Linear Algebra for Machine Learning, Level III: Eigenvectors (ML Foundations Series)

• Focus on Eigenvectors and Eigenvalues: This class delves into the critical concepts of eigenvectors and eigenvalues, essential for decomposing matrices—a technique pivotal for understanding and applying various ML algorithms effectively.
• Comprehensive Application in ML: By covering significant machine learning applications such as singular value decomposition (SVD) for dimensionality reduction, the Moore-Penrose pseudoinverse for regression, and principal component analysis (PCA) for pattern recognition, the course bridges theoretical concepts with practical utility in real-world scenarios.
• Advanced Understanding and Skill Development: Building upon the foundational tensors of Linear Algebra for Machine Learning: Intro and matrix properties from Linear Algebra for Machine Learning, Level II: Matrix Tensors, this course equips learners with advanced knowledge and skills, preparing them for sophisticated analyses and applications in ML and beyond.

The Machine Learning Foundations series of online trainings provides a comprehensive overview of all of the subjects — mathematics, statistics, and computer science — that underlie contemporary machine learning techniques, including deep learning and other artificial intelligence approaches. Extensive curriculum detail can be found at the course’s GitHub repo. All of the classes in the ML Foundations series bring theory to life through the combination of vivid full-color illustrations, straightforward Python examples within hands-on Jupyter notebook demos, and comprehension exercises with fully-worked solutions.

The focus is on providing you with a practical, functional understanding of the content covered. Context will be given for each topic, highlighting its relevance to machine learning. You will be better positioned to understand cutting-edge machine learning papers and you will be provided with resources for digging even deeper into topics that pique your curiosity.

There are 14 classes in the series, organized into four subject areas:

Linear Algebra (three classes)

• Linear Algebra for Machine Learning: Intro
• Linear Algebra for Machine Learning, Level II: Matrix Tensors
• Linear Algebra for Machine Learning, Level III: Eigenvectors

Calculus (four classes)

• Calculus for Machine Learning: Intro
• Calculus for Machine Learning, Level II: Automatic Differentiation
• Calculus for Machine Learning, Level III: Partial Derivatives
• Calculus for Machine Learning, Level IV: Gradients & Integrals

Probability and Statistics (four classes)

• Intro to Probability
• Probability II and Information Theory
• Intro to Statistics
• Statistics II: Regression and Bayesian

Computer Science (three classes)

• Intro to Data Structures and Algorithms
• DSA II: Hashing, Trees, and Graphs
• Optimization

Each of the four subject areas are fairly independent; however, theory within a given subject area generally builds over the 3-4 classes — topics in later classes of a given subject area often assume an understanding of topics from earlier classes. Work through the individual classes based on your particular interests or your existing familiarity with the material.

(Note that at any given time, only a subset of the ML Foundations classes will be scheduled and open for registration. To be pushed notifications of upcoming classes in the series, sign up for the instructor’s email newsletter at jonkrohn.com.)

This class, Linear Algebra for Machine Learning Level III: Eigenvectors, builds on the tensors of Linear Algebra for Machine Learning Intro and the matrix properties of Linear Algebra for Machine Learning Level II to decompose matrices into their characteristic elements. These characteristic elements — called eigenvectors and eigenvalues — are used in a wide range of ML approaches. We’ll explore some of these approaches in theory and in practice during class, including singular value decomposition (SVD) for dimensionality reduction, the Moore-Penrose pseudoinverse for regression, and principal component analysis (PCA) for identifying meaningful patterns.