Classification

Definition

Classification is the task of assigning an input to a category.

Example:

input -> category

More concrete:

email -> spam or not spam
image -> cat or dog
measurement -> pass or fail

Classification = choosing a class for an input.

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Class

A class is one possible category.

Example:

spam
not spam

or:

cat
dog
bird

The classifier's job is to pick one of the allowed classes.

A class is an output category.

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Input

The input is the thing being classified.

Example:

email text
image data
person measurements
sensor readings

In this series, we often represent input as a vector.

Example:

input = [x1, x2, x3]

Classification often starts with vector data.

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Output

The output is the predicted class.

Example:

input: [2, 5]
output: class A

The output is not just a number unless the classes are encoded numerically.

Example:

0 = not spam
1 = spam

The number is an encoding of the class.

Classification output is a category, even when represented by a number.

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Classification vs Regression

Classification predicts a category.

Regression predicts a numerical value.

Classification:

input -> cat
input -> dog

Regression:

input -> price
input -> temperature

This chapter focuses on classification.

Classification chooses a class. Regression estimates a value.

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Decision Rule

A classifier needs a rule for deciding the class.

Example:

if score >= 0:
  class A
else:
  class B

The rule turns a computed score into a category.

Classification requires a decision rule.

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Why Classification Matters Here

The previous chapter ended with weighted sums.

Classification asks:

Can a weighted sum produce a decision?

That question leads to perceptrons.

A perceptron is a simple classifier built from:

input vector
weights
weighted sum
threshold
class output

Classification is where weighted vector computation becomes a decision.

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Final Summary

• Classification assigns inputs to categories.
• A class is a possible category.
• Inputs are often represented as vectors.
• Outputs are predicted classes.
• Classification differs from regression.
• A classifier needs a decision rule.
• Perceptrons are simple linear classifiers.