Advanced Data Analysis using Wavelets and Machine Learning
Advanced Data Analysis using Wavelets and Machine Learning, available at $79.99, has an average rating of 4.55, with 47 lectures, based on 20 reviews, and has 6254 subscribers.
You will learn about Understand the principles and applications of Fourier analysis and wavelets (with emphasis on the physical insights rather than the mathematics) Use Fourier series and transforms to analyze data in various domains Apply machine learning methods to different problems Extract features from data using wavelets Understand the importance of sparsity of natural data Understand the revolutionary concept of compressed sensing, with realistic examples. Discover the governing equations of a dynamical system from time series data (SINDy algorithm) Implement efficient Machine Learning algorithms with Matlab Understand and apply the Singular Value Decomposition (SVD) (we even prove it!) Learn how to use the SVD to approximate images Understand the Least Squares Method (LSM) from practical examples Understand and apply the Fast Fourier Transform (FFT) – one of the most important algorithms ever discovered Understand and apply the Discrete Cosine Transform (DCT) Learn how to derive the Inverse Wavelet Transform Learn how to derive the Inverse Discrete Cosine Transform Learn how to derive the Inverse Fourier Transform Learn how to derive the Uncertainty Principle, and how this affects the time-frequency resolution This course is ideal for individuals who are data scientists who seek to reinforce their understanding of Machine Learning techniques and step up their game or Wannabe data analysts or A.I. enthusiasts or ML engineers or software developers or applied mathematicians or physicists or Researchers or Programmers or Anyone who wants to learn how to use advanced algorithms to solve real problems with data. It is especially useful for those who are interested in machine learning and data analysis. It is particularly useful for data scientists who seek to reinforce their understanding of Machine Learning techniques and step up their game or Wannabe data analysts or A.I. enthusiasts or ML engineers or software developers or applied mathematicians or physicists or Researchers or Programmers or Anyone who wants to learn how to use advanced algorithms to solve real problems with data. It is especially useful for those who are interested in machine learning and data analysis.
Enroll now: Advanced Data Analysis using Wavelets and Machine Learning
Summary
Title: Advanced Data Analysis using Wavelets and Machine Learning
Price: $79.99
Average Rating: 4.55
Number of Lectures: 47
Number of Published Lectures: 47
Number of Curriculum Items: 47
Number of Published Curriculum Objects: 47
Original Price: $199.99
Quality Status: approved
Status: Live
What You Will Learn
- Understand the principles and applications of Fourier analysis and wavelets (with emphasis on the physical insights rather than the mathematics)
- Use Fourier series and transforms to analyze data in various domains
- Apply machine learning methods to different problems
- Extract features from data using wavelets
- Understand the importance of sparsity of natural data
- Understand the revolutionary concept of compressed sensing, with realistic examples.
- Discover the governing equations of a dynamical system from time series data (SINDy algorithm)
- Implement efficient Machine Learning algorithms with Matlab
- Understand and apply the Singular Value Decomposition (SVD) (we even prove it!)
- Learn how to use the SVD to approximate images
- Understand the Least Squares Method (LSM) from practical examples
- Understand and apply the Fast Fourier Transform (FFT) – one of the most important algorithms ever discovered
- Understand and apply the Discrete Cosine Transform (DCT)
- Learn how to derive the Inverse Wavelet Transform
- Learn how to derive the Inverse Discrete Cosine Transform
- Learn how to derive the Inverse Fourier Transform
- Learn how to derive the Uncertainty Principle, and how this affects the time-frequency resolution
Who Should Attend
- data scientists who seek to reinforce their understanding of Machine Learning techniques and step up their game
- Wannabe data analysts or A.I. enthusiasts
- ML engineers
- software developers
- applied mathematicians
- physicists
- Researchers
- Programmers
- Anyone who wants to learn how to use advanced algorithms to solve real problems with data. It is especially useful for those who are interested in machine learning and data analysis.
Target Audiences
- data scientists who seek to reinforce their understanding of Machine Learning techniques and step up their game
- Wannabe data analysts or A.I. enthusiasts
- ML engineers
- software developers
- applied mathematicians
- physicists
- Researchers
- Programmers
- Anyone who wants to learn how to use advanced algorithms to solve real problems with data. It is especially useful for those who are interested in machine learning and data analysis.
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:
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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.
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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.
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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).
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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:
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Understand the principles and applications of Fourier analysis and wavelets
-
Use Fourier series and transforms to analyze data in various domains
-
Apply machine learning methods to different problems
-
Extract features from data using wavelets
-
Understand the importance of sparsity of natural data, as well as the revolutionary concept of compressed sensing, with realistic examples.
-
Discover the governing equations of a dynamical system from time series data (SINDy algorithm).
I hope you enjoy this course and find it useful for your personal and professional goals.
————————————————————————————————————————————
Let’s provide some more details about the main parts of this course:
Part 1 constitutes a preliminary introduction to Fourier and Wavelet Analysis. Special focus will be put on understanding the most relevant concepts related to these fundamental topics.
In part 2, the Fourier series and the Fourier Transform are introduced. Although the most important mathematical formulae are shown, the focus is not on the mathematics. One of the key points of this part is to show one possible application of the Fourier Transform: the spectral derivative. Then, we introduce the concept of Wavelets more in detail by showing some applications of Multiresolution Analysis.
