PCA & multivariate signal processing, applied to neural data from Udemy

What's inside

Learning objectives

Understand advanced linear algebra methods
Includes a 3+ hour "crash course" on linear algebra
Apply advanced linear algebra methods in matlab and python
Simulate multivariate data for testing analysis methods

Analyzing multivariate time series datasets
Appreciate the challenges neuroscientists are struggling with!
Learn about modern neuroscience data analysis

Understand advanced linear algebra methods
Includes a 3+ hour "crash course" on linear algebra
Apply advanced linear algebra methods in matlab and python
Simulate multivariate data for testing analysis methods
Analyzing multivariate time series datasets
Appreciate the challenges neuroscientists are struggling with!
Learn about modern neuroscience data analysis

Syllabus

Introduction

Figure out if this course is right for you, and if so, how best to learn from this course.

Learn the general goals of neuroscience research, and why neuroscience is moving towards big multivariate datasets.

Definition of spatial filters, analogy to temporal filters, and different flavors of linear spatial filters.

Learn the myriad advantages of spatial filters in multivariate neuroscience.

Know the several interpretations of the word “dimension,” and the definition used in this course.

Understand the different interpretations of “source,” know which definition is used in this course, and appreciate the importance of source separation.

Mechanisms of source mixing, the idea and importance of unmixing, and some key source separation terminology.

Reducing dimensionality and separating sources are very different. This video explains why.

Know the difference between linear and nonlinear filters, and why linear filters are appropriate in many areas of neuroscience.

Want to know whether you can apply source separation methods to your data? Watch this video to find out!

Learn about the concepts, assumptions, and representations of correlations and covariances.

Learn the element-wise and matrix equations for covariances. Have some pointers for what to look for when viewing covariance matrices.

Create covariance matrices of simulated data.

Create covariance matrices of real EEG data.

See why covariance matrices must be symmetric.

See the theory implemented in MATLAB.

The "quadratic form" provides a way of understanding and visualizing the beautiful geometry of a covariance matrix.

Create and visualize the quadratic form of a covariance matrix in MATLAB.

Learn the objective and math of PCA.

Build geometric intuition of PCA using dots and surfaces.

Have step-by-step instructions for computing a PCA on multichannel data.

Follow the instructions to perform a PCA!

See a mathematical proof that all PCs (covariance eigenvectors) are orthogonal.

Learn how to interpret the eigenvalues.

Perform PCA of simulated EEG data.

Perform PCA of real EEG data.

Make sure you can use the pca() function.

Understand what happens when you don't mean-center data before computing a covariance matrix.

Understand why singular value decomposition of a data matrix will give the same results as eigendecomposition of a covariance matrix.

Demonstration of the equivalence of SVD and eigendecomposition for PCA.

Learn how to use PCA to observe the state-space of a system.

Demonstration of 2D state-space analysis in real EEG data.

PCA on phase-locked vs. total signal.

Learn why PCA is not good for source separation in multivariate neural datasets.

Conceptual idea of why and how to generalize PCA for an appropriate and general source separation algorithm.

Build geometric intuition of GED using the quadratic form of covariance matrices.

Learn the math (linear algebra) that underlies the solution to GED-based source separation.

Understand why the spatial filter is applied to the data, while the spatial pattern is interpreted.

Understand the origin of eigenvector sign indeterminancy, and how to "fix" the component sign.

See how GED can separate two independent sources in simulated EEG data.

A discussion of how to construct the two covariance matrices.

See GED in action in task-related real EEG data!

Use GED to create optimal spatial filters for narrowband spectral activity.

PCA and GED can be combined for compression/source separation, which is good for large-scale datasets.

Apply your knowledge about two-stage compression/separation to real EEG data!

Increase spatial precision by reducing large dimensions using (partial) whitening.

Apply your knowledge about ZCA and two-stage compression/separation to real EEG data!

Consider the consequences of covariance non-stationarities on source separation results.

Demonstrate the effects of covariance changes on resulting source projection topographies.

Learn the math and theory of shrinkage regularization.

Shrinkage regularization applied in MATLAB.

How to let the data tell you how much to regularize.

Don't worry, you didn't break the universe.

See a demonstration of GED and factor analysis (with default settings) on source separation.

What happens in your brain when you turn on a strobe light?

Learn about the key analysis motivations for a spatial filter for SSVEP.

The RESS analysis pipeline in words and pictures.

See RESS applied in action on real EEG data.

Theoretical/conceptual overview of ICA

See ICA in a simple example in a small dataset.

Independent components analysis in simulated EEG data.

