Difference between revisions of "BCI"
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== Datasets == | == Datasets == | ||
== ERP data == | == ERP data == | ||
| − | Event-related potential, see [https://en.wikipedia.org/wiki/Event-related_potential ERP] and [https://en.wikipedia.org/wiki/P300_(neuroscience) P300] is triggered by a stimulus and registered over [https://en.wikipedia.org/wiki/Electroencephalography EEG] monitor electrodes after the stimulus onset and before it | + | Event-related potential, see [https://en.wikipedia.org/wiki/Event-related_potential ERP] and [https://en.wikipedia.org/wiki/P300_(neuroscience) P300] is triggered by a stimulus and registered over [https://en.wikipedia.org/wiki/Electroencephalography EEG] monitor electrodes after the stimulus onset and before it. |
| + | The listed EEG datasets are expected to be of a maximum number of events to [[Error analysis|test the models]]. So the idea of collecting these data is to analyze a model on various data. | ||
| + | |||
| + | The ERP refers to the classification problem. The stimulus belongs to a class label from a given set. The event, starting from the stimulus onset, is a classification object. The Object description is the time series from tmin to tmax over the [https://en.wikipedia.org/wiki/10%E2%80%9320_system_(EEG) electrodes]. Usually, tmax = 1200 ms and tmin = -300 ms. So the data set is a 3-way design matrix <math>X</math> and a binary vector <math>y</math>. Sometimes the design matrix is 2-way after an EEG feature extraction procedure. | ||
== Continuous data == | == Continuous data == | ||
Revision as of 21:59, 20 April 2023
Contents
Datasets
ERP data
Event-related potential, see ERP and P300 is triggered by a stimulus and registered over EEG monitor electrodes after the stimulus onset and before it.
The listed EEG datasets are expected to be of a maximum number of events to test the models. So the idea of collecting these data is to analyze a model on various data.
The ERP refers to the classification problem. The stimulus belongs to a class label from a given set. The event, starting from the stimulus onset, is a classification object. The Object description is the time series from tmin to tmax over the electrodes. Usually, tmax = 1200 ms and tmin = -300 ms. So the data set is a 3-way design matrix \(X\) and a binary vector \(y\). Sometimes the design matrix is 2-way after an EEG feature extraction procedure.
Continuous data
Tools
Experiments
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
- non-parametric phase space Hankel matrix
- convoluion ?
- forecasting with SSA
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
- factorization
- spectral decomposition
- SVD
- ??? SVD in Hilbert space
Why do 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
- PPCA
- How to tell stochastic from deterministic variable? Are expectation and variance deterministic?
- Recap: joint and conditional distribution, marginalization.
- Sampling principle
- VAE as PPCA encoder-decoder