Chevron Left
Back to Mathematics for Machine Learning: PCA

Mathematics for Machine Learning: PCA, Imperial College London

510 ratings
102 reviews

About this Course

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 machine learning algorithms....

Top reviews


Jul 17, 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.


May 01, 2018

This course was definitely a bit more complex, not so much in assignments but in the core concepts handled, than the others in the specialisation. Overall, it was fun to do this course!

Filter by:

98 Reviews

By Israel Jiménez Lorant

Jan 06, 2019

Great course !! Definitely it's an intermediate course so if you don't have a college level in lineal algebra and calculus you'll struggle with the videos and the notebooks (besides you need basic level programing in python and numpy)

The videos are kinda hard but it seems that Marc it's a great mathematician and also he shares a great e-book written by him that has everything seen in the course and more, so with this you can get all the knowledge need it to understand PCA.

I don't understand why it's only 4 stars rated; again if you want to learn linear algebra and calculus, this is not the place... you need to have the needed level to suceed.

By Oleg Biller

Jan 06, 2019

Excellent focus on important topics that lead up to PCA

By Xi Chen

Dec 31, 2018

Great course. Cover rigorous materials.

By Hasan Ahmad

Dec 31, 2018

What a great opportunity this course offers to learn from the best in this simplified manner. Thank you Coursera and Imperial College London!

By Hashaam Siddiq

Dec 30, 2018

This course does not include real-world examples as compared with other 2 courses in the series. The other lecturers energy was quite obvious and the lecturer in this course does nothing extra. This is the traditional teaching method where we should keep on grasping theory without understanding applications.

While I have learned many new concepts, I am 100% unsure I have not understood the course in general.

The assignments in the course was poorly constructed and the lectures did not explain anything more about numpy methods.

I will not recommend this course to anyone.

By Cesar Arthur Paul Castro Johanson

Dec 23, 2018

Good content, just need to fix the assignments' platform.

By Sergii Tkachov

Dec 22, 2018

Course is targeted more on pure math derivations, rather then real world applications. For my opinion, it doesn't fit well with other courses in this specialisation. it goes too Deep in math derivations. It should fit for students interested in mathematics and not engineers, who want to get more insights in ML related math.

By imran sarwar

Dec 20, 2018

Great Coverage of the Topic

By Naggita Keziah

Dec 19, 2018

Great course. Rich well explained material.

By k vinay kumar

Nov 30, 2018

its a good course to learn mathematics essential for machine learning