Explain the Perceptron learning algorithm. Describe the weight and bias update rules and illustrate the algorithm with a suitable example.

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## Perceptron learning algorithm

A perceptron is a linear binary classifier. For input vector $x$, weights $w$, and bias $b$, compute $z=w^Tx+b$ and predict 1 when $z\ge0$, otherwise 0.

For target $y\in\{0,1\}$ and prediction $\hat y$, update on mistakes:

$$w\leftarrow w+\eta(y-\hat y)x,\qquad b\leftarrow b+\eta(y-\hat y)$$

where $\eta>0$ is the learning rate. Repeat over training examples until a stopping condition is reached. The algorithm converges in finite updates for linearly separable data; it may not converge for non-separable data.

```mermaid
flowchart TD
A[Initialize weights and bias] --> B[Choose training example]
B --> C[Compute prediction]
C --> D{Correct?}
D -->|No| E[Update weights and bias]
D -->|Yes| F[Next example]
E --> F
F --> G{Stopping condition met?}
G -->|No| B
G -->|Yes| H[Return classifier]
```

Perceptron learning algorithm

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