Back to Mathematics for Machine Learning: PCA

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2,810 ratings

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698 reviews

This intermediate-level course introduces the mathematical foundations to derive Principal Component Analysis (PCA), a fundamental dimensionality reduction technique. We'll cover some basic statistics of data sets, such as mean values and variances, we'll compute distances and angles between vectors using inner products and derive orthogonal projections of data onto lower-dimensional subspaces. Using all these tools, we'll then derive PCA as a method that minimizes the average squared reconstruction error between data points and their reconstruction.
At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge.
The lectures, examples and exercises require:
1. Some ability of abstract thinking
2. Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis)
3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization)
4. Basic knowledge in python programming and numpy
Disclaimer: This course is substantially more abstract and requires more programming than the other two courses of the specialization. However, this type of abstract thinking, algebraic manipulation and programming is necessary if you want to understand and develop machine learning algorithms....

WS

Jul 6, 2021

Now i feel confident about pursuing machine learning courses in the future as I have learned most of the mathematics which will be helpful in building the base for machine learning, data science.

JS

Jul 16, 2018

This is one hell of an inspiring course that demystified the difficult concepts and math behind PCA. Excellent instructors in imparting the these knowledge with easy-to-understand illustrations.

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By Lee F

•Sep 28, 2018

This was the toughest of the three modules. It gave me a strong foundation to continue pusrsuing machine learning.

By Nileshkumar R P

•May 6, 2020

This course was tough but awesome. Lots of things i learnt from this course. Great course indeed and worth doing.

By Carlos J B A

•May 17, 2021

Undoubtedly one of the best courses I have taken on mathematics for Machine Learning with world-class teachers.

By Kuntal T

•Feb 15, 2021

one of the best course to learn whats happening in machine learning and how it make sense through mathematics.

By 037 N S

•Jul 30, 2020

The PCA part Was a bit tricky barely handle the concepts.

thank you imperial team for such interactive course

By Krzysztof

•Aug 21, 2019

One of the most challenging course in my life - almost impossible without python and mathematics background.

By Javier d V

•Jun 25, 2021

Great course. An intermediate mathematical background is requiered. This is a strength in terms of learning

By Pratama A A

•Aug 25, 2020

Need more Effort to grasp the materials explained_-" you need to be patience,the lecturer is really on top

By Nelson S S

•Jul 29, 2020

Excellent course ... Quite challenging, a little difficult but I have learned a lot ... Thank you ...

By sameen n

•Sep 6, 2019

Amazing course and provides basic introduction for the PCA. Need for programming help in this course.

By Brian H

•Feb 24, 2020

Great course. I appreciate the rigor and clear mathematical explanations provided by Dr. Deisenroth.

By Natalya T

•Feb 25, 2019

exellent course! nice python wokring enviroment and very good explanation at each topic. thank you!

By Aishik R

•Jan 18, 2020

Excellent and to-the-point explanations, useful assignments to make the concepts etched in memory

By Haoquan F

•Feb 13, 2022

It's overall wonderful but the week 4's programming assignment really struggled and confused me.

By KAMASANI V R

•Jun 20, 2020

This course helped me in getting a deeper knowledge on Principal Component Analysis. Thank You.

By Wei X

•Oct 16, 2018

concise and to the point. Might want to introduce a bit the technique of Lagrangin multiplier

By Leonardo H T S

•May 2, 2021

This was an amazing course, I really enjoyed it and learn a lot!

Thank you so much, greetings

By Wahyu N A M

•Mar 27, 2021

I'm struggle with assigments of week 4 about implementing PCA. But, yeaah finally i got this

By Mayank

•Dec 3, 2020

This course cleared so many concepts and enabled me to further master the subject on my own.

By Ripple S

•Mar 17, 2020

I learnt a lot from this course and now I think I am much more familiar with this algorithm.

By Farhan F

•Mar 26, 2022

This is very very very very very challengging, but i can do it because i try try and try

By Haofei M

•Apr 22, 2020

extremely informative and really help me understand the basic math in Machine learning

By Deepak T

•Apr 17, 2020

Course was challenging, so does the math. It was a very excellent learning experience!

By Mohammad A M

•Nov 14, 2019

This course is also so helpful, and the lecturer is so predominant on what he taught.

By Alfonso J

•Oct 20, 2019

Truly hardcore course if your are a noob in reduced order modelling. Very challenging

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