Back to Mathematics for Machine Learning: PCA

4.0

1,002 ratings

•

206 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....

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:

By Oleg B

•Jan 06, 2019

Excellent focus on important topics that lead up to PCA

By Dora J

•Feb 04, 2019

Great course including many useful refreshers on foundational concepts like inner products, projections, Lagrangian etc.

By Abdu M

•Jan 20, 2019

Best course out of the series so far. A fine balance between theory and derivations, and practice with the programming assignments. It seems that they have solved their programming assignment issues (the first one still has some problems with the grader I believe). This course does require you to have some prior experience, though, so if you are new to programming or linear algebra (not just the concepts but how to apply them) it's bets to take the first two courses with some additional help (maybe Khan academy or even MIT OCW. I will certainly refer to this course in the future, as well as the professor's book on Mathematics for ML.

By Ratnakar

•Jul 13, 2018

This is by far the best course I have taken. The Instructor is exceptional in setting the stage to understand the complex topic by letting us know the motivation of every concept, making us understand the fundamentals right, deep diving into the core of the topic and them nicely summarizing the topic along with the applications.

By Shounak D

•Sep 15, 2018

Great course !

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 Wei X

•Oct 16, 2018

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

By ELINGUI P U

•May 26, 2018

Very hard to follow, but you need to do it to understand machine learning very well.

By Jayant V

•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!

By Carlos S

•Jun 11, 2018

What you need to understand PCA!!!

By Karthik

•May 03, 2018

RRhis cl

By Shanxue J

•May 23, 2018

Truly exceptional

By 林澤佑

•Mar 14, 2018

Practices and quiz are designed well while I will suggest to put more hints on programming parts, e.g., PCA. Overall, this series of course are pretty useful for beginner.

By FRANCK R S

•Jul 07, 2018

Very interesting and challenging subject: PSA, this MOOC together with the other 2 Mathematics for Machine Learning are one of the most useful I have ever made, actually they helped a lot in my other Machine learning and Deep learning studies! I highly recommend this fascinating MOOC

By Diego S

•May 02, 2018

Difficult! But I did it :D And I learnt a lot...

By Prime S

•Jun 24, 2018

Nicely explained. Could be further improved by adding some noted or sources of derivation of some expressions, like references to matrix calculus

By ChristopherKing

•Apr 18, 2018

The whole content of this course is fantastic, not all details were covered in the video, but main ideas were expressed in a great way buy math formulations. Pay attention to those vectors and matrices, especially their dimensions, this will help you solve problem quickly. More important, matrix is just a way to express a bunch of similar things, knowing the meaning of those basis vectors is important.

By mohit t

•May 13, 2018

Perfect course. It takes up more time and effort than the other two courses in the specialization. But what you learn by the end of it is totally worth the effort. Note that this is an Intermediate course compared to the other two which are beginner. So the extra rigor is expected.

By Xavier B S

•Apr 05, 2018

Excellent course - challenging yet rewarding with good feedback from the teaching staff.

The video and the transparent white board are also great - look forward to seeing more MOOCs from Imperial as well as the release of the upcoming book

By Christine D

•Apr 14, 2018

I found this course really excellent. Very clear explanations with very hepful illustrations.

I was looking for course on PCA, thank you for this one

By J G

•May 12, 2018

This is a good course, you learn about the foundations of PCA.

By HARSH K D

•Jun 28, 2018

good

By chaomenghsuan

•Jul 18, 2018

This one is harder, I took longer time to figure out the assignments. Some of the concept that appeared in the assignments were not included in the lectures. I do hope that the assignments could have clearer instructions.

By Eli C

•Jul 22, 2018

very challenging and rewarding course

By Andrey

•Sep 17, 2018

Great course!

Coursera provides universal access to the world’s best education,
partnering with top universities and organizations to offer courses online.