

Comment on the decision boundaries formed by the network.

Report

Prepare a detailed report documenting the theory, implementation, experimentation, and analysis.

Include code snippets, plots, and performance metrics in the report.

Conclude with insights and learnings from the assignment.

Submission Guidelines:

Create a whole Pdf file contains and submit it:

The MATLAB code files for the neural network implementation.

The MATLAB Live Script $($or equivalent$)$ with the experimentation and plots.

Sample Datasets:

Simple Dataset:

XOR Gate: $(0,0)->0,(0,1)->1,(1,0)->1,(1,1)->0(0,0)\backslash$rightarrow $0,(0,1)\backslash$rightarrow $1,(1,0)\backslash$rightarrow $1,(1,1)\backslash$rightarrow $0(0,0)->0,(0,1)->1,(1,0)->1,(1,1)->0$

Complex Dataset:

Iris Dataset $($available from UCI Machine Learning Repository$)$

MNIST Dataset $($available from Yann LeCun's website$)($provide me every step and complete codes $)$