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
von
Über diesen Kurs
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 Reduction
- Python Programming
- Linear Algebra
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
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.
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.
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.
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.
Bewertungen
- 5 stars51,05 %
- 4 stars22,58 %
- 3 stars12,80 %
- 2 stars6,73 %
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Top-Bewertungen von MATHEMATICS FOR MACHINE LEARNING: PCA
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.
Challenging, but doable. Has some bugs in coding assignments, but clearing them out makes you understand things better. Get ready to spend extra time understanding the concepts.
It is a bit difficult and jumpy. You will need some hard work to fill in the missing links of knowledge which not explicite on the lectrue. Overall, great experience.
The course is generally good but the assignment setting definitely needs to be rectified. Thanks anyway for this course. An important element of machine learning.
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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