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.
Este curso forma parte de Programa Especializado - Matemática aplicada al aprendizaje automático
ofrecido por
Programa Especializado - Matemática aplicada al aprendizaje automáticoImperial College LondonAcerca de este Curso
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Resultados profesionales del estudiante
50%
comenzó una nueva carrera después de completar estos cursos
48%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel intermedio
Aprox. 20 horas para completar
Inglés (English)
Subtítulos: Inglés (English)
Habilidades que obtendrás
Dimensionality ReductionPython ProgrammingLinear Algebra
Resultados profesionales del estudiante
50%
comenzó una nueva carrera después de completar estos cursos
48%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel intermedio
Aprox. 20 horas para completar
Inglés (English)
Subtítulos: Inglés (English)
ofrecido por
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.
Programa - Qué aprenderás en este curso
6 horas para completar
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.
6 horas para completar
8 videos (Total 27 minutos), 7 lecturas, 4 cuestionarios
8 videos
Welcome to module 141s
Mean of a dataset4m
Variance of one-dimensional datasets4m
Variance of higher-dimensional datasets5m
Effect on the mean4m
Effect on the (co)variance3m
See you next module!27s
7 lecturas
About Imperial College & the team5m
How to be successful in this course5m
Grading policy5m
Additional readings & helpful references10m
Mini numpy tutorial1h
Set up Jupyter notebook environment offline10m
Symmetric, positive definite matrices10m
3 ejercicios de práctica
Mean of datasets15m
Variance of 1D datasets15m
Covariance matrix of a two-dimensional dataset15m
4 horas para completar
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.
4 horas para completar
8 videos (Total 36 minutos), 1 lectura, 5 cuestionarios
8 videos
Dot product4m
Inner product: definition5m
Inner product: length of vectors7m
Inner product: distances between vectors3m
Inner product: angles and orthogonality5m
Inner products of functions and random variables (optional)7m
Heading for the next module!35s
1 lectura
Basis vectors20m
4 ejercicios de práctica
Dot product30m
Properties of inner products20m
General inner products: lengths and distances20m
Angles between vectors using a non-standard inner product20m
4 horas para completar
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 horas para completar
6 videos (Total 25 minutos), 1 lectura, 3 cuestionarios
6 videos
Projection onto 1D subspaces7m
Example: projection onto 1D subspaces3m
Projections onto higher-dimensional subspaces8m
Example: projection onto a 2D subspace3m
This was module 3!32s
1 lectura
Full derivation of the projection20m
2 ejercicios de práctica
Projection onto a 1-dimensional subspace25m
Project 3D data onto a 2D subspace40m
5 horas para completar
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 horas para completar
10 videos (Total 52 minutos), 5 lecturas, 2 cuestionarios
10 videos
Problem setting and PCA objective7m
Finding the coordinates of the projected data5m
Reformulation of the objective10m
Finding the basis vectors that span the principal subspace7m
Steps of PCA4m
PCA in high dimensions5m
Other interpretations of PCA (optional)7m
Summary of this module42s
This was the course on PCA56s
5 lecturas
Vector spaces20m
Orthogonal complements10m
Multivariate chain rule10m
Lagrange multipliers10m
Did you like the course? Let us know!10m
1 ejercicio de práctica
Chain rule practice20m
Reseñas
Principales reseñas sobre MATHEMATICS FOR MACHINE LEARNING: PCA
por JS16 de jul. de 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 NS18 de jun. de 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.
por CJ28 de feb. de 2019
Great capstone for the three-class Mathematics for Machine Learning series. Assignments were way harder and programming debugging skills had to be appropiate in order to finish the class.
por JV30 de abr. de 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!
Acerca de Programa especializado: Matemática aplicada al aprendizaje automático
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 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.
Preguntas Frecuentes
¿Cuándo podré acceder a las lecciones y tareas?
El acceso a las clases y las asignaciones depende del tipo de inscripción que tengas. Si tomas un curso en modo de oyente, verás la mayoría de los materiales del curso en forma gratuita. Para acceder a asignaciones calificadas y obtener un certificado, deberás comprar la experiencia de Certificado, ya sea durante o después de participar como oyente. Si no ves la opción de oyente:
- es posible que el curso no ofrezca la opción de participar como oyente. En cambio, puedes intentar con una Prueba gratis o postularte para recibir ayuda económica.
- Es posible que el curso ofrezca la opción 'Curso completo, sin certificado'. Esta opción te permite ver todos los materiales del curso, enviar las evaluaciones requeridas y obtener una calificación final. También significa que no podrás comprar una experiencia de Certificado.
¿Qué recibiré si me suscribo a este Programa especializado?
Cuando te inscribes en un curso, obtienes acceso a todos los cursos que forman parte del Programa especializado y te darán un Certificado cuando completes el trabajo. Se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes auditar el curso sin costo.
Is financial aid available?
Sí, Coursera ofrece ayuda económica a los estudiantes que no pueden pagar la tarifa. Solicítala haciendo clic en el enlace de Ayuda económica que está debajo del botón “Inscribirse” a la izquierda. Se te pedirá que completes una solicitud. Recibirás una notificación en caso de que se apruebe. Deberás completar este paso para cada uno de los cursos que forman parte del Programa especializado, incluido el proyecto final. Obtén más información.
What level of programming is required to do this course?
You will need good python knowledge to get through the course.
How difficult is this course in comparison to the other two of this specialization?
This course is significantly harder and different in style: it uses more abstract concepts and requires much more programming experience than the other two courses. Therefore, when you complete the full specialization, you will be equipped with a much more diverse set of skills.
¿Recibiré crédito universitario por completar el Curso?
Este Curso no otorga crédito universitario, pero algunas universidades pueden aceptar los Certificados del curso para obtener crédito. Consulta con tu institución para obtener más información. Los Títulos en línea y los Certificados Mastertrack™ de Coursera brindan la oportunidad de obtener créditos universitarios.
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