About this Course

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Intermediate Level
Approx. 19 hours to complete
English
Subtitles: English

What you will learn

  • Implement mathematical concepts using real-world data

  • Derive PCA from a projection perspective

  • Understand how orthogonal projections work

  • Master PCA

Skills you will gain

Dimensionality ReductionPython ProgrammingLinear Algebra

Learner Career Outcomes

50%

started a new career after completing these courses

48%

got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 19 hours to complete
English
Subtitles: English

Offered by

Imperial College London logo

Imperial College London

Syllabus - What you will learn from this course

Content RatingThumbs Up80%(4,326 ratings)Info
Week
1

Week 1

5 hours to complete

Statistics of Datasets

5 hours to complete
8 videos (Total 27 min), 6 readings, 4 quizzes
8 videos
Welcome to module 141s
Mean of a dataset4m
Variance of one-dimensional datasets4m
Variance of higher-dimensional datasets5m
Effect on the mean4m
Effect on the (co)variance3m
See you next module!27s
6 readings
About Imperial College & the team5m
How to be successful in this course5m
Grading policy5m
Additional readings & helpful references5m
Set up Jupyter notebook environment offline10m
Symmetric, positive definite matrices10m
3 practice exercises
Mean of datasets15m
Variance of 1D datasets15m
Covariance matrix of a two-dimensional dataset15m
Week
2

Week 2

4 hours to complete

Inner Products

4 hours to complete
8 videos (Total 36 min), 1 reading, 5 quizzes
8 videos
Dot product4m
Inner product: definition5m
Inner product: length of vectors7m
Inner product: distances between vectors3m
Inner product: angles and orthogonality5m
Inner products of functions and random variables (optional)7m
Heading for the next module!35s
1 reading
Basis vectors20m
4 practice exercises
Dot product10m
Properties of inner products20m
General inner products: lengths and distances20m
Angles between vectors using a non-standard inner product20m
Week
3

Week 3

4 hours to complete

Orthogonal Projections

4 hours to complete
6 videos (Total 25 min), 1 reading, 3 quizzes
6 videos
Projection onto 1D subspaces7m
Example: projection onto 1D subspaces3m
Projections onto higher-dimensional subspaces8m
Example: projection onto a 2D subspace3m
This was module 3!32s
1 reading
Full derivation of the projection20m
2 practice exercises
Projection onto a 1-dimensional subspace25m
Project 3D data onto a 2D subspace40m
Week
4

Week 4

5 hours to complete

Principal Component Analysis

5 hours to complete
10 videos (Total 52 min), 5 readings, 2 quizzes
10 videos
Problem setting and PCA objective7m
Finding the coordinates of the projected data5m
Reformulation of the objective10m
Finding the basis vectors that span the principal subspace7m
Steps of PCA4m
PCA in high dimensions5m
Other interpretations of PCA (optional)7m
Summary of this module42s
This was the course on PCA56s
5 readings
Vector spaces20m
Orthogonal complements10m
Multivariate chain rule10m
Lagrange multipliers10m
Did you like the course? Let us know!10m
1 practice exercise
Chain rule practice20m

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About the Mathematics for Machine Learning Specialization

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....
Mathematics for Machine Learning

Frequently Asked Questions

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    • The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
  • 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.

  • If you subscribed, you get a 7-day free trial during which you can cancel at no penalty. After that, we don’t give refunds, but you can cancel your subscription at any time. See our full refund policy.

  • Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You'll be prompted to complete an application and will be notified if you are approved. You'll need to complete this step for each course in the Specialization, including the Capstone Project. Learn more.

  • You will need good python knowledge to get through the course.

  • 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.

  • This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.

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