Step function

As explained in Grokking Machine Learning

A threshold function that maps an input to one of discrete constant values according to whether the input crosses a specified threshold.

A step function turns a score into a discrete prediction: it returns 1 when the input is nonnegative and 0 when the input is negative. section 5.1

For a perceptron, calculate a weighted score first, then apply the step function: ŷ = step(ax₁ + bx₂ + c). The threshold divides the input space into two zones. section 5.1

Use the function in three straightforward steps:

• Represent labels numerically, such as happy = 1 and sad = 0. section 5.1
• Compute the model score from the features, weights, and bias. section 5.4
• Return 1 for a score of zero or greater; otherwise return 0. section 5.4

Classifying alien moods

Suppose a classifier scores an alien sentence using the counts of words such as aack and beep. A nonnegative score predicts happy, while a negative score predicts sad. The same rule works when the classifier separates points with a line or separates higher-dimensional data with a plane. section 5.1 section 5.4

Figure 5.8 The step function is useful in the study of perceptron models. The output of the step function is 0 when the input is negative and 1 otherwise.

View the graph showing the abrupt change from output 0 for negative inputs to output 1 otherwise. section 5.1

How Grokking Machine Learning covers it

How deep it goes

Defines the threshold rule, writes its formula, graphs its output, and implements it in Python before using it in a perceptron.

Examples

Uses alien moods, word-count features, separating lines, and Python prediction code as concrete examples.

What it assumes

Assumes numerical features and labels, then builds from score calculation to thresholded prediction.

What you can do after

Apply it via a Python prediction function to convert a perceptron score into a binary label.

How it connects

Links binary classification to perceptrons, activation functions, linear classifiers, and gradient descent.

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Also explained in

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  Natural Language Processing in Action, Second EditionA step function maps a value to one of discrete outputs according to whether it crosses a specified threshold.

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Related concepts

• activation functionkind of · An activation function maps a neural-network unit’s or layer’s input to an output, often introducing nonlinearity into the network’s computation.
• perceptronused by · A perceptron is a single-layer computational model and linear classifier that combines weighted inputs with a bias and applies a threshold or activation rule.
• generationused by · Generation is the computational production of outputs from supplied inputs or context, often by applying a model to produce predictions or new content.
• cumulative distribution functionused by · A cumulative distribution function gives the probability that a random variable is less than or equal to each specified value.
• sigmoidalternative to · A sigmoid is a smooth, bounded, S-shaped function that maps real-valued inputs between two limiting values, commonly zero and one.
• language modelused by · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.

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