Detailed Implementation of Three-Layer BP Neural Network

BP neural network is a classic feedforward network structure in machine learning, particularly suitable for solving nonlinear classification and regression problems. Below describes how to construct a complete three-layer BP network (input layer - hidden layer - output layer) in MATLAB and its core implementation logic: Network Initialization Determine the number of input/output nodes (based on data feature dimensions) and hidden layer neurons (typically determined through empirical formulas or experimentation). When creating network objects using the `newff` function, specify transfer functions for each layer (e.g., tansig for hidden layer, purelin for output layer) and set training algorithms (such as traingdx for gradient descent with momentum). Data Preprocessing Input data requires normalization (using functions like `mapminmax`) to the [-1,1] range to prevent training oscillations caused by dimensional differences. Split the dataset into training, validation, and test sets (recommended ratio 7:2:1). Key Parameter Configuration Configure maximum iterations (epochs), error goal, learning rate (lr), and momentum factor (mc) through `net.trainParam`. Note that excessive learning rates cause oscillations while too small rates lead to slow convergence. Training Process When calling the `train` function, the network automatically performs forward propagation to calculate output errors, then adjusts weights through backpropagation. Each iteration displays current errors, and overfitting can be detected through error curves (early stopping required when validation set errors increase). Result Validation Use the `sim` function for test set predictions, evaluating performance through confusion matrices (for classification problems) or mean squared error (for regression problems). Decision boundaries or prediction curves can be visualized to observe fitting effects. Extension Considerations Hidden layer node count can be determined through trial-and-error or using the formula sqrt(n+m)+a (where n,m are input/output nodes, a is a constant between 1-10) Implement L2 regularization (net.performParam.regularization) to prevent overfitting Using Bayesian regularization training algorithm (trainbr) can automatically optimize weight decay coefficients Code Implementation Notes: - Use `net = newff(P,T,[S1 S2...],{TF1 TF2...},BTF)` to create network with specified architecture - Normalize data: `[Pn,minp,maxp] = mapminmax(P)` - Training call: `[net,tr] = train(net,P,T)` - Simulation: `Y = sim(net,Ptest)` - Monitor training progress through `tr.perf` (performance) and `tr.vperf` (validation performance)