À propos de ce cours
76,824 consultations récentes

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 18 heures pour terminer

Recommandé : 4 weeks of study, 4-5 hours/week...

Anglais

Sous-titres : Anglais

Compétences que vous acquerrez

Python ProgrammingPrincipal Component Analysis (PCA)Projection MatrixMathematical Optimization

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau intermédiaire

Approx. 18 heures pour terminer

Recommandé : 4 weeks of study, 4-5 hours/week...

Anglais

Sous-titres : Anglais

Programme du cours : ce que vous apprendrez dans ce cours

Semaine
1
5 heures pour terminer

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....
8 vidéos (Total 27 min), 6 lectures, 4 quiz
8 vidéos
Welcome to module 141s
Mean of a dataset4 min
Variance of one-dimensional datasets4 min
Variance of higher-dimensional datasets5 min
Effect on the mean4 min
Effect on the (co)variance3 min
See you next module!27s
6 lectures
About Imperial College & the team5 min
How to be successful in this course5 min
Grading policy5 min
Additional readings & helpful references5 min
Set up Jupyter notebook environment offline10 min
Symmetric, positive definite matrices10 min
3 exercices pour s'entraîner
Mean of datasets15 min
Variance of 1D datasets15 min
Covariance matrix of a two-dimensional dataset15 min
Semaine
2
4 heures pour terminer

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....
8 vidéos (Total 36 min), 1 lecture, 5 quiz
8 vidéos
Dot product4 min
Inner product: definition5 min
Inner product: length of vectors7 min
Inner product: distances between vectors3 min
Inner product: angles and orthogonality5 min
Inner products of functions and random variables (optional)7 min
Heading for the next module!35s
1 lecture
Basis vectors20 min
4 exercices pour s'entraîner
Dot product10 min
Properties of inner products20 min
General inner products: lengths and distances20 min
Angles between vectors using a non-standard inner product20 min
Semaine
3
4 heures pour terminer

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....
6 vidéos (Total 25 min), 1 lecture, 3 quiz
6 vidéos
Projection onto 1D subspaces7 min
Example: projection onto 1D subspaces3 min
Projections onto higher-dimensional subspaces8 min
Example: projection onto a 2D subspace3 min
This was module 3!32s
1 lecture
Full derivation of the projection20 min
2 exercices pour s'entraîner
Projection onto a 1-dimensional subspace25 min
Project 3D data onto a 2D subspace40 min
Semaine
4
5 heures pour terminer

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. ...
10 vidéos (Total 52 min), 5 lectures, 2 quiz
10 vidéos
Problem setting and PCA objective7 min
Finding the coordinates of the projected data5 min
Reformulation of the objective10 min
Finding the basis vectors that span the principal subspace7 min
Steps of PCA4 min
PCA in high dimensions5 min
Other interpretations of PCA (optional)7 min
Summary of this module42s
This was the course on PCA56s
5 lectures
Vector spaces20 min
Orthogonal complements10 min
Multivariate chain rule10 min
Lagrange multipliers10 min
Did you like the course? Let us know!10 min
1 exercice pour s'entraîner
Chain rule practice20 min
4.0
149 avisChevron Right

50%

a commencé une nouvelle carrière après avoir terminé ces cours

50%

a bénéficié d'un avantage concret dans sa carrière grâce à ce cours

10%

a obtenu une augmentation de salaire ou une promotion

Meilleurs avis

par 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.

par 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!

Enseignant

Avatar

Marc P. Deisenroth

Lecturer in Statistical Machine Learning
Department of Computing

À propos de 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....

À propos de la Spécialisation 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

Foire Aux Questions

  • Une fois que vous êtes inscrit(e) pour un Certificat, vous pouvez accéder à toutes les vidéos de cours, et à tous les quiz et exercices de programmation (le cas échéant). Vous pouvez soumettre des devoirs à examiner par vos pairs et en examiner vous-même uniquement après le début de votre session. Si vous préférez explorer le cours sans l'acheter, vous ne serez peut-être pas en mesure d'accéder à certains devoirs.

  • Lorsque vous vous inscrivez au cours, vous bénéficiez d'un accès à tous les cours de la Spécialisation, et vous obtenez un Certificat lorsque vous avez réussi. Votre Certificat électronique est alors ajouté à votre page Accomplissements. À partir de cette page, vous pouvez imprimer votre Certificat ou l'ajouter à votre profil LinkedIn. Si vous souhaitez seulement lire et visualiser le contenu du cours, vous pouvez accéder gratuitement au cours en tant qu'auditeur libre.

D'autres questions ? Visitez le Centre d'Aide pour les Etudiants.