Previous Lecture: Covered perceptron concept, neurons, and prediction.
Goal of the Lecture: Demonstrate how to train perceptron weights and biases from scratch, including mathematics, coding, and animation.
Key Concepts Covered
Data and Linear Separability
Observation: Data should be linearly separable; can classify data into two classes using a line.
Find a line that can separate data properly for classification.
Iterative Line Adjustment
Process:
Start with a random line.
Adjust the line iteratively by checking points and moving the line.
Goal: Achieve convergence after a set number of iterations.
Identifying Positive and Negative Regions
Use mathematical tools (ex: Desmos) to identify which region (positive or negative) a point belongs to.
Equation Example: 2X + 3y + 5 = 0
Points where 3y + 5 > 0 are in the positive region.
Points where 3y + 5 < 0 are in the negative region.
Transformations for Adjusting Line
Types of Transformations:
Moving line up/down by changing constant term.
Rotating line by changing coefficients of x and y.
Training Process
Steps:
Identify incorrectly classified points.
Adjust weights and biases step by step using learning rate.
Update the line iteratively until proper classification is achieved.
Formal Algorithm (Simplified)
Initialize: Random weights and biases.
Loop: For each epoch (fixed number of iterations, e.g., 1000 times):
Select a random data point.
Check if it's misclassified.
Update weights and biases using learning rate.
Coding Perceptron Algorithm
Model Equation: w0 + w1*x1 + w2*x2 = 0
w0 (bias), w1, and w2 (weights)
Prediction Logic: If w1*x1 + w2*x2 > 0, classify as positive; else, classify as negative.
Updating Weights: Adjust using the identified misclassified points and learning rate.
Implementation Steps
Define function for perceptron that takes data (X, Y) and returns weights.
Initialize bias and weights with zeros.
Loop over epochs to randomly select a point, predict, and update weights using the identified rule.
Utilize visualization tools to animate and visualize the line movement and classification over iterations.
Summary
Perceptron training involves mathematical intuition, coding logic, and iterative improvement.
Correctly adjusting weights converge the model for accurate classification.
Conclusion
Key Takeaway: Understanding and training perceptron involves systematic mathematical adjustments, coding practice, and testing. Proper visualization aids in better understanding.