CSCI 3151 - M19 - Feature maps & the kernel trick

This module develops the idea of feature maps and the kernel trick for extending linear models to nonlinear decision boundaries. We introduce feature maps formally, define valid kernel functions (linear, polynomial, RBF), and explain the role of the kernel matrix and positive semi-definiteness. Using small synthetic datasets and the handwritten digits dataset, we compare linear models with kernelized SVMs, examining how kernel and hyperparameter choices (e.g., C, gamma) affect performance. Practical issues such as scaling for kernels, model selection, and evaluation metrics are highlighted, along with a short discussion of ethical and reliability concerns. By the end, students should understand how kernel methods “hide” high-dimensional feature spaces inside familiar optimization frameworks and when such methods are appropriate.

Course module page:
https://web.cs.dal.ca/~rudzicz/Teaching/CSCI3151/2026/index.html#module=3151-M19-kernel-trick

Видео CSCI 3151 - M19 - Feature maps & the kernel trick канала Atlantic AI Institute