Support Vector Machines by Hand: Separating Lines, Margins, Hinge Loss, Soft Margins, Kernel Tables & Support Vectors
Draw the widest street between two classes. You will score points against a separating line, measure functional and geometric margins, compute the hinge loss, take soft-margin training steps with a fixed learning rate, spot the support vectors, build polynomial and radial kernel tables, classify with given weights per support vector and extend to several classes, with every cell checked as you go.
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About this course
This course builds a support vector machine one cell at a time on fictional toy data. You score tiles against a separating line and predict classes by sign, measure functional and geometric margins with ‖w‖ and rescale a line to read its street width 2 ÷ ‖w‖. You compute the hinge loss, label points inside the margin or misclassified, and compare three lines with the soft-margin objective for three values of C. You take sub-gradient steps with a fixed learning rate and chart the objective per epoch, rebuild w and b from α values and support vectors, build polynomial and radial kernel tables and classify with Σ α·y·K + b and one-vs-rest.
Lessons
- A Separating Line: Scores, Signs and Predicted Classes Pro
- Margins: Functional Margin, Geometric Margin and the Width of the Street Pro
- Hinge Loss: Points Outside, Inside and on the Wrong Side of the Margin Pro
- Soft Margins and C: Trading a Wide Street Against Hinge Loss Pro
- Training by Sub-Gradient Steps: Update Rules, a Fixed Learning Rate and the Objective per Epoch Pro
- Support Vectors: The Few Tiles That Hold the Line Pro
- Kernels: Feature Maps for a Ring-Shaped Set, Polynomial and Radial Kernel Tables Pro
- Capstone: Kernel Decisions Σ α·y·K + b and Several Classes with One-vs-Rest Pro