ICs are supposed to be non-Gaussian. What do they really look like?!

Learn what "overfitting" means and what implications it has for source separation (hint: it's not all bad!).

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Provides a strong foundation in matrix-based data analysis methods, which are essential for analyzing neural time series data and extracting meaningful insights from complex datasets

Covers PCA, GED, and ICA, which are powerful dimensionality reduction and source-separation techniques widely used in neuroscience to uncover hidden patterns and structures in neural data

Includes a 3+ hour "crash course" on linear algebra, which helps learners without a strong math background grasp the fundamental concepts needed for the course

Uses MATLAB and Python, which are industry-standard tools for data analysis and scientific computing, making the skills learned directly applicable to real-world research

Explains the difference between linear and nonlinear filters, which helps learners understand why linear filters are appropriate in many areas of neuroscience

Requires learners to download course materials, including MATLAB and Python code, which may require learners to have access to software and computing resources

Reviews summary

Pca & multivariate signal processing for neural data

According to learners, this course offers a largely positive exploration of PCA & multivariate signal processing specifically applied to neural data. Students found the course to be technically rigorous yet approachable, particularly appreciating the inclusion of a linear algebra crash course which helps bridge necessary foundational knowledge. The use of both MATLAB and Python code provides practical applications that help solidify theoretical concepts. While considered demanding and requiring a solid foundation in math and programming, many students found the content highly valuable and directly applicable to research or professional work in neuroscience.

Uses both MATLAB and Python code.

"It was great that the course offered code in both MATLAB and Python, catering to different users."

"I primarily use Python, so having the Python code available alongside the MATLAB examples was very convenient."

"Being exposed to both MATLAB and Python implementations was a useful learning experience."

Crash course helps bridge knowledge gaps.

"The linear algebra crash course section was a lifesaver, it really refreshed my understanding of the necessary math."

"For someone who needed a refresher on linear algebra, this part of the course was invaluable."

"Even with some math background, the review helped ensure I was prepared for the signal processing methods."

Hands-on code helps solidify concepts.

"The code examples in both MATLAB and Python were extremely helpful for seeing how the methods work in practice."

"Applying the concepts through the provided code significantly enhanced my understanding."

"I liked being able to work with simulated and real neural data examples using the code."

Complex topics explained well.

"The instructor explains difficult topics like GED and ICA in a very clear and understandable way."

"I really appreciated the way the linear algebra concepts were reviewed and applied to the signal processing methods."

"Even though the material is advanced, the lectures break it down effectively, making it digestible."

Requires solid math/programming foundation.

"This course is quite challenging and definitely requires a strong background in linear algebra and programming."

"The pace can be fast, especially if you are not already comfortable with matrix operations and coding."

"I found the prerequisites mentioned in the course description were accurate, it's not for complete beginners in the underlying math."

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 PCA & multivariate signal processing, applied to neural data with these activities:

Review Linear Algebra Fundamentals

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Solidify your understanding of linear algebra concepts before diving into PCA and multivariate analysis. This will make the course material more accessible and easier to grasp.

Browse courses on Eigenvalues

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Review vector and matrix operations.
Practice solving linear equation systems.
Study eigenvalues and eigenvectors.

Read 'Introduction to Linear Algebra' by Gilbert Strang

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Supplement the course's linear algebra crash course with a thorough textbook. This will provide a more in-depth understanding of the mathematical foundations.

View Introduction to Linear Algebra. Sixth... on Amazon

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Read chapters on matrices and vectors.
Study sections on eigenvalues and eigenvectors.
Work through example problems.

Implement PCA from Scratch

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Reinforce your understanding of PCA by implementing it from scratch using MATLAB or Python. This hands-on exercise will solidify your knowledge of the underlying algorithms.

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Write code to calculate the covariance matrix.
Implement eigenvalue decomposition.
Project data onto principal components.

Four other activities

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Show all seven activities

Create a PCA Visualization

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Deepen your understanding of PCA by creating a visualization that illustrates how it reduces dimensionality. This will help you develop a more intuitive grasp of the technique.

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Choose a dataset to visualize.
Apply PCA to reduce dimensionality.
Create a plot showing the original and reduced data.

Analyze Neural Data with PCA and ICA

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Apply PCA and ICA to a real neural dataset to identify meaningful patterns and sources of activity. This project will provide valuable experience in applying these techniques to real-world data.

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Obtain a neural dataset.
Preprocess the data.
Apply PCA and ICA.
Interpret the results.

