Linear Algebra and Feature Selection

Curriculum

• Linear Algebra Essentials

  15 Lessons 76 Min

  Here, we’ll cover the linear algebra concepts behind the machine learning algorithms for dimensionality reduction. We'll learn about vectors and matrices, linear equations, eigenvalues and eigenvectors, and more.

  What Does the Course Cover Free Why Linear Algebra? Free Solving Quadratic Equations Free Vectors Free Matrices Free The Transpose of Vectors and Matrices, the Identity Matrix Free Linear Independence and Linear Span of Vectors Free Basis of a Vector Space, Determinant of a Matrix, Inverse of a Matrix Free Solving Equations of the Form A*x=b Free The Gauss Method Free Other Solutions to the Equation A*x=b Free Determining Linear Independence of a Random Set of Vectors Eigenvalues and Eigenvectors Calculating Eigenvalues Calculating Eigenvectors
• Dimensionality Reduction Motivation

  2 Lessons 7 Min

  This section explains the intricacies of the dimensionality reduction process and clarifies why this technique is essential when working with large datasets.

  Feature Selection, Feature Extraction, and Dimensionality Reduction The Curse of Dimensionality
• Principal Component Analysis (PCA)

  4 Lessons 31 Min

  In this part of the course, we explore the Principal Component Analysis (PCA) - one of the most widely used algorithms for dimensionality reduction. We'll demonstrate a practical example combining both feature extraction and feature selection techniques to achieve the desired goal - reducing the number of dimensions in our dataset.

  Principal Component Analysis – Overview A Step-by-Step Explanation of PCA on California Estates – Example The Theory Behind PCA PCA Covariance Matrix in Jupyter – Analysis and Interpretation
• Linear Discriminant Analysis (LDA)

  11 Lessons 60 Min

  In this section, we'll cover another dimensionality reduction technique called Linear Discriminant Analysis (LDA). Here, we'll go through another practical example, showing the methodology behind LDA and its efficiency. We'll also make a comparison between this algorithm and PCA, introducing the advantages of both approaches.

  Overall Mean and Class Means Linear Discriminant Analysis – Overview LDA: Calculating Within- and Between-Class Scatter Matrices A Step-by-Step Еxplanation of LDA on a Wine Quality Dataset – Example Calculating the Within- and Between-Class Scatter Matrices Calculating Eigenvectors and Eigenvalues for the LDA Analysis of LDA LDA vs. PCA Setting Up the Classifier to Compare LDA and PCA Coding the Classifier for LDA and PCA Analysis of the Training and Testing Times for the Classifier and Its Accuracy