Back to Mathematics for Machine Learning: PCA

4.0

932 ratings

•

190 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 Hashaam S

•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 Eric P

•Apr 26, 2019

There is little reason to take this course except for gaining the satisfaction of completing the three courses in the series. There are briefer, more satisfying introductions to PCA elsewhere. This course has too little of what made the other courses in the series so good and shares too much of their shortcomings. Where the other two courses excelled in demonstrating an intuitive understanding of both the maths and their applications, this course really avoids all effort at intuition or examples and instead just throws formula after formula at you. You are then given programming assignments where at least half the effort is to try to understand what is being asked before you start to work to implement it. This leaves you more with a feeling of only having completed assignments and less a sense that you’ve developed a capability in either the maths or their applications. In the end, I am left with a strong desire to learn more about the maths of PCA and their application only because I am eager to hear the subject matter explained by someone else.

The other two courses demonstrated the potential of how good e-learning can be. This course is just another example of its shortcomings.

By Maximilian W

•Apr 29, 2019

The first two courses in the Mathematics for Machine Learning specialisation are excellent - even amongst the best online or traditional maths courses I have taken. This course was seriously lacking. Not in content, or even the ability of the lecturer, but rather in how the information is conveyed. There are some excellent reviews which elaborate further in to the problems with this course, so I will not labour over them all. In essence, if you are learning in your own free time, the poorer information transfer is not appreciated.

However, this course is important, but if you are unsure of whether or not to invest your time into starting this course (now) , I think the following questions are good to ask. Are you:

1) fairly competent in maths, at least significantly beyond the first two courses. This is not because the underlying maths is hard, but the way the information is conveyed, will require more firm knowledge, or, are you:

2) willing to be frustrated, and grab additional resources. You need to be patient to get the most out of this course. The previous courses were great at guiding, and in large part spoon feeding. This course is different, and you have to be happy with that.

3) proficient at numpy and python. I would invest time before the course working on basic numpy skills, as this will make the assignments much easier, and allow you to focus on implementation of learning rather than debugging, and pulling out of hair.

The two star review is because this course didn't provide the high quality expected from the first courses, however the content and end learning result can not be questioned as poor.

By Ткаченко В Е

•Mar 24, 2019

Algebra course is excellent. Calculus course is good. PCA is so bad that I am still upset that I spent my time on it.

By Chris M

•Apr 27, 2019

Unfortunately this course does is of much lower quality than the previous courses of the specialization. There is no progression towards the assignments which basically ask you to implement something without any context. There was even a technical issue with the grader for the first assignment.

If you want to complete it to finish the specialization, you need to seek help in the forums as there are a lot of helpful answers.

By Avirup G

•Feb 18, 2019

Very poorly written/performed material with inadequate coding help. The engagement level is quite low. Will not recommend if you have novice programming background or new to math concepts.

By Miguel V

•Mar 20, 2019

I am very disappointed with this course. It was very hard to follow, and not because this is challenging, but partly because the instructor is not so good. I had to read a lot on my own to be able to complete some assignments. I hope you can improve the content of this course. The best course of this specialization is the second one, and this is the worst.

By José D

•Oct 31, 2018

This course is harder that the the two first ones. You have to do a lot more by yourself. There will be some frustrations with assignments that are not always easy or clear, with confusing python/numpy notations not really introduced during the course. Also, most assignment didn't work online, so I had to install python3 and jupyter to work on them locally and submit them manually. You should expect to spend more time than announced. All in all, I've learned new things and that's the most important. I believe there are room for improvement for this course.

By Martin B

•Oct 22, 2018

Overall: worthwhile content, but poor execution. Especially assignments need improvement.

Good points:

-The contents tend to be worthwhile.

-The instructor is thorough and clear.

Bad Points :

-To those who are not as familiar with mathematical terminology the instructor is a tough act to follow sometimes.

-The great disappointment of this course lies in the assignments. They don't really add to my understanding of the mathematics involved, and are quite often a distraction because the assignments are quite inflexible in terms of coding: you'll have to stick quite close to what the instructor envisions, or you will fail. This is especially frustrating because you will have a hard time figuring out whether you failed because your code was faulty or because your conceptual understanding was faulty.