Read 'Independent Component Analysis' by Aapo Hyvärinen

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Expand your knowledge of ICA with a comprehensive textbook. This will provide a deeper understanding of the theory and applications of this technique.

View Independent Component Analysis on Amazon

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Read chapters on ICA algorithms.
Study sections on applications of ICA.
Explore advanced topics in ICA.

Present Findings on PCA/ICA Application

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Consolidate your learning by preparing a presentation summarizing your findings from applying PCA and ICA to neural data. This will help you communicate your understanding of these techniques to others.

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Summarize your analysis methods.
Present your key findings.
Discuss the implications of your results.

Career center

Learners who complete PCA & multivariate signal processing, applied to neural data will develop knowledge and skills that may be useful to these careers:

Computational Neuroscientist

A Computational Neuroscientist develops and uses computational models and data analysis techniques to understand the brain. Given that the course focuses on matrix-based data analysis methods specifically applied to neural data, with emphasis on multivariate dimensionality reduction and source-separation methods, this course may prepare you for a role as a computational neuroscientist. Principal components analysis and independent components analysis are techniques that are helpful for analyzing complex neural datasets. The course also provides hands-on experience with MATLAB and Python, which helps develop your computational skills.

See salaries and explore the career path for Computational Neuroscientist

Neuroimaging Analyst

A Neuroimaging Analyst processes and analyzes brain imaging data, such as fMRI and EEG. The course content aligns very closely with the responsibilities of this role, covering techniques for analyzing multivariate time series datasets and reducing dimensionality. Principal components analysis, generalized eigendecomposition, and independent components analysis are essential tools for neuroimaging analysis. The hands-on exercises with MATLAB and Python would be invaluable for a Neuroimaging Analyst.

See salaries and explore the career path for Neuroimaging Analyst

Research Scientist

A Research Scientist conducts research in various fields, including neuroscience and related disciplines. The course is designed to equip researchers with the tools and knowledge to analyze multivariate neural data. The course's emphasis on matrix-based data analysis, dimensionality reduction, and source separation techniques such as principal components analysis and independent components analysis may be useful for conducting cutting-edge research. Familiarity with MATLAB and Python, combined with a strong understanding of linear algebra, would be useful for a research scientist.

See salaries and explore the career path for Research Scientist

Systems Neuroscientist

A Systems Neuroscientist studies the neural circuits and systems that underlie behavior. This course may provide valuable tools for analyzing complex neural datasets and understanding the spatiotemporal structure of brain activity. Familiarity with principal components analysis and independent components analysis, as well as hands-on experience with MATLAB and Python, would be useful for a systems neuroscientist.

See salaries and explore the career path for Systems Neuroscientist

Neuroscience Data Scientist

A Neuroscience Data Scientist develops and applies computational methods to analyze large-scale neural datasets. Since the course focuses on matrix-based data analysis methods in neural time series data, with emphasis on multivariate dimensionality reduction and source-separation methods such as principal components analysis and independent components analysis, this course helps build a strong foundation for analyzing high-dimensional neuroscience data. You'll gain practical experience with MATLAB and Python, crucial tools in a data scientist's toolkit. Exposure to the challenges faced by neuroscientists will provide valuable context for this neuroscience data scientist role. This course may be useful for anyone interested in becoming a neuroscience data scientist.

See salaries and explore the career path for Neuroscience Data Scientist

Signal Processing Engineer

A Signal Processing Engineer designs and implements algorithms for processing signals, including neural signals. The course content directly aligns with the responsibilities of this role, as it focuses on multivariate signal processing techniques applied to neural data. The course covers dimensionality reduction and source separation methods, which are essential for extracting meaningful information from complex signals. Hands-on experience with MATLAB and Python, combined with a strong foundation in linear algebra, helps prepare you for a fulfilling career as a signal processing engineer.

See salaries and explore the career path for Signal Processing Engineer

Bioinformatics Analyst

A Bioinformatics Analyst analyzes biological data, often including neural data, to extract meaningful insights. Given that the course covers multivariate dimensionality reduction techniques like principal components analysis and independent components analysis and their application to neural time series data, it may provide you with valuable tools for analyzing complex datasets in bioinformatics. The course's focus on linear algebra and its implementation in MATLAB and Python would translate directly to the requirements of this role. Exposure to real-world neuroscience challenges helps develop practical problem-solving skills for a future Bioinformatics Analyst.

See salaries and explore the career path for Bioinformatics Analyst

Research Engineer

A Research Engineer focuses on developing and implementing new technologies and methodologies for research purposes. The course's emphasis on advanced linear algebra methods and their application to neural data may be useful for designing and implementing novel data analysis pipelines. This course may be useful for a research engineer who wishes to work in the field of neuroscience.

