Single Layered Neural Networks in R Programming

A Single Layered Neural Network (SLNN), also called a perceptron, is the simplest form of a neural network where all inputs connect directly to the output through a single set of weights. It is used for tasks like basic pattern recognition, binary classification and simple prediction problems.

A Single Layered Neural Network has:

• One input layer
• One output layer
• No hidden layers
• Straightforward weight updates
• Easy implementation and fast training

It works well when the data is linearly separable.

Architecture of a Single Layered Neural Network

• Let input vector be x = (x1, x2, …, xn)
• Let weights be w = (w1, w2, …, wn)
• Network computes:y = f( w.x+ b) where f is the activation function.

Common Activation Functions

• Step Function: for Perceptron
• Sigmoid: for probability outputs
• Linear Activation: for regression tasks

Step-by-Step Implementation of Single Layered Neural Network in R

Below is the complete step-by-step implementation from scratch

Step 1: Create Dataset

# Simple OR dataset
x1 <- c(0, 0, 1, 1)
x2 <- c(0, 1, 0, 1)
y  <- c(0, 1, 1, 1)  # OR output

Step 2: Initialize Weights and Bias

print("Hello World!")set.seed(10)

w1 <- runif(1)
w2 <- runif(1)
b  <- runif(1)

lr <- 0.1  # learning rate

Step 3: Activation Function (Step Function)

activation <- function(net) {
  if (net >= 0) return(1)
  else return(0)
}

Step 4: Train the Network (Perceptron Learning Rule)

for (epoch in 1:20) {
  
  for (i in 1:length(y)) {
    
    # Forward pass
    net <- w1 * x1[i] + w2 * x2[i] + b
    y_pred <- activation(net)
    
    # Error
    error <- y[i] - y_pred
    
    # Weight update
    w1 <- w1 + lr * error * x1[i]
    w2 <- w2 + lr * error * x2[i]
    b  <- b  + lr * error
  }
}

Step 5: Make Predictions

for (i in 1:4) {
  net <- w1 * x1[i] + w2 * x2[i] + b
  print(activation(net))
}

Output:

[1] 0
[1] 1
[1] 1
[1] 1

Limitations of Single Layered Neural Networks

• Cannot solve non-linear problems like XOR
• No hidden layers, limited learning ability
• Works only for linearly separable data
• Simple decision boundaries