Linearly separable
Linearly separable describes labeled data whose classes can be divided by a single linear decision boundary in feature space.
Grokking Machine Learning
The property of a labeled dataset whose classes can be separated by a single linear boundary.
- How it is used
- Frames linear separability as the test that motivates nonlinear classifiers and kernel methods.
- 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.
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Machine Learning Algorithms in Depth
Linearly separable data is data whose classes can be separated by a linear decision boundary.
- How it is used
- Supports perceptron classification by providing the assumption under which mistake-driven parameter updates converge.
- How deep it goes
- Defines the convergence assumption and links it to updates, data order, shuffling, and implementation, without deriving separability geometrically.
- Examples
- Uses iris feature data, a from-scratch perceptron, and test predictions based on the learned decision boundary.
- What you can do after
- Apply it via a perceptron to understand when finite mistake-driven convergence is expected.
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Deep Learning with R, Third Edition
Linearly separable data is data whose classes can be divided by a linear decision boundary.
- How it is used
- Uses separable synthetic data to teach a complete linear classifier trained with gradient descent.
- 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 you can do after
- Builds a linear classifier from scratch in TensorFlow and visualizes its predictions and learned boundary.
Read how Deep Learning with R, Third Edition explains linearly separable →
Related concepts
- feature interactionaddressed by · A feature interaction is a joint effect in which a model’s output or behavior depends on a combination of input features rather than on each feature independently.
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