Difference between revisions of "BCI"
From Research management course
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| − | Brain-Computer Interfaces and Functional Data Analysis | + | ==Brain-Computer Interfaces and Functional Data Analysis== |
| + | This course is ''under construction''. It enlightens fundamental mathematical concepts of brain signal analysis. | ||
| + | |||
| + | Each class combines five parts: | ||
| + | # Comprehensive introduction | ||
| + | # Practical example with code and homework | ||
| + | # Algebraic part of modeling | ||
| + | # Statistical part of modeling | ||
| + | # Join them in Hilbert (or any convenient) space | ||
| + | # Quiz for the next part (could be in the beginning) to show the theory to catch up | ||
| + | |||
| + | ==Linear models== | ||
| + | ===SSA, SVD, PCA=== | ||
| + | |||
| + | ===Acceleroneter data=== | ||
| + | * Energy | ||
| + | |||
| + | |||
| + | ===Tensor product and spectral decomposition=== | ||
| + | * vector, covector, dot product | ||
| + | * linear operator | ||
| + | * in Euclidean and (Hilbert space with useful example) dot product=bilinear form | ||
| + | * bilinear form | ||
| + | * | ||
| + | |||
| + | Why we go from Eucledian to Hilbert space? Was: a vector as a number of measurements. Now it is a finite number of samples. Then it is a distribution of samples. The distribution is a point in the Hilbert space. We can make an inner product and tensor product of two and more distributions. Machine learning: given samples, multivariate distribution can be represented as a (direct?) sum of elements' tensor products. | ||
| + | |||
| + | ===PPCA=== | ||
| + | |||
| + | |||
==Introduction to BCI== | ==Introduction to BCI== | ||
Revision as of 03:07, 25 March 2023
Contents
Brain-Computer Interfaces and Functional Data Analysis
This course is under construction. It enlightens fundamental mathematical concepts of brain signal analysis.
Each class combines five parts:
- Comprehensive introduction
- Practical example with code and homework
- Algebraic part of modeling
- Statistical part of modeling
- Join them in Hilbert (or any convenient) space
- Quiz for the next part (could be in the beginning) to show the theory to catch up
Linear models
SSA, SVD, PCA
Acceleroneter data
- Energy
Tensor product and spectral decomposition
- vector, covector, dot product
- linear operator
- in Euclidean and (Hilbert space with useful example) dot product=bilinear form
- bilinear form
Why we go from Eucledian to Hilbert space? Was: a vector as a number of measurements. Now it is a finite number of samples. Then it is a distribution of samples. The distribution is a point in the Hilbert space. We can make an inner product and tensor product of two and more distributions. Machine learning: given samples, multivariate distribution can be represented as a (direct?) sum of elements' tensor products.