Вернуться к Mathematics for Machine Learning: PCA

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Оценки: 2,579

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Рецензии: 643

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

16 июля 2018 г.

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

18 июня 2020 г.

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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автор: Michael-John B

•16 мая 2020 г.

If I could give it negative stars I would.

автор: Mohamed S

•1 июня 2020 г.

topics are poorly explained and confusing

автор: Israel J L

•6 янв. 2019 г.

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.

автор: Veeramani. S

•6 сент. 2020 г.

Good Explanation. Very helpful for learning an application of mathematics through this course

автор: Makozz Q

•5 июля 2020 г.

I'd like to say thanks to everyone who has made this learning experience possible.

Thank you, Marc. Your explanations combined with the book "Mathematics for Machine Learning" have come really handy.

It has been an amazing journey to see how linear algebra marries multivariate calculus to give birth to to PCA.

Being a linguist, I must admit I'm quite new to Python and the domain of machine learning. It would be great if you could add some polishing touches to the programming assignments, especially the one in Week 4 (PCA): waiting for a long time until the system finishes crunching the code was quite a slow experience. If that has to do with a student's sloppy code, please add some recommendations inside the assignment on how to avoid this trap. If that is caused by some technical issues on the server side, please take a moment to look at this.

That you have added the Python tutorial is really helpful. Could you also consider updating it with some details on how to sort eigenvectors and eigenvalues to collect these into a covariance matrix. This piece was mighty tough.

Thank you once again. Keep on!

автор: Henry N

•27 авг. 2020 г.

Overall this was a pretty good course - some other reviews comment on how some things are glossed over in the videos but you'll get the most out of it if the other courses in the specialisation are fresh in your mind (e.g. you'll have to know about eigenvectors/eigenvalues, Gaussian elimination, derivatives and the chain rule etc. as these are referred to and used but not explained in detail - but these are covered in the first 2 courses). The main problem is with the assignments - for some weeks there's not enough guidance about what the functions should be returning, so these should be better documented; the other issue is that some of the code that we are not required to edit doesn't actually work - for instance, my implementation of PCA passed the grader but the visualisations in the week 4 notebook didn't work.

автор: Andrea V

•22 июня 2019 г.

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.

автор: Arka S

•27 мая 2020 г.

Frankly, after the high of the first two courses of this specialisation, this one was a low. Instruction was typical of most Universities; heavily analytical and monotonous. This was not a proper way, especially for such a complicated (for beginners) topic like PCA. This course could've been executed in a much better way.

Still a lot of insight is there to be gained, and I learnt quite a few things. The simplification of the cost (or loss) function was explained well, and I had quite a few 'Aha!' moments in this course as well (in Weeks 3 and 4), albeit not as much as I did in the first two courses (Lin Alg and Multivariate Calc).

автор: Ruarob T

•30 июня 2019 г.

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)

автор: Berkay E

•9 авг. 2019 г.

-Some of the contents are not clear.

+It gets great intuition for new learners in machine learning.

автор: sairavikanth t

•29 апр. 2018 г.

Lot of Math. Couldn't get proper intuition regarding PCA, was lost in understanding math equations

автор: Jessica P

•6 авг. 2019 г.

I agree with the others. Course didn't merge well with the 1st two which were perfect!

автор: Clara M L

•1 мая 2018 г.

Not as good as the other two courses but still very intuitive

автор: Shilin G

•27 июня 2019 г.

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.

автор: Patrick G

•17 мая 2020 г.

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.

автор: Ustinov A

•28 мая 2019 г.

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.

автор: Yougui Q

•2 июня 2020 г.

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.

автор: D. H

•30 сент. 2020 г.

The system is problematic, just take a look those complains in the forum. I also got very frustrated from the last assignment.

автор: Yiqing W

•28 мар. 2019 г.

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

автор: Narongdej S

•29 июня 2019 г.

Confusing for beginners; the explanations are too abrupt

автор: David S

•3 апр. 2021 г.

Of the ten or so courses that I have completed on coursera and other platforms, this one has been the most poorly taught. Usually I give four or five stars. This course gets two, which I feel is charitable.

A few examples of why I rated this course so poorly come to mind

· Instead of video lectures students are repeatedly sent to Wikipedia or similar

· The lecturer’s 417-page text was available, but without worked examples and no reference between lecture material and text

· Examples on the videos often skipped steps

· Often the videos did not have enough information to do the quizzes

· The instructor has not been on the discussion forum for 16 months

· Uninspiring assignments (and laughably low estimated times to complete)

· Intermediate level Python is required, but not mentioned as a prerequisite

I know that ‘style’ is subjective, but the institution (Imperial College London) and Coursera really should have given the lecturer some training on how to appear to enjoy teaching. Personally I would not want to attend this school for fear of being stuck with this lecturer for a semester.

The negativity of this review is unfortunate since Principal Component Analysis is an important and popular concept in statistics, math and machine learning. I hope this course is replaced in the near future. In the meantime solid on-line resources teaching the same material are available. Unfortunately I needed those resources – and an outside tutor – to pass this course.

автор: Kenny C

•22 июля 2020 г.

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.

автор: Osaama S

•22 авг. 2020 г.

Relative to the first two courses, this one unforutanately focused a lot less on building the intuition and more on proofs and theorems. The instructor did not offer insight into the "why" and "how" of projections and it was left on us to figure out how to connect eigenvectors and projections to derive PCA. The instructor also offered zero insight into the inner products properties. Big thanks to Susan Huang for explaining so many challenging and theoretical concepts on discussion forums in such beautiful detail.

автор: Astankov D A

•26 мая 2020 г.

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.

автор: Karl

•30 мая 2020 г.

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.

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