Linear Algebra And Feature Selection In Python

Acquire the Theoretical and Practical Foundations That Would Allow You to Learn Machine Learning With Understanding

What you'll learn

Understand the math behind machine learning models

Become familiar with basic and advanced linear algebra notions

Be able to solve linear equations

Determine independency of a set of vectors

Calculate eigenvalues and eigenvectors

Perform Linear Discriminant Analysis

Perform Dimensionality Reduction in Python

Carry out Principal Components Analysis

Compare the performance of PCA and LDA for classification with SVMs

Requirements

Suitable for beginners. Some understanding of Python basics and math would be an advantage.

Description

Do you want to learn linear algebra?You have come to the right place!First and foremost, we want to congratulate you because you have realized the importance of obtaining this skill. Whether you want to pursue a career in data science, machine learning, data analysis, software engineering, or statistics, you will need to know how to apply linear algebra.This course will allow you to become a professional who understands the math on which algorithms are built, rather than someone who applies them blindly without knowing what happens behind the scenes.But let’s answer a pressing question you probably have at this point: “What can I expect from this course and how it will help my professional development?”In brief, we will provide you with the theoretical and practical foundations for two fundamental parts of data science and statistical analysis – linear algebra and dimensionality reduction.Linear algebra is often overlooked in data science courses, despite being of paramount importance. Most instructors tend to focus on the practical application of specific frameworks rather than starting with the fundamentals, which leaves you with knowledge gaps and a lack of full understanding. In this course, we give you an opportunity to build a strong foundation that would allow you to grasp complex ML and AI topics.The course starts by introducing basic algebra notions such as vectors, matrices, identity matrices, the linear span of vectors, and more. We’ll use them to solve practical linear equations, determine linear independence of a random set of vectors, and calculate eigenvectors and eigenvalues, all preparing you for the second part of our learning journey - dimensionality reduction.The concept of dimensionality reduction is crucial in data science, statistical analysis, and machine learning. This isn’t surprising, as the ability to determine the important features in a dataset is essential - especially in today’s data-driven age when one must be able to work with very large datasets.Imagine you have hundreds or even thousands of attributes in your data. Working with such complex information could lead to a variety of problems – slow training time, the possibility of multicollinearity, the curse of dimensionality, or even overfitting the training data.Dimensionality reduction can help you avoid all these issues, by selecting the parts of the data which actually carry important information and disregarding the less impactful ones.In this course, we’ll discuss two staple techniques for dimensionality reduction – Principal Components Analysis (PCA), and Linear Discriminant Analysis (LDA). These methods transform the data you work with and create new features that carry most of the variance related to a given dataset. First, you will learn the theory behind PCA and LDA. Then, going through two complete examples in Python, you will see how data transformation occurs in practice. For this purpose, you will get one step-by-step application of PCA and one of LDA. Finally, we will compare the two algorithms in terms of speed and accuracy.We’ve put a lot of effort to make this course the perfect foundational training for anyone who wants to become a data analyst, data scientist, or machine learning engineer.

Overview

Section 1: Linear Algebra Essentials

Lecture 1 What Does The Course Cover

Lecture 2 Why Linear Algebra?

Lecture 3 Solving Quadratic Equations

Lecture 4 Vectors

Lecture 5 Matrices

Lecture 6 The Transpose of Vectors and Matrices, the Identity Matrix

Lecture 7 Linear Independence and Linear Span of Vectors

Lecture 8 Basis of a Vector Space, Determinant of a Matrix, Inverse of a Matrix

Lecture 9 Solving Equations of the Form Ax=b

Lecture 10 The Gauss Method

Lecture 11 Other Solutions to the Equation Ax=b

Lecture 12 Determining Linear Independence of a Random Set of Vectors

Lecture 13 Eigenvalues and Eigenvectors

Lecture 14 Calculating Eigenvalues

Lecture 15 Calculating Eigenvectors

Section 2: Dimensionality Reduction Motivation

Lecture 16 Feature Selection, Feature Extraction, and Dimensionality Reduction

Lecture 17 The Curse of Dimensionality

Section 3: Principal Component Analysis (PCA)

Lecture 18 An Overview of PCA

Lecture 19 A Step-by-Step Explanation of PCA on California Estates – Example

Lecture 20 The Theory Behind PCA

Lecture 21 PCA Covariance Matrix in Jupyter – Analysis and Interpretation

Section 4: Linear Discriminant Analysis (LDA)

Lecture 22 Overall Mean and Class Means

Lecture 23 An Overview of LDA

Lecture 24 LDA: Calculating the Within- and Between-Class Scatter Matrices

Lecture 25 A Step-by-Step Еxplanation of LDA on a Wine Quality Dataset – Example

Lecture 26 Calculating the Within- and Between-Class Scatter Matrices

Lecture 27 Calculating Eigenvectors and Eigenvalues for the LDA

Lecture 28 Analysis of LDA

Lecture 29 LDA vs. PCA

Lecture 30 Setting Up the Classifier to Compare LDA and PCA

Lecture 31 Coding the Classifier for LDA and PCA

Lecture 32 Analysis of the Training and Testing Times for the Classifier and Its Accuracy

Ideal for beginner data science and machine learning students,Aspiring data analysts,Aspiring data scientists,Aspiring machine learning engineers,People who want to level-up their career and add value to their company,Anyone who wants to start a career in data science or machine learning