17 August 2018
Linear Algebra for Neuroscientists
Do you have large-scale neuroscience datasets and lots of ideas, but need a better understanding of how to work with your data? Then this course is for you! In one intense week you will learn several key mathematical concepts in multichannel neuroscience analyses with a focus on dimensionality reduction, source separation, and synchronization, and how to implement them in Matlab.
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 and 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 the concepts discussed in lecture in Matlab. Labwork is done individually or in small groups of 2-3 students. 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 chocolates to keep you motivated. You must bring a laptop with Matlab or Octave (a free Matlab-like software) installed.
Master, PhD, Postdoc, Professional. This course is designed for PhD students, postdocs, and senior researchers who are interested in learning about cutting-edge multivariate data analysis methods that are suitable for hypothesis testing and exploration in multichannel recordings (“big data”). Some experience with Matlab is necessary. Master’s students are welcome if they have had some experience with neuroscience data analysis. The course material is applicable to any multichannel data, including electrophysiology (spikes/LFP/EEG/MEG) and functional imaging (fMRI/2P/Ca/voltage).
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 parameters.
3. Understand eigendecomposition and its use in dimensionality reduction and source separation.
4. Simulate multivariate data to evaluate analysis methods and model overfitting.
EUR 585: The fee includes the registration fees, course materials, access to library and IT facilities, coffee/tea, lunch, and a number of social activities.
We offer several reduced fees:
€ 527 early bird discount – deadline 1 April 2018 (10%)
€ 497 partner + RU discount (15%)
€ 439 early bird + partner discount (25%)