Mathematics for Machine Learning PCA
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:
- Some ability of abstract thinking
- Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis)
- Basic background in multivariate calculus (e.g., partial derivatives, basic optimization)
- 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.
Implement mathematical concepts using real-world data
Derive PCA from a projection perspective
Understand how orthogonal projections work
Syllabus
Syllabus - What you will learn from this course
Week 1
Statistics of Datasets
Week 2
Inner Products
Week 3
Orthogonal Projections
Week 4
Principal Component Analysis
FAQ
When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.
What level of programming is required to do this course?
You will need good python knowledge to get through the course.
How difficult is this course in comparison to the other two of this specialization?
This course is significantly harder and different in style: it uses more abstract concepts and requires much more programming experience than the other two courses. Therefore, when you complete the full specialization, you will be equipped with a much more diverse set of skills.
Reviews
This course is well worth the time. I have a better understanding of one of the most foundational and biologically plausible machine learning algorithms used today! Love it.
Overall the course was great. The only thing was that there was a lot I didn't understand from the videos. The recommended textbook resource was a great help.
Really clear and well explained. The concepts are treated in detail enough to be applied. Very happy to have invested my time in this course. I strongly recomend it.
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.
