Imperial College London
Mathematics for Machine Learning: PCA
Imperial College London

Mathematics for Machine Learning: PCA

This course is part of Mathematics for Machine Learning Specialization

Taught in English

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Course

Gain insight into a topic and learn the fundamentals

4.0

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Intermediate level
Some related experience required
20 hours (approximately)
Flexible schedule
Learn at your own pace

What you'll learn

  • Implement mathematical concepts using real-world data

  • Derive PCA from a projection perspective

  • Understand how orthogonal projections work

  • Master PCA

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Assessments

11 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.0

(3,041 reviews)

|

80%

Intermediate level
Some related experience required
20 hours (approximately)
Flexible schedule
Learn at your own pace

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This course is part of the Mathematics for Machine Learning Specialization
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There are 4 modules in this course

Principal Component Analysis (PCA) is one of the most important dimensionality reduction algorithms in machine learning. In this course, we lay the mathematical foundations to derive and understand PCA from a geometric point of view. In this module, we learn how to summarize datasets (e.g., images) using basic statistics, such as the mean and the variance. We also look at properties of the mean and the variance when we shift or scale the original data set. We will provide mathematical intuition as well as the skills to derive the results. We will also implement our results in code (jupyter notebooks), which will allow us to practice our mathematical understand to compute averages of image data sets. Therefore, some python/numpy background will be necessary to get through this course. Note: If you have taken the other two courses of this specialization, this one will be harder (mostly because of the programming assignments). However, if you make it through the first week of this course, you will make it through the full course with high probability.

What's included

8 videos6 readings3 quizzes1 programming assignment1 discussion prompt2 ungraded labs1 plugin

Data can be interpreted as vectors. Vectors allow us to talk about geometric concepts, such as lengths, distances and angles to characterize similarity between vectors. This will become important later in the course when we discuss PCA. In this module, we will introduce and practice the concept of an inner product. Inner products allow us to talk about geometric concepts in vector spaces. More specifically, we will start with the dot product (which we may still know from school) as a special case of an inner product, and then move toward a more general concept of an inner product, which play an integral part in some areas of machine learning, such as kernel machines (this includes support vector machines and Gaussian processes). We have a lot of exercises in this module to practice and understand the concept of inner products.

What's included

8 videos1 reading4 quizzes1 programming assignment2 ungraded labs

In this module, we will look at orthogonal projections of vectors, which live in a high-dimensional vector space, onto lower-dimensional subspaces. This will play an important role in the next module when we derive PCA. We will start off with a geometric motivation of what an orthogonal projection is and work our way through the corresponding derivation. We will end up with a single equation that allows us to project any vector onto a lower-dimensional subspace. However, we will also understand how this equation came about. As in the other modules, we will have both pen-and-paper practice and a small programming example with a jupyter notebook.

What's included

6 videos1 reading2 quizzes1 programming assignment1 ungraded lab

We can think of dimensionality reduction as a way of compressing data with some loss, similar to jpg or mp3. Principal Component Analysis (PCA) is one of the most fundamental dimensionality reduction techniques that are used in machine learning. In this module, we use the results from the first three modules of this course and derive PCA from a geometric point of view. Within this course, this module is the most challenging one, and we will go through an explicit derivation of PCA plus some coding exercises that will make us a proficient user of PCA.

What's included

10 videos5 readings2 quizzes1 programming assignment2 ungraded labs1 plugin

Instructor

Instructor ratings
3.9 (406 ratings)
Marc Peter Deisenroth
Imperial College London
1 Course87,243 learners

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