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

1,188 ratings
253 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 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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76 - 100 of 249 Reviews for Mathematics for Machine Learning: PCA

By Hritik K S

Jun 20, 2019

Maths is just like knowing myself very well!

By Abhishek M

Jun 22, 2019

Very nice course. It will be great to have a course on Statistics for Machine learning covering advanced concepts in probability theory. Thank you for offering such a great course. I have learnt a lot and enjoyed fully.

By Gergo G

May 15, 2019

This course is really challenging. A strong mathematical background is necessary or it needs to be developed during the lectures and self-study. The professor's explanations are clear, and still lead to complex ideas which is great. Programming assignments are also difficult, however they serve as a superb opportunity to develop your skills in Python.

By David

May 29, 2019

This was indeed a very challenging course. It was also very rewarding, and I felt that the instruction was great and relevant to the assigned tasks. The first two courses in the specialization were very high quality, and in my opinion this one lives up to the expectations that they set.

By Arnab M

Jun 03, 2019

A great course. Learnt a lot, a lot of Linear Algebra, Projections/ Geometry/ all of these Mathematical ideas would help greatly in understanding of Machine Learning concepts and applying them to real world data!!..

By Sujeet B

Jul 21, 2019

Tough, but great!

By David N

Jul 24, 2019

Great course

By Akshat S

Jul 24, 2019

I will present my self with some amazing songs!!

Excellent staircase to the heaven for learning PCA.

Breaking the habit of struggling with hardcore bookish mathematics.

Loose yourself in this adventure!!

By Greg E

Jul 27, 2019

I have thoroughly enjoyed every course of this specialization. Thank you very much.

By Samresh

Aug 10, 2019

Nice Course.

By Krzysztof

Aug 21, 2019

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

By Wang S

Oct 21, 2019

A little bit difficult but helpful, thank you!

By Alfonso J

Oct 20, 2019

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

By Harish S

Nov 24, 2019

This was a difficult course but still very informative.

By Moez B

Nov 25, 2019

Excellent course. The fourth week material is the hardest for folks not comfortable with linear algebra and vectorization in numpy and scipy.

By Roshan C

Nov 23, 2019

the course was very much intuitive and helpful to grasp the knowledge of PCA

By Sameen N

Sep 06, 2019

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

By Tarek L

Sep 11, 2019

This is a difficult course, but it really gave me an appreciation of the mathematics behind machine learning. I encourage anyone doing this course to read Deisenroth's free book Mathematics for Machine Learning ( to better understand the notation and technique used to get to the proofs. If anything, the rigor of this course inspired me to further pursue learning in mathematics to strengthen my machine learning foundation.

By Idris R

Nov 02, 2019

Great, challenging course. The instructor will expect much of you as the material is not spoon fed. At times this is frustrating but yet that's the best way to build your own intuition. This is a *hard* course and I imagine most of machine learning is like this. Fun, rewarding, and challenging. You'll flex your math and programming muscles.

By Shahriyar R

Sep 14, 2019

The hardest one but still useful, very informative neat concepts

By Lahiru D

Sep 16, 2019

Great course. Assignments are tough and challenging.

By Vo T T

Sep 19, 2019

This course is very helpful for me to understand Math for ML. Thank you Professors at Imperial College London so much!

By Laszlo C

Dec 06, 2019

This is an excellent course first covers statistics, looks back to inner products and projections, thereafter it connects all of that and introduces PCA. The knowledge that you've gathered throughout the first two courses gets applied here. Granted, it's more abstract and challenging than the others, I wouldn't give a worse rating just because of that. You'll need to dive into certain topics on your own and if you strengthen your coding skills for the programming exercises. Nevertheless, it's just as highly rewarding as the first two.

By Faruk Y

Sep 22, 2019

Lectures and programming assignments were selected nicely to teach the math of PCA

By Arijit B

Nov 05, 2019

Excellent course and extremely difficult one to grasp at one go. Regards Arijit Bose