Informações sobre o curso
4.0
417 classificações
90 avaliações
Programa de cursos integrados
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Nível intermediário

Nível intermediário

Horas para completar

Aprox. 18 horas para completar

Sugerido: 4 weeks of study, 4-5 hours/week...
Idiomas disponíveis

Inglês

Legendas: Inglês...

Habilidades que você terá

Python ProgrammingPrincipal Component Analysis (PCA)Projection MatrixMathematical Optimization
Programa de cursos integrados
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Nível intermediário

Nível intermediário

Horas para completar

Aprox. 18 horas para completar

Sugerido: 4 weeks of study, 4-5 hours/week...
Idiomas disponíveis

Inglês

Legendas: Inglês...

Programa - O que você aprenderá com este curso

Semana
1
Horas para completar
5 horas para concluir

Statistics of Datasets

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....
Reading
8 vídeos (Total de 27 min), 5 leituras, 4 testes
Video8 videos
Welcome to module 1min
Mean of a dataset4min
Variance of one-dimensional datasets4min
Variance of higher-dimensional datasets5min
Effect on the mean4min
Effect on the (co)variance3min
See you next module!min
Reading5 leituras
About Imperial College & the team5min
How to be successful in this course5min
Grading policy5min
Additional readings & helpful references5min
Symmetric, positive definite matrices10min
Quiz3 exercícios práticos
Mean of datasets15min
Variance of 1D datasets15min
Covariance matrix of a two-dimensional dataset15min
Semana
2
Horas para completar
4 horas para concluir

Inner Products

Data can be interpreted as vectors. Vectors allow us to talk about geometric concepts, such as lengths, distances and angles to characterise 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....
Reading
8 vídeos (Total de 36 min), 1 leitura, 5 testes
Video8 videos
Dot product4min
Inner product: definition5min
Inner product: length of vectors7min
Inner product: distances between vectors3min
Inner product: angles and orthogonality5min
Inner products of functions and random variables (optional)7min
Heading for the next module!min
Reading1 leituras
Basis vectors20min
Quiz4 exercícios práticos
Dot product10min
Properties of inner products20min
General inner products: lengths and distances20min
Angles between vectors using a non-standard inner product20min
Semana
3
Horas para completar
4 horas para concluir

Orthogonal Projections

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....
Reading
6 vídeos (Total de 25 min), 1 leitura, 3 testes
Video6 videos
Projection onto 1D subspaces7min
Example: projection onto 1D subspaces3min
Projections onto higher-dimensional subspaces8min
Example: projection onto a 2D subspace3min
This was module 3!min
Reading1 leituras
Full derivation of the projection20min
Quiz2 exercícios práticos
Projection onto a 1-dimensional subspace25min
Project 3D data onto a 2D subspace40min
Semana
4
Horas para completar
5 horas para concluir

Principal Component Analysis

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. ...
Reading
10 vídeos (Total de 52 min), 5 leituras, 2 testes
Video10 videos
Problem setting and PCA objective7min
Finding the coordinates of the projected data5min
Reformulation of the objective10min
Finding the basis vectors that span the principal subspace7min
Steps of PCA4min
PCA in high dimensions5min
Other interpretations of PCA (optional)7min
Summary of this modulemin
This was the course on PCAmin
Reading5 leituras
Vector spaces20min
Orthogonal complements10min
Multivariate chain rule10min
Lagrange multipliers10min
Did you like the course? Let us know!10min
Quiz1 exercício prático
Chain rule practice20min
4.0

Melhores avaliações

por JSJul 17th 2018

This is one hell of an inspiring course that demystified the difficult concepts and math behind PCA. Excellent instructors in imparting the these knowledge with easy-to-understand illustrations.

por JVMay 1st 2018

This course was definitely a bit more complex, not so much in assignments but in the core concepts handled, than the others in the specialisation. Overall, it was fun to do this course!

Instrutores

Avatar

Marc P. Deisenroth

Lecturer in Statistical Machine Learning
Department of Computing

Sobre Imperial College London

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

Sobre o Programa de cursos integrados Mathematics for Machine Learning

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 basic 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

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