Lectures related to Singular Value Decomposition: Image Compression and Applications

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

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

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

Unsupervised Learning: Principal Component Analysis

Covers unsupervised learning with a focus on Principal Component Analysis and the Singular Value Decomposition.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Tucker Decomposition: Multilinear rank and applications in data compression

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Dimensionality Reduction

Explores Singular Value Decomposition and Principal Component Analysis for dimensionality reduction, with applications in visualization and efficiency.

Singular Value Decomposition

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

Signal Representations

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Singular Value Decomposition, Pseudoinverse

Covers Singular Value Decomposition and Pseudoinverse, explaining their applications in data compression and linear systems.

Principal Component Analysis: Applications and Limitations

Explores the applications and limitations of Principal Component Analysis, including denoising, compression, and regression.

PCA: Directions of Largest Variance

Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.

Unsupervised learning: Young-Eckart-Mirsky theorem and intro to PCA

Introduces the Young-Eckart-Mirsky theorem and PCA for unsupervised learning and data visualization.

Singular Value Decomposition: Applications and Interpretation

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

Convex Optimization: Linear Algebra Review

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Singular Value Decomposition

Introduces Singular Value Decomposition (SVD) in linear algebra, covering matrix factorization and properties with practical examples.

Singular Value Decomposition: Theory and Applications

Explores Singular Value Decomposition theory, properties, uniqueness, matrix approximation, and dimensionality reduction applications.