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Learner Reviews & Feedback for Mathematics for Machine Learning: PCA by Imperial College London

2,329 ratings
582 reviews

About the 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 and develop machine learning algorithms....

Top reviews

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.

Jun 18, 2020

Relatively tougher than previous two courses in the specialization. I'd suggest giving more time and being patient in pursuit of completing this course and understanding the concepts involved.

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376 - 400 of 581 Reviews for Mathematics for Machine Learning: PCA

By Manish C

May 6, 2020

Best course for machine learning enthusiast

By Thijs S

Sep 28, 2020

The last assignment could use improvement.

By J N B P

Sep 10, 2020

Good for intermediates in linear algebra.

By Romesh M P

Jan 16, 2020

Too much non-video lectures (lot to read)

By Tanmoy S

Jul 13, 2020

The last course could have been better.

By Kailash Y

Jul 9, 2020

Challenging but in a good way.

By Mark R

Jan 22, 2019

Good, short, overview of PCA

By Changxin W

Jan 28, 2019

Many errors of homework

By Poomphob S

Jun 18, 2020

so challenging for me

By Sammy R

Dec 25, 2019

Needs more details

By Shreyas S S

Jun 20, 2020

Good Course


Aug 28, 2020

kinda long

By Harrison B

Apr 18, 2020

Broadly speaking, this is a good course. However, the feeling is that it should be twice as long and with more videos. There is simply not enough instruction to facilitate clear learning and completion of this course is down to an individual's desire to read around and problem solve.

In particular, the programming assignments - whilst not technically difficult, lack clear articulation of expectation, which is compounded by pythons slightly inconvenient handling of matrices. Writing vectorised code which involves 1 x N or N x 1 matrices and transpositions often results in zero marks; with no clue whether the code is wrong, the student has misunderstood the expectation or python is refusing to recognise a N x 1 matrix. This could br helped by including more discriptions about the data sets and the variables being used, as well as the expectation of the output.

There are a lot of positives about this course, the videos are well made and are clear. Excellent supplementary learning if you're doing undergraduate Linear Algebra or other Machine Learning courses; just a bit too cramped for a standalone course (even with the others in the specialisation being well understood). Perhaps a four course could be added to this specialisation for "The Basics of Python for Machine Learning" where a student covers all the relevant coding knowledge?

By Mark P

Jul 29, 2019

This course had a lot of potential but there were a number of inconsistencies, cut/paste comment bugs, that make it more challenging than it needs to be. The comments in the notebook exercises should be triple-checked with the text above to ensure consistency of variables. Far too often these would be mixed up, or the input/output descriptions would be incorrect. Or the unit test would have different dimensions. Lectures often left out steps - e.g. "because of orthonormal basis, we can simplify and remove a bunch of terms" - how exactly? A extra few seconds of explanations would allow students to follow more closely. Notation in lectures is sloppy - sometimes terms would be missing and then the video would quietly cut to a correction. "j's" and "i's" indices were interchanged frequently making the derivations how to follow. Also, this isn't a course on unit testing - some more tests should be included to help students debug individual functions rather than relying on the final algorithm (e.g. PCA to work). It should be explained why the "1/N" term for XX^T is not necessary even though it's in the lectures. On the plus side, the added written notes were welcome and fairly well done.

By Yuchi C

Feb 23, 2020

The lectures (especially the last module) are fast-paced and intense, they're informative and very interesting to do. To complete and fully understand the course contents, heavy self-research is apparently required for students with no to no foundation.

I do not believe that the programming assignments match well with the lectures, they're more about programming than testing knowledge. Compared to the assignments in the first two courses from the same specialisation, the assignments in this course are very difficult for students with little to no coding experience. I highly advise explanation and solutions to the assignments to be published after completion (if possible) so that students get to know where they went wrong.

Overall, I enjoyed the course despite having spent too much time on the programming assignments, trying to spot my mistakes without any direction and dealing with the unstable programming environment.

By Philippe R

May 16, 2018

Very mixed feelings about this course. First three weeks are OK, but going from week 3 to week 4 is like a HUGE step in difficulty if you really want to follow it all. Which is a pity because week 4 is the whole purpose for the course!

I learned "some" about the subject, but not to the level that I can say I understand it fully.

The assignments are OK, but the instructions are not always all that clear, leaving you at times wondering what is expected from you. And not that it is specific to this course, but the grader feedback is not all that helpful. If that is the only information you rely on to figure out where you may have gone wrong in a programming assignment, fixing your mistakes is likely to take quite some time.

