Back to Mathematics for Machine Learning: PCA

4.0

1,140 ratings

•

237 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!

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By Andrea V

•Jun 22, 2019

This course is hard, and contains a lot of mathematical derivations and concepts that might be overwhelming for somebody not completely fresh in maths. Nevertheless, it offers a good balance between rigour and practical application, and if some lectures turn out to be too complicated, there's always the chance to deepen the matter more quitely using the course material or online resources. I think that the course would have benefited from a more aneddoctical approach at times: for instance restating in english what the general purpose of PCA is, could help the less mathematically inclined to better seize the idea. But I know this is not always easy to do.

By Yiqing W

•Mar 28, 2019

The teaching is good but some programming assignment is not so good

By Ustinov A

•May 28, 2019

Unfortunately, mistakes in grader and a bad python environment spoilt the impression. I lose hours because of it during 1, 2 and 4 week. It's not enough exercises last week. You should add more examples for every step of PCA for better understanding.

By Narongdej S

•Jun 29, 2019

Confusing for beginners; the explanations are too abrupt

By Shilin G

•Jun 27, 2019

Not as good as previous two courses. I understand it is an intermediate course, but still, the video does not help you do the quiz, e.g. the video uses 2x2 matrices for example while quiz is mainly about 3x3 - then why not include a 3x3 example? Programming assignment is not clear either, some places you have to change the shape of matrix but it is not explained why this is necessary (and actually it is not). A lot of room for improvement here.

By Andrei

•Nov 01, 2018

terrible assignments

By Yana K

•Apr 18, 2019

Not really well structured. Too much in-depth details, too little intuition given. Didn't help to understand PCA. Had to constantly look for other resources online. Pity, because first 2 courses in the specialisation were really good.

By Patrick F

•Feb 01, 2019

The programming tasks are very bad documented and have errors.

By 용석 권

•Jan 30, 2019

Programming assignments' quality is too bad to follow it. Their lecture's explanation and assignments' notation are not matched. Moreover, the code is sometimes ridiculous.

By Naveen K

•Aug 09, 2018

I've finished all the two previous courses in this specialization.I was shocked at seeing the content and programming assignments given to us.It was totally different.They expect a lot from us.Content is not up to the mark.First two courses was awesome.But this course is an exact opposite to the first two.Totally disappointed!! I was hoping to finish this specialization.But it seems I cannot. I didn't expect this.

By Valeria B

•Jun 26, 2019

Too few examples given during the lessons. More examples could greatly improve understanding and the solution of quizzes and programming assignment.

I had to integrate this course with multiple sources I looked up for by myself, so I'm really wondering if I wisely spent my money on this course.

By Rachel S

•Jul 09, 2019

After the first two courses in the specialisation, this one was truly disappointing. You are warned at the beginning that this course is challenging. This is true, but there is absolutely no reason why it should be THIS challenging. There are several factors that make this course more difficult than it needs to be. The poor pacing leads to a bizarre mix of repetitive trivial questions and vague assignments with poor explanation and over-reliance on reading external sources. Nobody wants constant hand-holding but the lack of direction will lead to you wasting far too much time chasing down minor technical errors and figuring out what on earth is being asked of you. Finishing this course was a slog and I just wanted to wash my hands of it. The first two courses in this specialisation are great and I highly recommend them, but I would not be happy if I had paid £38 for this course.

By Ong J R

•Aug 11, 2018

Concepts weren't taught well and programming exercises are full of errors. Very difficult to debug and find out if I am on track during the programming exercises. Lecturer lacks passion and ability to convey core concepts well to audience. Hard to follow up on the mathematical derivation with the simple stuff that we were taught in module 1 and 2.

By Naggita K

•Dec 19, 2018

Great course. Rich well explained material.

By imran s

•Dec 20, 2018

Great Coverage of the Topic

By Xi C

•Dec 31, 2018

Great course. Cover rigorous materials.

By Hasan A

•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 Dora J

•Feb 04, 2019

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

By Aymeric N

•Nov 25, 2018

This course demystifies the Principal Components Analysis through practical implementation. It gives me solid foundations for learning further data science techniques.

By Oleg B

•Jan 06, 2019

Excellent focus on important topics that lead up to PCA

By Tichakunda

•Jan 18, 2019

good course, rigorous proof and practical exercises

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 Akshaya

•Jan 25, 2019

This was a tough course. But worth it.

By Natalya T

•Feb 25, 2019

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

By Bálint - H F

•Mar 20, 2019

Great !

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