Lectures related to Latent Factor Analysis: Movie Genre Classification

Singular Value Decomposition

Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Singular Value Decomposition

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions for solving linear systems and simulating dynamics.

Spectral Decomposition and SVD

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Singular Value Decomposition: Example

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Singular Value Decomposition: Image Compression and Applications

Covers Singular Value Decomposition, focusing on its application in image compression and data representation.

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.

Jordan Normal Form: Theory and Applications

Explores the Jordan normal form and its applications in linear algebra, focusing on diagonalization and cyclic bases.

Singular Value Decomposition: Applications and Interpretation

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

Orthogonal Projections and Reflections

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Spectral Clustering: Theory and Applications

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.