Perceptron

As explained in Machine Learning Algorithms in Depth

A linear binary classifier that predicts a class from the sign of a weighted sum of input features.

A perceptron is a linear binary classifier. For a feature vector x, weights θ, and offset θ₀, it predicts h(x) = sign(θ·x + θ₀), assigning a label of +1 or −1. The equation θ·x + θ₀ = 0 defines its decision boundary: a hyperplane whose normal vector is θ. section 5.2

Training is mistake-driven. Compare each prediction with its ground-truth label y; a negative product y·h(x) indicates disagreement. The implementation initializes θ and θ₀ to zero, repeatedly samples training examples, and updates when y(θ·x + θ₀) ≤ 0. These updates move the decision boundary toward fewer classification mistakes. section 5.2 section 5.8

Iris binary classification

Fit the classifier to iris features, then compare predicted and actual labels in a confusion matrix. True positives and true negatives are correct predictions; false positives and false negatives are mistakes. The same counts support measures such as true positive rate and false positive rate. section 5.2

Figure 5.2 Linear classifier a decision boundary

The two-dimensional diagram shows how a linear decision boundary separates the +1 and −1 sides. section 5.2

How Machine Learning Algorithms in Depth covers it

How deep it goes

Derives the prediction rule and decision-boundary geometry, then gives a from-scratch training implementation and evaluation measures.

Examples

Uses iris binary classification, a two-dimensional decision-boundary figure, implementation pseudocode, and a confusion matrix.

What it assumes

Uses feature vectors, inner products, signed labels, and indicator notation while defining the classifier and its evaluation measures.

What you can do after

Build it from scratch and evaluate its binary predictions with a confusion matrix.

How it connects

Connects linear classifiers to hyperplanes, indicator functions, confusion matrices, ROC curves, and precision-recall curves.

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Also explained in

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  Grokking Machine LearningA processing unit or model that computes a weighted combination of inputs, adds a bias, and applies an activation function.
• 

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  Math and Architectures of Deep LearningA simple linear threshold unit that computes a weighted sum of inputs.
• 

  liveBookmanning.com
  Natural Language Processing in Action, Second EditionA perceptron is a single-layer computational model that computes a weighted sum of inputs and applies a thresholding activation to make a decision.
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  liveBookmanning.com
  Grokking AI Algorithms, Second EditionA perceptron is a computational unit and binary linear classifier that combines weighted inputs with a bias and applies an activation rule.

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This explainer was generated by Manning's knowledge graph from the text of Machine Learning Algorithms in Depth. The section links point to the parts of the book it draws on.