Course Summary
This course focuses on the concept of Principal Component Analysis (PCA) and its applications in Machine Learning. It covers the theory behind PCA, and how to implement it in Python using the Scikit-learn library.Key Learning Points
- Understand the concept of PCA and its applications in Machine Learning
- Learn theory behind PCA and how to implement it in Python using Scikit-learn library
- Explore different use cases of PCA in real-world scenarios
Related Topics for further study
Learning Outcomes
- Understand the concept of PCA and its applications in Machine Learning
- Implement PCA in Python using the Scikit-learn library
- Apply PCA in real-world scenarios
Prerequisites or good to have knowledge before taking this course
- Basic knowledge of Python programming
- Familiarity with basic Machine Learning concepts
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
Similar Courses
- Machine Learning
- Data Science Essentials
- Applied Data Science with Python
Related Education Paths
- IBM Data Science Professional Certificate
- Applied Data Science with Python Specialization
- Machine Learning Engineering for Production Specialization
Related Books
Description
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.
Knowledge
- Implement mathematical concepts using real-world data
- Derive PCA from a projection perspective
- Understand how orthogonal projections work
- Master PCA
Outline
- 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
- Did you like the course? Let us know!
- Chain rule practice
Summary of User Reviews
This course on PCA in Machine Learning is highly rated by users. Many users found the course to be well-structured and easy to follow. One key aspect that many users thought was good was the practical applications of PCA in real-world scenarios.Pros from User Reviews
- Well-structured and easy to follow course
- Practical applications of PCA in real-world scenarios
- Clear explanations of concepts
Cons from User Reviews
- Some users found the course too basic
- Lack of depth in certain areas
- Not enough coding exercises
Marc Peter Deisenroth
4 Raiting
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