By JICHEN W

•Oct 27, 2018

Explanation of course material is not clear

By Brock I

•Nov 21, 2018

Way too hard compared to the other courses in the specialization. I feel like I wasted my money on this.

By sreekar

•Oct 23, 2018

The instruction is absolutely bad and not worth it. However, if you have patience to re-watch, refer to other supporting materials, learn on your own a lot and then have patience to deal with programming asssignments ,...then you might find the final result useful.

By Alexandra S

•Sep 26, 2018

Worth auditing because the video lessons are good but unless you have solid Python programming experience, the assignments and some quiz questions will take you days instead of hours. The course info states that you would need 'Basic knowledge in python programming and numpy'. This is to be understood as 'solid practice, at least intermediate level'. 'Basic knowledge' simply does not make it possible to finish these exercises within the given timeframe (1-2 or even 3-4 hours).

As many others, despite having no problem with the maths, I gave up during week 1 because of this issue and of not having this amount of free time while already working full time. This should be emphasised in the course description, apart from the extra mathematical creativity that already appears there. And it should also appear in the description of the whole specialisation, which states that programming experience 'comes in handy but is not necessary'. Many people who start doing the courses are determined to finish the whole specialisation.

By Bryan S

•Feb 19, 2019

This course needs a lot of work to get to the level of quality of its two predecessors.

By Sanjay k

•Aug 14, 2018

I was frustrated at several points during the course - I had to scour the internet for material to improve my understanding which defeated the purpose of taking the course (math and intuition behind PCA for instance). I felt as if the instructor was reproducing material from textbook on the board. I would guess that the abandonment rate for this course is relatively high (in-spite of the introductory nature) because of monotonous delivery and lack of intuitive explanation of concepts (vs. Khan Academy/Andrew Ng for instance).

By Sergii T

•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 João C L S

•May 02, 2019

It is a good course but some problems must be reported. Despite the previous courses from the specialization, I missed the conceptual explanations, the development of intuitive understanding. The support is almost inexistent: questions on forums are not answered by lecturers or mentors, some programming exercises requires knowledge not even mentioned on classes and I feel it is a non necessary knowledge at all to the purpose of the course. Some tutorials would help. Only other students make things clearer at some points. Some lectures have "magic passes" not explained, specially on PCA subject itself, week 4. Maybe the courser could have a additional week to teach things in a better way.

By Christian R

•Jul 24, 2018

Frustrating. Videos and material does not cover what it is asked for in the quizzes and assignments.

By Harshit D

•Jul 30, 2018

Loved the first two courses but felt like killing myself in this course. One of the worst professors i have ever encountered.

By James P

•Jun 10, 2018

After taking/passing the two previous courses, this course is very disappointing. The programming assignments are more about numpy/python peculiarities (which dimension is D or N) and deciphering cryptographic specifications (X is documented as an input but not a parameter to the function). The misleading templates appear to be intentional - it is not clear what educational purpose this serves. The difficulty in this course is not conceptual understanding - it is difficult because the assignments are intentionally confusing. Another point regarding programming in general. This course prefers implementing numerous functions (no testing), generating large amounts of random data as input, and assuming all goes well. Perhaps each function should be tested for correctness individually with known input/output - this is not a novel idea.

By Israel J L

•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 Rahul M

•Jun 29, 2019

The instruction content was superb, though the tests were unrelated to content. I realize that there is a lot of criticism of the course here, but if you understand and code in Python, they are not hard. I wish the course staff had made the Jupyter notebooks more clear, giving us an understanding of what was required, if that was done this is a good, though very hard (in terms of mathematics) course.

By Jong H S

•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.

By Ruarob T

•Jun 30, 2019

Make sure you have time and be ready for python code debug. If you are just an average programmer with limited python exposure like me. It will take you a day to complete the programming assignment.

Note: the assignment and class VDO seems a distant - google a lot during the assignment/quiz

Note: Programming has little clue - personally, I think I spend so much time on programming (distracting me away from going back to Math review)

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.

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