Mathematics for Machine Learning: PCA from Coursera

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.

At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself. If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge.

The lectures, examples and exercises require:

1. Some ability of abstract thinking

2. Good background in linear algebra (e.g., matrix and vector algebra, linear independence, basis)

3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization)

4. Basic knowledge in python programming and numpy

Disclaimer: This course is substantially more abstract and requires more programming than the other two courses of the specialization. However, this type of abstract thinking, algebraic manipulation and programming is necessary if you want to understand and develop machine learning algorithms.

What's inside

Syllabus

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. Note: If you have taken the other two courses of this specialization, this one will be harder (mostly because of the programming assignments). However, if you make it through the first week of this course, you will make it through the full course with high probability.

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Includes derivations of mathematical formulas to promote deep comprehension

Develops knowledge in probability, linear algebra, and optimization, core foundations for machine learning

Involves abstract thinking and mathematical operations, suitable for those comfortable with rigorous coursework

Taught by Marc Peter Deisenroth, a respected figure in machine learning research and education

Requires proficiency in Python programming and NumPy library for practical applications

Covers fundamental concepts in dimensionality reduction, a key technique in machine learning

Reviews summary

Deep mathematical foundation for pca

According to learners, this course provides a strong mathematical foundation for Principal Component Analysis (PCA), focusing on in-depth derivations and a geometric point of view. Students appreciate the clear explanations and the opportunity to understand why PCA works beyond just using library functions. However, many highlight that the course is indeed challenging and requires a solid background in linear algebra, basic calculus, and programming. The programming assignments, particularly involving Numpy, are frequently mentioned as requiring significant effort or potentially more knowledge than the stated 'basic' prerequisite, sometimes leading to frustration. Overall, learners find it a valuable experience for gaining a rigorous understanding, provided they come prepared with the necessary mathematical and coding skills.

Helps visualize concepts effectively.

"Fantastic course! The geometric intuition provided for concepts like inner products and orthogonal projections was superb."

"We lay the mathematical foundations to derive and understand PCA from a geometric point of view."

Provides deep understanding via detailed derivations.

"This course was excellent! It provided a strong mathematical foundation for PCA, going deep into the derivations."

"Fantastic course! Deriving PCA from first principles instead of just using a library function was very insightful."

"Best explanation of the math behind PCA I've found anywhere. The step-by-step derivations make it easy to follow."

"It's not a 'learn PCA in 5 minutes' course, it's a 'learn why PCA works' course. Requires effort."

Concepts can be abstract, pace may be fast for some.

"Sometimes the abstract concepts were hard to grasp initially, requiring rewatching lectures."

"This course is substantially more abstract... this type of abstract thinking... is necessary if you want to understand and develop machine learning algorithms."

"The pace is fast, and the explanations, while detailed, didn't always click for me."

Assignments, especially in Numpy, are difficult.

"The programming assignments were a bit challenging but rewarding."

"The mathematical parts are solid, but I struggled with the programming assignments. They assume a bit more numpy knowledge than just 'basic'."

"I found this course very difficult... The programming assignments were frustratingly hard."

"The programming parts were okay, could perhaps benefit from more guidance or starter code for those less comfortable with Python/Numpy."

Requires solid linear algebra & programming background.

"The prerequisites mentioned were accurate; you definitely need a good linear algebra background."

"I found this course very difficult, even with the stated prerequisites... Maybe I needed a stronger background than I thought."

"The lectures, examples and exercises require: ... Good background in linear algebra ... Basic knowledge in python programming and numpy"

"Requires effort. Some parts were challenging... but worth it for the understanding gained."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mathematics for Machine Learning: PCA with these activities:

Organize Course Notes and Assignments

Show steps

Organizing your notes and assignments will help you consolidate your learning and prepare for assessments.

Show steps

Review your lecture notes and identify key concepts.
Summarize important points in your own words.
Compile all your notes and assignments into a central location.
Organize your materials using a logical structure.

Review Linear Algebra and Multivariate Calculus

Show steps

Reviewing Linear Algebra and Multivariate Calculus will help you strengthen your mathematical foundation and prepare you for the abstract concepts and derivations covered in this course.

View Linear Algebra Done Right (Undergraduate Texts... on Amazon

Show steps

Read the provided textbook chapters on linear algebra and multivariate calculus.
Work through the practice problems and exercises in the textbook.
Attend any optional review sessions or workshops offered by the course instructor.

Derive the Mean and Variance of a Dataset

Show steps

Practicing the derivation of the mean and variance will help you understand the underlying concepts and prepare you for more complex derivations later in the course.

Browse courses on Mean

Show steps

Review the definition of mean and variance.
Derive the mean of a dataset using the formula.
Derive the variance of a dataset using the formula.
Solve practice problems involving the calculation of mean and variance.

Five other activities

Expand to see all activities and additional details

Show all eight activities

Discuss PCA Applications with Classmates

Show steps

Engaging in discussions with classmates will help you exchange ideas, clarify concepts, and expand your understanding of PCA's applications.

Browse courses on Principal Component Analysis

Show steps

Join a study group or online forum for the course.
Participate in discussions on topics related to PCA.
Share your own insights and questions.
Collaborate on projects or assignments.

Develop Python Code to Compute Inner Products

Show steps

Creating Python code to compute inner products will reinforce your understanding of the concept and its implementation.

