Basics of Linear Algebra for AI and ML [with code]: Part 1

AI Data Scientist Expert

Linear algebra serves as the backbone for many machine learning algorithms. Understanding operations like eigenvalue and SVD is essential for dimensionality reduction, which allows for handling high-dimensional datasets effectively. For example, PCA utilizes SVD to transform data into a lower-dimensional form while preserving variance, making it a critical technique in preprocessing steps of data-driven models.

AI Machine Learning Engineer

The practical application of these linear algebra concepts directly influences machine learning model efficiency. Each operation from matrix multiplication to eigenvalue decomposition governs how algorithms learn from data. For instance, solving systems of linear equations using matrix equations is crucial in linear regression—often used in predicting outcomes based on various features in datasets such as house pricing.

Vectors

Each data point in machine learning, such as house price predictions, is represented as a vector.

Matrices

A dataset for multiple houses can be represented as a matrix, capturing different features per observation.

Eigenvalue Decomposition

It is used to understand data correlations and dimensionality reduction in algorithms.

Singular Value Decomposition (SVD)

SVD is fundamental in applications like Principal Component Analysis (PCA) for simplifying datasets.