This is exemplified with Matlab, without using rigorous mathematical formulae. The student can follow and get the intuition even if they have no access to Matlab.
Another important achievement of this part is to convey a simple but thorough explanation of the well-known computational FFT method.
There are also some extras on the Inverse Wavelet Transform and the Uncertainty principle (here we see more mathematics, but this is an extra, if you want to skip it, just do it).
In part 3, some machine learning techniques are introduced: the methods of curve-fitting, gradient descent, linear regression, Singular Value Decomposition (SVD), feature extraction, classification, Gaussian Mixture Model (GMM). The objective in this part is to show some practical applications and cast light on their usefulness.
We will also focus on sparsity and compressed sensing, which are related concepts in signal processing. Sparsity means that a signal can be represented by a few non-zero coefficients in some domain, such as frequency or wavelet. Compressed sensing means that a signal can be reconstructed from fewer measurements than the Nyquist–Shannon sampling theorem requires, by exploiting its sparsity and using optimization techniques. These concepts are useful for reducing the dimensionality and complexity of data in machine learning applications, such as image processing or radar imaging.
Part 4 is a self-contained introduction to dynamical models. The models contained in this part are the prey-predator model, the model of epidemics, the logistic model of population growth.
The student will learn how to implement these models using free and open-source software called Scilab (quite similar to Matlab).
Related to Part 4, there is an application of machine learning technique called SINDy,which is an acronym for Sparse Identification of Nonlinear Dynamics. It is a machine learning algorithm that can discover the governing equations of a dynamical system from time series data. The main idea is to assume that the system can be described by a sparse set of nonlinear functions, and then use a sparsity-promoting regression technique to find the coefficients of these functions that best fit the data. This way, SINDy can recover interpretable and parsimonious models of complex systems.
Note: For some of the lectures of the course, I was inspired by S.L. Brunton and J. N. Kutz’s book titled “Data-Driven Science and Engineering”. This book is an excellent source of information to dig deeper on most (although not all) of the topics discussed in the course.
Course Curriculum
Chapter 1: Overview of Fourier and Wavelet Analysis
Lecture 1: Overview of Fourier Analysis
Lecture 2: Space-Frequency resolution for the Short Time Fourier Transform
Lecture 3: Wavelets and Space-Frequency resolution
Chapter 2: Data Analysis with Fourier Series and Transform
Lecture 1: Summary of Fourier Series and Fourier Transform
Lecture 2: Notation for the Fourier Transform
Lecture 3: Fourier Transform of the derivative of a function
Lecture 4: The importance of the Fast Fourier Transform (FFT)
Lecture 5: Spectral derivative
Lecture 6: Wavelets and Multiresolution Analysis
Lecture 7: Extra: Why the Dirac delta helps derive the Inverse Fourier Transform
Lecture 8: Extra: Mathematical derivation of the Inverse Wavelet Transform
Lecture 9: Extra: Uncertainty principle – mathematical proof
Chapter 3: Methods in Machine Learning
Lecture 1: Curve fitting
Lecture 2: Example of curve fitting – least squares method
Lecture 3: Gradient descent
Lecture 4: Singular Value Decomposition – SVD
Lecture 5: Approximation of images with the SVD
Lecture 6: Supervised machine learning – extraction of features with SVD and Wavelets
Lecture 7: Linear regression: least squares method in matrix form
Lecture 8: Linear regression: sensitivity to outliers in the data
Lecture 9: Classification/decision trees
Lecture 10: Gaussian Mixture Models
Lecture 11: Example of Gaussian mixture model
Chapter 4: Sparsity and Compressed Sensing
Lecture 1: Sparsity and compressed sensing: intro to sparsity
Lecture 2: Sparsity and compressed sensing: why "natural" signals are compressible
Lecture 3: Sparsity and compressed sensing: intro to compressed sensing
Lecture 4: Example of compressed sensing
Lecture 5: Definition of the Discrete Cosine Transform (DCT) and its inverse
Lecture 6: Extra: formula which is crucial to finding the Inverse Discrete Cosine Transform
Chapter 5: Dynamical systems
Lecture 1: Introduction to the section on mathematical models
Lecture 2: Pure prey-predator model
Lecture 3: Equilibrium points and their stability
Lecture 4: Equilibrium points in the prey-predator model
Lecture 5: Introduction to Scilab
Lecture 6: Constructing the model with Scilab part 1
Lecture 7: Constructing the model with Scilab part 2
Lecture 8: How parameters affect the output of the model
Lecture 9: Influence of fishing on the model
Lecture 10: Addition of logistic terms to the model
Lecture 11: Model on the evolution of epidemics
Lecture 12: Mathematical analysis of stability
Lecture 13: Simulation and mathematics of the logistic model with one population
Chapter 6: Machine learning applied to dynamical systems
Lecture 1: Dynamical systems and chaos: Lorenz system
Lecture 2: Machine learning to find dynamical models behind data (SYNDy algorithm)
Chapter 7: Proof of the SVD decomposition
Lecture 1: Introduction to this section on the proof of the SVD
Lecture 2: Diagonalization theorem in Linear Algebra
Lecture 3: Intuition behind the Singular Value Decomposition (SVD)
Instructors
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Emanuele Pesaresi
PhD in Mechanics and Advanced Engineering Sciences
Rating Distribution
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- 2 stars: 0 votes
- 3 stars: 2 votes
- 4 stars: 2 votes
- 5 stars: 16 votes
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