Description

Welcome to my course on Machine Learning and Data Analysis, a course that may train you tips on how to use superior algorithms to unravel actual issues with knowledge. I’m Emanuele, a mechanical engineer with a PhD in superior algorithms, and I will likely be your teacher for this course.

This course consists of 4 essential components:

  • Half 1: Overview on Fourier Analysis and Wavelets. You’ll be taught the fundamentals of those two highly effective mathematical instruments for analyzing indicators and photos in numerous domains.

  • Half 2: Data Analysis with Fourier Collection, Transforms and Wavelets. You’ll discover ways to apply these strategies to course of and discover knowledge effectively and successfully, each in time and frequency domains.

  • Half 3: Machine Learning Strategies. You’ll discover ways to use methods that allow computer systems to be taught from knowledge and make clever predictions or selections, comparable to linear regression, curve becoming, least squares, gradient descent, Singular Worth Decomposition (and extra).

  • Half 4: Dynamical Techniques. You’ll discover ways to mannequin and perceive advanced and nonlinear phenomena that change over time, using mathematical equations. We may also apply machine studying methods to dynamical techniques, such because the SINDy algorithm.

By the top of this course, it is possible for you to to:

  • Perceive the rules and functions of Fourier evaluation and wavelets

  • Use Fourier sequence and transforms to research knowledge in varied domains

  • Apply machine studying strategies to completely different issues

  • Extract options from knowledge using wavelets

  • Perceive the significance of sparsity of pure knowledge, in addition to the revolutionary idea of compressed sensing, with life like examples.

  • Uncover the governing equations of a dynamical system from time sequence knowledge (SINDy algorithm).

I hope you take pleasure in this course and discover it helpful to your private and skilled targets.

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Let’s present some extra particulars about the principle components of this course: 

Half 1 constitutes a preliminary introduction to Fourier and Wavelet Analysis. Particular focus will likely be placed on understanding probably the most related ideas associated to those elementary matters.

Partly 2, the Fourier sequence and the Fourier Remodel are launched. Though a very powerful mathematical formulae are proven, the main target shouldn’t be on the arithmetic. One of many key factors of this half is to point out one attainable software of the Fourier Remodel: the spectral by-product. Then, we introduce the idea of Wavelets extra intimately by exhibiting some functions of Multiresolution Analysis.

That is exemplified with Matlab, with out using rigorous mathematical formulae. The coed can comply with and get the instinct even when they haven’t any entry to Matlab.

One other vital achievement of this half is to convey a easy however thorough clarification of the well-known computational FFT technique.

There are additionally some extras on the Inverse Wavelet Remodel and the Uncertainty precept (right here we see extra arithmetic, however that is an additional, if you wish to skip it, simply do it).

Partly 3, some machine studying methods are launched: the strategies of curve-fitting, gradient descent, linear regression, Singular Worth Decomposition (SVD), characteristic extraction, classification, Gaussian Combination Mannequin (GMM). The target on this half is to point out some sensible functions and solid mild on their usefulness.

We may also give attention to sparsity and compressed sensing, that are associated ideas in sign processing. Sparsity implies that a sign may be represented by just a few non-zero coefficients in some area, comparable to frequency or wavelet. Compressed sensing implies that a sign may be reconstructed from fewer measurements than the Nyquist–Shannon sampling theorem requires, by exploiting its sparsity and using optimization methods. These ideas are helpful for decreasing the dimensionality and complexity of knowledge in machine studying functions, comparable to picture processing or radar imaging.

Half 4 is a self-contained introduction to dynamical fashions. The fashions contained on this half are the prey-predator mannequin, the mannequin of epidemics, the logistic mannequin of inhabitants progress.

The coed will discover ways to implement these fashions using free and open-source software program known as Scilab (fairly just like Matlab).

Associated to Half 4, there may be an software of machine studying approach known as SINDy, which is an acronym for Sparse Identification of Nonlinear Dynamics. It’s a machine studying algorithm that may uncover the governing equations of a dynamical system from time sequence knowledge. The principle thought is to imagine that the system may be described by a sparse set of nonlinear features, and then use a sparsity-promoting regression approach to search out the coefficients of those features that greatest match the information. This fashion, SINDy can recuperate interpretable and parsimonious fashions of advanced techniques.

Observe: For a few of the lectures of the course, I used to be impressed by S.L. Brunton and J. N. Kutz’s e-book titled “Data-Pushed Science and Engineering”. This e-book is a wonderful supply of knowledge to dig deeper on most (though not all) of the matters mentioned within the course.

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