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This lecture covers the concept of polynomial feature expansion in SVMs, the role of high-dimensional spaces in classification, and Cover's Theorem. It explains how SVMs can handle non-linear separable data using the kernel trick and the importance of support vectors. The instructor also discusses the Lagrangian formulation, constrained optimization, and the dual problem in SVMs. Additionally, it explores the practical applications of SVMs in image analysis, such as SLIC superpixels and mitochondria segmentation.