Mathematics for Machine Learning: PCA
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Mathematics for Machine Learning: PCA at Coursera Overview
Duration | 18 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
Mathematics for Machine Learning: PCA at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 3 of 3 in the Mathematics for Machine Learning Specialization
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Intermediate Level
- Approx. 18 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
Mathematics for Machine Learning: PCA at Coursera Course details
- 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.
Mathematics for Machine Learning: PCA at Coursera Curriculum
Statistics of Datasets
Introduction to the course
Welcome to module 1
Mean of a dataset
Variance of one-dimensional datasets
Variance of higher-dimensional datasets
Effect on the mean
Effect on the (co)variance
See you next module!
About Imperial College & the team
How to be successful in this course
Grading policy
Additional readings & helpful references
Set up Jupyter notebook environment offline
Symmetric, positive definite matrices
Mean of datasets
Variance of 1D datasets
Covariance matrix of a two-dimensional dataset
Inner Products
Welcome to module 2
Dot product
Inner product: definition
Inner product: length of vectors
Inner product: distances between vectors
Inner product: angles and orthogonality
Inner products of functions and random variables (optional)
Heading for the next module!
Basis vectors
Dot product
Properties of inner products
General inner products: lengths and distances
Angles between vectors using a non-standard inner product
Orthogonal Projections
Welcome to module 3
Projection onto 1D subspaces
Example: projection onto 1D subspaces
Projections onto higher-dimensional subspaces
Example: projection onto a 2D subspace
This was module 3!
Full derivation of the projection
Projection onto a 1-dimensional subspace
Project 3D data onto a 2D subspace
Principal Component Analysis
Welcome to module 4
Problem setting and PCA objective
Finding the coordinates of the projected data
Reformulation of the objective
Finding the basis vectors that span the principal subspace
Steps of PCA
PCA in high dimensions
Other interpretations of PCA (optional)
Summary of this module
This was the course on PCA
Vector spaces
Orthogonal complements
Multivariate chain rule
Lagrange multipliers
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Chain rule practice
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