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Biomedical Engineer

A Biomedical Engineer applies engineering principles to solve problems in medicine and biology. The course's focus on signal processing and data analysis techniques, particularly in the context of neural data, may be useful for biomedical engineers working with neuroimaging data or developing brain-computer interfaces. The course's coverage of linear algebra and its implementation in MATLAB and Python would be useful for a biomedical engineer. The skills that you develop may be useful for analyzing complex biomedical datasets.

See salaries and explore the career path for Biomedical Engineer

Machine Learning Engineer

A Machine Learning Engineer develops and implements machine learning algorithms. The course covers principal components analysis and independent components analysis, which are fundamental techniques in machine learning for dimensionality reduction and feature extraction. The course provides hands-on experience with MATLAB and Python, which helps build practical skills in implementing and applying these algorithms. Understanding the challenges of analyzing high-dimensional neural data may be useful when adapting machine learning techniques to various real-world problems as a machine learning engineer.

See salaries and explore the career path for Machine Learning Engineer

EEG Technician

An EEG Technician records and analyzes electrical activity in the brain using electroencephalography (EEG). The course directly addresses the analysis of EEG data, covering techniques for dimensionality reduction and source separation. It provides a solid foundation in the mathematical principles behind these techniques and hands-on experience with MATLAB and Python. This knowledge enables the EEG technician to perform more informed and sophisticated data analysis, leading to more accurate diagnoses and treatment plans.

See salaries and explore the career path for EEG Technician

Quantitative Analyst

A Quantitative Analyst, often working in finance, uses mathematical and statistical models to solve complex problems. Given the course's mathematically rigorous approach to matrix-based data analysis and its focus on techniques like principal components analysis and independent components analysis this may provide a quantitative analyst with valuable tools for analyzing large datasets. The course's coverage of linear algebra may be useful for developing and implementing quantitative models. The skills acquired in this course would be useful for a quantitative analyst.

See salaries and explore the career path for Quantitative Analyst

Data Science Consultant

A Data Science Consultant advises organizations on how to leverage data to solve business problems. While the course focuses on neuroscience data, the underlying principles of data analysis and dimensionality reduction are applicable to a wide range of industries. A solid understanding of principal components analysis and independent components analysis, combined with practical experience in MATLAB and Python, would be valuable assets for a Data Science Consultant.

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Data Engineer

A Data Engineer builds and maintains the infrastructure for data storage and processing. While this role is less directly involved in data analysis, it is a highly correlated field. A solid understanding of data analysis techniques, such as principal components analysis and independent components analysis, gained from the course, help inform decisions about data storage and processing strategies. The course's emphasis on handling large datasets in MATLAB and Python helps equip you with the necessary skills to manage and optimize data infrastructure as a data engineer.

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Data Visualization Specialist

A Data Visualization Specialist transforms complex data into visual representations that are easy to understand. While the course focuses primarily on data analysis techniques, the ability to effectively visualize high-dimensional data is crucial for communicating findings. Understanding the underlying principles of dimensionality reduction, such as those taught in the course, helps create more insightful and informative visualizations. The experience gained with MATLAB and Python, combined with a strong understanding of linear algebra, would be useful for visualizing a variety of datasets as a data visualization specialist.

See salaries and explore the career path for Data Visualization Specialist

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in PCA & multivariate signal processing, applied to neural data.

Introduction to Linear Algebra (Sixth Edition)

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Provides a comprehensive introduction to linear algebra, covering essential topics like vector spaces, matrices, eigenvalues, and singular value decomposition. It's a valuable resource for building a strong foundation in the mathematical concepts underlying PCA and multivariate signal processing. The book is commonly used as a textbook at academic institutions. It provides additional depth to the linear algebra crash course provided in the syllabus.

(中文) Introduction to Linear Algebra. Sixth...

Paperback

$$$$

Independent Component Analysis

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Provides a detailed and mathematically rigorous treatment of independent component analysis (ICA). It covers the theory, algorithms, and applications of ICA in various fields. While more advanced, it's a valuable resource for those seeking a deeper understanding of ICA beyond the course material. This book is more valuable as additional reading than it is as a current reference.

Independent Component Analysis

Hardcover

$$$$

PCA & multivariate signal processing, applied to neural data

What's inside

Learning objectives

Syllabus

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Reviews summary

Pca & multivariate signal processing for neural data

Activities

Career center

Reading list

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