Volver a Mathematics for Machine Learning: PCA

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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....

WS

6 de jul. de 2021

Now i feel confident about pursuing machine learning courses in the future as I have learned most of the mathematics which will be helpful in building the base for machine learning, data science.

JS

16 de jul. de 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.

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por Thijs S

•28 de sep. de 2020

The last assignment could use improvement.

por andre w

•27 de mar. de 2022

a really good course but also really hard

por J N B P

•10 de sep. de 2020

Good for intermediates in linear algebra.

por Romesh M P

•16 de ene. de 2020

Too much non-video lectures (lot to read)

por 3047 T

•13 de jul. de 2020

The last course could have been better.

por Kailash Y

•9 de jul. de 2020

Challenging but in a good way.

por Muhammad F T S

•28 de mar. de 2021

this was hard but insightful

por Mark R

•22 de ene. de 2019

Good, short, overview of PCA

por Changson O

•28 de ene. de 2019

Many errors of homework

por Poomphob S

•18 de jun. de 2020

so challenging for me

por Sammy R

•25 de dic. de 2019

Needs more details

por Shreyas S S

•20 de jun. de 2020

Good Course

por NITESH J

•28 de ago. de 2020

kinda long

por Egi R T

•14 de jul. de 2022

Good

por Raihan N J M

•12 de mar. de 2021

okk

por Harrison B

•18 de abr. de 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?

por Mark P

•29 de jul. de 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.

por Keith C

•8 de ago. de 2021

This course was very different from the other two courses in the Mathematics Specialisation: Linear Algebra and Multivariate Calculus. The tutor approached PCA from a more algebraic or mathematic approach, rather than a more intuitive and visual approach. Most concepts covered in Week 2 and 3 were already covered in the earlier chapters, the tutor introduced new mathematical notations that only served to confuse me... It was really tough trying to understand some of the mathematical symbols that he was just using freely during the explanations. In the last chapter, he spent a long time using proofs to explain that the PCA is an eigenvector and eigenvalue problem. I struggled so much. But, the beautiful thing about PCA is that it brings together bits of Linear Algebra, Multivariate Calculus, and Statistics. PCA wraps up this specialisation nicely. All the best for those who are deciding to take this to complete the specialisation!

por Yuchi C

•23 de feb. de 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.

por Leandro C F

•1 de abr. de 2021

In many reviews of this course it was said that, unlike the others in the specialization, it is much more difficult. And this is true.

The first course was very intuitive, which ended up generating positive expectations in the others. Unfortunately this course was not at all intuitive. It was very focus on the math and in many cases the professor does not explain the meaning of the calculations. For example, dealing with inner product, when will we use any form other than the dot product? These other alternatives has a physical meaning?

The exercises at the end of the topics are just about math and are not based on any real application, which is frustrating.

The last programming exercise is tricky because it doesn't work if we calculate the covariance matrix as taught in the videos. It only works if the calculate it using np.cov().

Despite this, the course is interesting and gives you some useful insights.

por Philippe R

•16 de may. de 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.

por P G

•23 de abr. de 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.

por Keshav B

•22 de ago. de 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.

por Nguyen N D

•14 de jul. de 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.

por Giann D

•7 de abr. de 2021

While I personally enjoyed the course, I think the huge difference in handling between the Linear Algebra and Multivariate Calculus topics was too much. Even Week 1 of this course took much effort to figure out and things just kept getting more difficult with Week 4 being a huge stumbling block. I think the problem lies in the professor's pedagogy where he puts so much emphasis on the derivation and often skips on some calculations which are not intuitive for all. I personally liked the quizzes where the questions sometimes require some level of thinking which was not directly mentioned in the session, however, I see that this was not well-received by most.

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