Binary Classification

Definition

Binary classification is classification with two possible classes.

Examples:

spam or not spam
pass or fail
yes or no
positive or negative

Binary classification = choosing between two classes.

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Binary Labels

The two classes are often encoded numerically.

Common encodings:

0 and 1

or:

-1 and 1

The perceptron often uses:

-1 and 1

because the learning rule becomes simple.

Binary labels are numeric representations of two classes.

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Binary Prediction

A binary classifier produces one of two outputs.

Example:

if score >= 0:
  prediction = 1
else:
  prediction = -1

The score is continuous or numerical.

The prediction is categorical.

The classifier turns a score into one of two labels.

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Decision Boundary

Binary classification divides the input space into two regions.

For a linear classifier:

dot(w, x) + b = 0

One side is class 1.

The other side is class -1.

A binary linear classifier splits space into two decision regions.

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Example

Suppose:

score = 2*x1 - x2 + 1

Decision:

score >= 0 -> class 1
score < 0  -> class -1

Input:

x = [3, 4]

Score:

2*3 - 4 + 1 = 3

Prediction:

class 1

Binary classification uses the sign of the score to choose a class.

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Binary vs Multi-Class

Binary classification has two classes.

Multi-class classification has more than two.

Binary:

cat or dog

Multi-class:

cat, dog, bird, horse

This chapter focuses on binary classification because the perceptron is easiest to understand there first.

Binary classification is the simplest classification setting.

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Why It Matters

Binary classification is the first step toward understanding learned decision systems.

It gives a clean structure:

input -> score -> threshold -> one of two classes

The perceptron is a direct implementation of that structure.

Binary classification is the simplest setting for perceptrons.

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Final Summary

• Binary classification chooses between two classes.
• Labels are often encoded as 0/1 or -1/1.
• Perceptrons commonly use -1/1.
• A score is converted into one of two predictions.
• A linear boundary divides the space into two regions.
• Binary classification is the simplest classification case.