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.
Dieser Kurs ist Teil der Spezialisierung Spezialisierung Mathematik für maschinelles Lernen
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Spezialisierung Mathematik für maschinelles LernenImperial College LondonÜber diesen Kurs
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Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Kurs 3 von 3 in
Stufe „Mittel“
Ca. 18 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
Was Sie lernen werden
Implement mathematical concepts using real-world data
Derive PCA from a projection perspective
Understand how orthogonal projections work
Master PCA
Kompetenzen, die Sie erwerben
Dimensionality ReductionPython ProgrammingLinear Algebra
Karriereergebnisse der Lernenden
47%
nahm einen neuen Beruf nach Abschluss dieser Kurse auf
44%
ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Kurs 3 von 3 in
Stufe „Mittel“
Ca. 18 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
von
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.
Lehrplan - Was Sie in diesem Kurs lernen werden
5 Stunden zum Abschließen
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. Therefore, some python/numpy background will be necessary to get through this course.
5 Stunden zum Abschließen
8 Videos (Gesamt 27 min), 6 Lektüren, 4 Quiz
5 Stunden zum Abschließen
Inner Products
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.
5 Stunden zum Abschließen
8 Videos (Gesamt 36 min), 1 Lektüre, 5 Quiz
4 Stunden zum Abschließen
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.
4 Stunden zum Abschließen
6 Videos (Gesamt 25 min), 1 Lektüre, 3 Quiz
5 Stunden zum Abschließen
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.
5 Stunden zum Abschließen
10 Videos (Gesamt 52 min), 5 Lektüren, 2 Quiz
Bewertungen
Top-Bewertungen von MATHEMATICS FOR MACHINE LEARNING: PCA
von DM17. Nov. 2020
The Programming assignments are quite challenging. The teaching part doesn't equip you with enough resources regarding numpy to get full marks in the Programming Assignments. Good teaching though.
von JS16. Juli 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.
von NS18. Juni 2020
Relatively tougher than previous two courses in the specialization. I'd suggest giving more time and being patient in pursuit of completing this course and understanding the concepts involved.
von JV30. Apr. 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!
Über den Spezialisierung Mathematik für maschinelles Lernen
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.
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