All in all, an "OK" course, but not one that I would take again. I will most likely resort to other sources to get a better understanding of the subject.

By Piotr G

Apr 23, 2018

This course is overall good in terms of the accuracy and obvious deep knowledge of the tutor. However, after the first two modules of this course I expected a completely different approach with way more conceptual thinking than writing proofs and long derivations which can be found on Wikipedia and other websites. It seems to me that there is a clear mismatch between the styles of the first 2 modules and the 3rd course. I'm giving it only three stars because this is not what I expected, I signed up for this track to gain additional conceptual overview of how maths in many machine learning applications works on high level. On the other side though, the assignments and quizzes were harder in this course which is a big plus.

By Keshav B

Aug 22, 2020

This is tough for me. On one hand I appreciate the academic nature of how this was presented. There were few frills and the instructor is focused purely on the maths. In that space it gets a 5/5. My issue is the course requires a _lot_ of dedication and a _lot_ of self study. More so than the previous courses. More examples and a clearer explanations would have helped much more. Additionally, the course states experience with numpy or python is unnecessary, but you are left to figure out the odd tricks that numpy offer that aren't inherently obvious.

How it can be improved: Clearer examples, better assignment explanation, and more visual feedback to help us understand if we did something correctly.

By Nguyen N D

Jul 14, 2020

The instructor had a broad knowledge pool but I think his explanation sometimes is really vague and hard to understand. It took me a lot of time to comprehend the content and to be honest, I was quite disappointed since I needed to read many other resources to fully understand. Comparing to the other 2 courses in the specialization, I don't highly recommend this course due to the fact that the compression of the information was not sufficient and inefficient. Plus, the coding assignment is harder with a few hints or explanations and will be more suitable for Python-experienced learners to get the structures of the code. Otherwise, as a beginner in the field, I found it hard.

By Michael P G

May 21, 2020

The mathematical skills needed to take this class exceed what was covered in the previous two classes of this specialization. The instructor provided reading materials that were just wikipedia pages, not designed to teach a newcomer.

The programming exercises were poorly designed. In some cases it was not at all clear what one is supposed to implement, what the shape of the input numpy arrays are, etc. In one case, the automated graded system provides inputs that are unlike the provided example inputs, so one has no idea what to be coding for.

I took all three courses in this specialization: the first two got 5 stars, this one gets only 3.

By Trevor F K

Jan 3, 2021

This course didn't really promote understanding. The lectures were a lot of derivations with little elaboration. I still learned the things, but had to spend a lot of time doing side research to understand the lectures. And I didn't appreciate that many of the readings were wikipedia pages.

The lab assignments were confusing. Not hard, but confusing. As in "what is being asked here?" and the automated feedback was not at all helpful. It is possible to pass all the tests in the lab but still not get 100%. Very frustrating and disappointing, especially since the first 2 courses of the specialization were so good

By Ben H

Aug 20, 2019

This course had a lot of potential, but unfortunately the pacing, structure, and teaching was not up to the standard of the other two courses in the specialisation. The teacher is clearly very knowledgable about his subject, and seems like a really nice person, but delivers the material in a very direct, formal mathematical style. This makes it much more difficult to gain intuitive insight into the subject matter.

Given the level of the past two courses, this felt like way too big a leap. Don't get me wrong — this course is still worthwhile, but could use some refining.

By Christopher R

Apr 13, 2020

The first two courses in this series were amazing and provided a very intuitive understanding of the mathematics. I felt like I had no idea what we i was actually trying to do this entire course and basically had to learn it all on my own. This was basically a punch in the face and required much more background knowledge of linear algebra/python than the previous classes provided. If you are going into this third course of MML I recommend you do some outside study beforehand to get up to speed or else you might be spinning your wheels and get frustrated.

By Dan M

Jun 4, 2020


There is a lot of interesting math to be learned, and some of the Jupyter notebooks provide cool examples of how you might use Numpy and Scipy to learn more about data sets and algorithms through various kinds of visualizations.


The lectures are dense with lots of complicated derivations that are moved through quite quickly.

The final programming assignment is a mess. In particular there are cells within the Jupyter notebook that take a VERY long time to execute even if you reduce the number of iterations.

By Vishvapalsinhji

Feb 8, 2021

I am doing Mathematics for Machine Learning specialization. I found this course hard to understand. I know some of you would say that it is designed for an intermediate learner. But what I think is, there is a lack of interaction from tutor while presenting concepts. Maybe it sounds rude opinion, but compares to the first two part of the specialization third one seems less interested. Other than that I liked the quiz and assignment which makes you think about the concepts in detail.