Neural Networks
In machine learning, a neural network is a computational model inspired by the structure and function of biological neural networks.
A perceptron is the simplest form of such a model, representing a single unit of computation.
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Neuron
Perceptron
A perceptron is the earliest form of a neural network unit, introduced by Frank Rosenblatt in 1958.
It is a binary classifier that makes predictions based on a linear combination of input features.
Components:
- Inputs: \((x_1, x_2, \dots, x_n)\)
- Weights: \((w_1, w_2, \dots, w_n)\) – relative importance of features
- Bias: \(b\), shifts the decision boundary
- Activation Function: step function threshold
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perceptron
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Perceptron
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Perceptron
Perceptron (Mathematics)
y =
\[\begin{cases}
1 & \text{if } \displaystyle \sum_{i=1}^{n} w_i x_i + b > 0 \\
0 & \text{if } \displaystyle \sum_{i=1}^{n} w_i x_i + b \leq 0
\end{cases}\]
The output is binary (0 or 1), making it suitable for linearly separable classification problems.
Example: Spam Filter
We design a perceptron with the following setup:
\(x_1\): number of times the word “free” appears
\(x_2\): whether the email has an attachment (0/1)
\(x_3\): length of the subject line
Weights: \(w_1 = 2,\; w_2 = 3,\; w_3 = -0.5\)
Bias: \(b = -4\)
