13 August 2021
Linear Algebra for Neuroscientists
Neuroscience is moving towards "big data," with new and improved brain measurement technologies that acquire an ever-increasing amount of data. Examples include multichannel LFP/tetrodes, high density MEEG, and optical imaging. Increases in the number of simultaneously recorded data allows new discoveries about spatiotemporal structure in the brain, but also presents new challenges for data analyses. Because data are stored in matrices, algorithms developed in matrix analysis will be extremely useful. On the other hand, linear algebra and matrix analysis are unfortunately rarely taught in neuroscience/biology/psychology courses.
The purpose of this course is to introduce you to matrix-based data analysis methods in neural time series data, with a focus on least-squares model fitting, multivariate dimensionality-reduction, and source-separation methods. The course is mathematically rigorous but is approachable to researchers with no formal mathematics background. MATLAB is the primary numerical processing engine but the material is easily portable to Python or any other language. The focus is on understanding methods and their implementation, rather than on using analysis toolboxes.
Each day will be a mix of lectures and hands-on labwork. In the labwork you will have the opportunity to implement in Matlab the concepts discussed in lecture. Labwork is done individually or in small groups of 4-5 other participants. There will be homework assignments to help you consolidate and develop your newly learned skills (homework is not graded, and solutions will be provided the following day).
This will be an intensive course designed for learning, but there will be plenty of coffee and jokes to keep you motivated.
You must bring a laptop with Matlab or Octave (a free Matlab-like software) installed.
Dr. Michael X Cohen, Associate professor
Donders Institute for Brain, Cognition and Behaviour
Radboud University Medical Center
The course is designed for PhD students, postdocs, and senior researchers who have experience with data analysis and want a deeper understanding of advanced data analysis methods.
Some experience with Matlab is necessary.
Masters students are welcomed if they have had some experience with neuroscience data analysis. The course focuses on analog electrophysiology signals (LFP/EEG/MEG), but the methods are applicable to imaging (fMRI or calcium/wide-field imaging) as well.
After this course you are able to:
1. Understand the key concepts in linear algebra including matrix multiplication, inverse, and projections, as well as know geometric and algebraic ways of representing data and analyses
2. Implement the least-squares algorithm to estimate general linear model
3. Understand eigendecomposition and its use in dimensionality reduction and source separation
4. Simulate multivariate data to evaluate analysis methods and model overfitting
EUR 350: online fee
We offer several reduced fees.