Advanced Data Analysis using Wavelets and Machine Learning

Welcome to my course on Machine Learning and Data Analysis, a course that will teach you how to use advanced algorithms to solve real problems with data. I am Emanuele, a mechanical engineer with a PhD in advanced algorithms, and I will be your instructor for this course. This course consists of four main parts:Part 1: Overview on Fourier Analysis and Wavelets.

You will learn the basics of these two powerful mathematical tools for analyzing signals and images in different domains. Part 2: Data Analysis with Fourier Series, Transforms and Wavelets. You will learn how to apply these methods to process and explore data efficiently and effectively, both in time and frequency domains.

Part 3: Machine Learning Methods. You will learn how to use techniques that enable computers to learn from data and make intelligent predictions or decisions, such as linear regression, curve fitting, least squares, gradient descent, Singular Value Decomposition (and more). Part 4: Dynamical Systems.

You will learn how to model and understand complex and nonlinear phenomena that change over time, using mathematical equations. We will also apply machine learning techniques to dynamical systems, such as the SINDy algorithm. By the end of this course, you will be able to:Understand the principles and applications of Fourier analysis and waveletsUse Fourier series and transforms to analyze data in various domainsApply machine learning methods to different problemsExtract features from data using waveletsUnderstand the importance of sparsity of natural data, as well as the revolutionary concept of compressed sensing, with realistic examples.