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Linearly separable

As explained in Deep Learning with R, Third Edition

Linearly separable data is data whose classes can be divided by a linear decision boundary.

Linearly separable data contains classes that a straight-line decision boundary can divide. In two dimensions, a linear classifier predicts w1*x + w2*y + b and learns its coefficients from labeled points. section 3.3.2

Two separable point clouds

Generate 1,000 negative and 1,000 positive two-dimensional samples, combine them with zero-or-one labels, and plot the classes. Train TensorFlow variables W and b with mean squared error and gradient descent. After 40 steps, the loss falls from 4.5364 to 0.0289; thresholding predictions at 0.5 separates the plotted points, and the learned boundary can be drawn as a red line.

How Deep Learning with R, Third Edition covers it

How deep it goes
Works through data generation, prediction, loss, gradients, updates, thresholding, and boundary plotting, without deeper classifier theory.
Examples
Uses two Gaussian point clouds in a two-dimensional plane, binary labels, training-loss output, prediction colors, and a plotted boundary.
What it assumes
Assumes tensors, variables, tensor operations, and gradient computation, while demonstrating their use in a full model.
What you can do after
Builds a linear classifier from scratch in TensorFlow and visualizes its predictions and learned boundary.
How it connects
Connects linear classifiers with affine transformations, gradient descent, mean squared error, and decision boundaries.
Cover of Deep Learning with R, Third Edition
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This explainer was generated by Manning's knowledge graph from the text of Deep Learning with R, Third Edition. The section links point to the parts of the book it draws on.