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Linearly separable

As explained in Grokking Machine Learning

The property of a labeled dataset whose classes can be separated by a single linear boundary.

A labeled dataset is linearly separable when one straight boundary can place its classes on opposite sides. In one dimension, that boundary is a point; in two dimensions, it is a line. When no such boundary exists, adding features can sometimes make the transformed dataset separable by a plane while producing a nonlinear boundary after projection. section 11.3

From a line to a curve

A dataset arranged in a circular pattern cannot be separated by a line. Raising each point by its squared distance from the origin creates a three-dimensional dataset that a plane can separate; projecting that plane back produces the circular classifier x1² + x2² = 1. Similarly, adding x1x2 helps separate a modified XOR dataset.

How Grokking Machine Learning covers it

How deep it goes
Defines separability geometrically and works through feature transformations, while deferring the full theory of kernels and feature maps.
Examples
Uses circular data, modified XOR, one-dimensional points, polynomial features, and RBF-transformed datasets.
What you can do after
Evaluate whether a dataset needs a nonlinear boundary and understand how feature transformations can make separation possible.
How it connects
Connects linear separability with support vector machines, nonlinear classifiers, kernel methods, feature maps, and radial basis functions.
Cover of Grokking Machine Learning
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