Lectures related to Mercer Theorem and Kernels

Kernels: Nonlinear Transformations

Explores kernels for simplifying data representation and making it linearly separable in feature spaces, including popular functions and practical exercises.

Feature Expansion: Kernels and KNN

Covers feature expansion, kernels, and K-nearest neighbors, including non-linearity, SVM, and Gaussian kernels.

Feature Maps and Kernels

Covers feature maps, Representer theorem, kernels, and RKHS in machine learning.

Kernel Regression: K-nearest Neighbors

Covers the concept of kernel regression and K-nearest neighbors for making data linearly separable.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Support Vector Machines: Kernel Tricks

Explores kernel tricks in support vector machines for efficient computation in high-dimensional spaces without explicit transformation.

Kernel Regression: Basics and Applications

Explores kernel regression, the curse of dimensionality, and random features in neural networks.

Linear Algebra in 3D: Images and Kernels

Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Kernel Methods: RKHS and Kernels

Explores RKHS, positive definite kernels, and the Moore-Aronszajn theorem in kernel methods.

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Regression: Exercises

Covers exercises on regression functions using RLS, WLS, and LWR.

Nonlinear SVM: Kernels and Dual Optimization

Explores transforming data with nonlinear maps, kernels, dual optimization, and interpreting SVM results.

Linear Transformations: Matrices and Kernels

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Linear Transformations: Isomorphism and Dimension

Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.

Vectors: Coordinate Calculations

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Linear Algebra: Linear Transformations and Matrices

Explores linear transformations, matrices, kernels, and images in algebra.