Back to Mathematics for Machine Learning: PCA

4.0

stars

2,205 ratings

•

548 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....

JS

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.

NS

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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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 Djambar

•May 17, 2020

Very challenging course in terms of computing ; one have to always go to the forum which is very active and function like StackOverFlow. You must have somme skills in PYthon, an intermediate level in matrix algebra and deserve a high amount of time and effort to do the assignments but at the end you get a good comprehension of PCA algorithm.

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 Yougui Q

•Jun 2, 2020

The course is relatively harder than the other two courses in this specialization. The lecturer didn't provide understandable examples while demonstrating the concepts. The grader for Python assignments didn't function well either.

By Yiqing W

•Mar 28, 2019

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

By Narongdej S

•Jun 29, 2019

Confusing for beginners; the explanations are too abrupt

By Roy A

•Sep 23, 2020

First 2 courses in this specialization was really good, so I'm very dissappointed here. My main issues are the following:

The lectures are not clear enough, for about 75% of the assignments, I had to look up alternative lectures on youtube to get the point, if I have to find the majority of the information outside of Coursera, then what is the point of the course?

Sometimes there are no examples in the lectures, other times, the examples are too basic. So once I got a more advanced question , I was clueless how to solve it. Sometimes the first question on a quiz is much more complex than the example in the lecture.

The lectures requires you to be very comfortable with math notation, which I'm not. As mentioned earlier, some more examples would have solved this for me, but as the examples are lacking, I was simply unable to understand what was being written on the lecture, and had to look elsewhere. Note that the math itself wasn't hard(once I found someone else to explain it), just understanding what the lecturer meant.

Some steps in lectures are missing, I guess they are obvious if you have the correct prerequisites, but to me it was just a black box. "We have x,y,x. So then we get x+z,y!", why? no idea, I still don't know why we get x+z.

Programming assignments are hard for the wrong reasons, the math is not that hard, the python and numpy is basic, but the explanations of what the function is supposed to do is not clear. When I got stuck, it was usually because I didn't understand what the output of a function was supposed to be. As this is a math course, I would expect the challenge to be the math, not something else.

To sum up the above points, I think the course lacks a good understanding of the base skills needed to complete the course. Since I had no problems with part 1 and 2, and then ran into a wall at part 3(PCA), I think these parts should be better synced, if they are to be part of the same specialization.

By Kenny C

•Jul 22, 2020

This course was very frustrating. I would say that I'm quite competent in math, but I still struggled, not necessarily because the content is challenging, but because the instructions are unclear. I like that the lectures go through derivations in detail, but the instructor often skips steps. Sometimes he would reference a property of matrices that were not talked about, and I would have to spend half an hour researching what that property was to follow what was happening. The quizzes were minimally helpful, as they were merely the same computation question repeated throughout the quiz, which does not help to build intuitive understanding. The programming assignments are unclear on instructions and had many bugs, even in the pre-written parts. A lot of time was spent on reading the NumPy documentation, as the assignments gave little indication of what functions should be used and how they should be used. Overall, despite having a mathematical derivation of PCA, the course is very confusing and frustrating, perhaps even to those competent in this area of study.

By Astankov D A

•May 26, 2020

Although the lecturer admits that the course is quite challenging at times, it is a poor justification for the terrible assignments with close to zero explanations, errors in functions and lots of misfunctioning code in general where the notebook keeps spinning in an infinite loop. I was very hesitant while rating this course - sometimes I wanted to give it 4 stars and sometimes just a single one. I ended up with just two due to the really bad final programming assignment.

By Karl

•May 30, 2020

Pretty bad in comparison to the previous 2 courses. Not sure if the topic was just harder or it was presented less clearly. Assignments were confusing and I spent a lot of time trying to work out what I was supposed to be doing. More relevant practice questions might have been better. Also course felt slightly detached and maybe collaboration between the tutors which seemed to be there in the previous course should have happened here.

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 Ali K

•Jun 3, 2020

the instructor is knowledgeable but he has no teaching skills what so ever. He makes things very confusing. An example at the end would be very useful. No step-wise algorithm is provided.

By Patrick F

•Feb 1, 2019

The programming tasks are very bad documented and have errors.

By Andrei

•Nov 1, 2018

terrible assignments

By Shubhayu D

•Jun 13, 2020

The first two courses in the specialization were extremely good. However, this course is nowhere close to them. Neither does the instructor provide enough intuition, nor do the assignments help in the learning process.

By Abhishek S

•Jun 7, 2020

The first two courses of this specialisation were awesome PCA being a hard topic is difficult to understand but the course was boring and not good compared to previous two.

By 용석 권

•Jan 29, 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 Benjamin F

•Nov 18, 2019

The didactic value of this course is rather low. The lectures do not explain the very concepts required to sovle the subsequent assigments, or do it in a very poor way.

By Kareem T M

•May 18, 2020

Worst Course I have ever token on Coursera, the instructor hadn't mention any examples or simplify the information.

By HARSHIT J

•Jun 11, 2020

Very tough course, the first 3 weeks are good, but the last week is as poorly explained as one can imagine

By Michael B

•May 16, 2020

If I could give it negative stars I would.

By Mohamed S

•Jun 1, 2020

topics are poorly explained and confusing

By Anton K

•Nov 14, 2020

By far, this is the best out of 3 courses in this specialization. It is hard though and in the weeks 3 and 4 I had to pause and rewind almost every 10 seconds of the videos and search some error in code labs on the web. But in the end this course showed me in great detail the process of PCA and I also learned a bit of linear algebra alongside it. Considering problems with this course, there were some points that got me a little bit dissapointed. I still don't get it why are we using the biased version of variance, sometimes the notation changed a little bit, (which is not a big problem but introduces some inconvience if the material is completely new to the learner), some of the math concepts were not covered in the "linear algebra" course. But the worst problem was a technical one: some parts of the labs that are not necessary for grading but are very important for learning were throwing errors. I hope that in the future versions they will be resolved.

By Marco v Z

•Jul 19, 2020

I was somewhat put off by critical comments about the third course in this series, but have to disagree with the reviewers. Yes, it is tougher and, yes, the instructor doesn't have the "schwung" of the other two instructors, but that doesn't affect the quality of this course. His walkthrough of the derivation of PCA is thorough and systematic, and builds on material that has been presented in the earlier lectures.

In fact, looking back on the entire specialisation, I would retrospectively grade the first two courses a notch lower (even if they're excellent), simply because they "sailed through" a bit too easily. The exercises in those courses required little thinking apart from recalling what was said in the lectures. In this course, exercises tended to go beyond or ahead of the material presented in the lectures. Solving them required active thinking, reading, and problem solving, which in the end brings a more thorough understanding.

By Heinz D

•Nov 21, 2020

Good and motivating lecturer with decent language, thank you! Challenging course but the relief at the end is great. I'd prefer if the lecturer wouldn't write his texts to the very border of the board because if I'm taking screenshots in PiP mode, the window's controls (close window, play, return to normal video mode) are overlapping.

Week 1: Pre-course survey contains the questions of rather a post-course survey. The lab / programming assignment contains misleading code segments and incomplete explanations.

Week 2: Quiz 'General inner products', dealing with 3-dimensional inner products is very challenging as the lecture only went - in an extreme hurry - through 2-dimensional examples.

Week 3: Programming Assignment contains misleading code segments / comments (e.g. contradiction concerning return variable in project_1d()).

Week 4: Video 'Problem setting and PCA objective' -> Download Link to the PCA book chapter goes to Nirvana.

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