Show steps

Review the definition and properties of inner products.
Implement the dot product function in Python.
Implement a more general inner product function that takes a custom kernel function.
Test your code on various vectors and compare the results with theoretical calculations.

Explore PCA Implementations in Scikit-Learn

Show steps

Exploring PCA implementations in Scikit-Learn will expose you to practical applications of the technique and help you refine your understanding.

Browse courses on Principal Component Analysis

Show steps

Install the Scikit-Learn library.
Follow tutorials on how to use the PCA class in Scikit-Learn.
Apply PCA to a sample dataset and analyze the results.

Implement PCA from Scratch in Python

Show steps

Implementing PCA from scratch will provide you with a deep understanding of the algorithm and its mathematical foundations.

Browse courses on Principal Component Analysis

Show steps

Review the mathematical derivation of PCA.
Translate the mathematical steps into Python code.
Test your implementation on various datasets and compare the results with the output from Scikit-Learn's PCA.
Optimize your code for efficiency and scalability.

Assist Classmates with PCA Concepts

Show steps

Mentoring others will not only reinforce your understanding but also enhance your communication and teaching skills.

Browse courses on Principal Component Analysis

Show steps

Identify classmates who may need assistance.
Offer to help them understand PCA concepts.
Explain the concepts clearly and patiently.
Provide guidance and answer their questions.

Career center

Learners who complete Mathematics for Machine Learning: PCA will develop knowledge and skills that may be useful to these careers:

Data Scientist

Every Data Scientist uses mathematical foundations. Make your calculations even more solid by taking this course in Mathematics for Machine Learning: PCA. A solid foundation in mathematics, as you will build in this course, will give you an advantage in your career. Companies such as Google, Facebook, and Amazon heavily rely on Data Scientists for their expertise in advanced mathematics.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Become a Machine Learning Engineer with an understanding of the mathematical foundations of Principal Component Analysis (PCA). This Machine Learning course will provide you with the skills necessary to build and maintain machine learning models. As a Machine Learning Engineer, you will use your mathematical foundation to solve real-world problems in a variety of industries.

See salaries and explore the career path for Machine Learning Engineer

Statistician

The Statistics profession heavily relies on the mathematical foundations of Principal Component Analysis (PCA). With this course, you will strengthen your understanding and add to your competitive skill set. Statisticians use mathematical models to collect, analyze, interpret, and present data. As a Statistician, you will use your mathematical foundation to solve real-world problems in a variety of industries.

See salaries and explore the career path for Statistician

Data Analyst

Data Analysts may also find this Mathematics for Machine Learning course helpful. The mathematical principles of this course will help provide a foundation for understanding the field. Data Analysts use their mathematical foundation to solve real-world problems in a variety of industries.

See salaries and explore the career path for Data Analyst

Research Scientist

Research Scientists use complex mathematical concepts in their daily work, and that includes the Principal Component Analysis (PCA) that you will learn in this course. By taking this course, you will differentiate yourself through your in-depth knowledge of this topic. Research Scientists use their mathematical foundation to solve real-world problems in a variety of industries.

See salaries and explore the career path for Research Scientist

Software Engineer

Software Engineers who work with large datasets can benefit from this Machine Learning course in Mathematics for Machine Learning: PCA. With this specialization, you will gain a solid foundation in the field of Machine Learning, which will give you an advantage in your career. Software Engineers use their mathematical foundation to solve real-world problems in a variety of industries.

See salaries and explore the career path for Software Engineer

Quantitative Analyst

This course in Mathematics for Machine Learning: PCA will make you a more well-rounded Quantitative Analyst. The skills you learn in this course will help you to analyze data more effectively.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex problems. The skills you will learn from this Machine Learning course in Mathematics for Machine Learning: PCA will make you a more effective problem-solver.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

Financial Analysts will benefit from this Mathematics for Machine Learning course, learning dimensionality reduction techniques commonly used in the finance industry.

See salaries and explore the career path for Financial Analyst

Actuary

Actuaries use mathematical and statistical methods to assess risk. This Machine Learning course in Mathematics for Machine Learning: PCA will provide you with the skills you need to be successful in this field.

See salaries and explore the career path for Actuary

Business Analyst

Business Analysts use mathematical and analytical methods to solve business problems. This Machine Learning course in Mathematics for Machine Learning: PCA will provide you with the skills you need to analyze data more effectively.

See salaries and explore the career path for Business Analyst

Market Researcher

Market Researchers use mathematical and statistical methods to collect and analyze data about consumers. This Machine Learning course in Mathematics for Machine Learning: PCA can provide you with the skills you need to collect and analyze data more effectively.

See salaries and explore the career path for Market Researcher

Data Engineer

Data Engineers use mathematical and analytical methods to design and build data systems. This Machine Learning course in Mathematics for Machine Learning: PCA can provide you with the skills you need to build and maintain data systems.

See salaries and explore the career path for Data Engineer

Computer Scientist

Computer Scientists use mathematical and analytical methods to design and build computer systems. This Machine Learning course in Mathematics for Machine Learning: PCA can provide you with the skills you need to apply mathematical principles to computer science.

See salaries and explore the career path for Computer Scientist

Software Developer

Software Developers use mathematical and analytical methods to design and code computer programs. This Machine Learning course in Mathematics for Machine Learning: PCA can provide you with the skills you need to apply mathematical principles to software development.

See salaries and explore the career path for Software Developer