View source for Projects/BCI-FDA: Brain-computer interface with Functional data analysis

{{#seo:
 |title=Brain-computer interface with Functional data analysis
 |titlemode=replace
 |keywords=Brain-computer interface
 |description=Brain-computer interface with Functional data analysis, Human behavioral analysis, and forecasting requires models that have to predict target variables of complex structures.
 }}
Brain-computer interface with Functional data analysis, Human behavioral analysis, and forecasting requires models that have to predict target variables of complex structures. We develop PLS and CCA (Projection to latent space and Canonic correlation analysis) methods towards the Multiview with continuous-time data representation.

== Generative time series decoding models == 
# '''The goal''' is to create a generative state-space model for BCI
# '''The impact'''  is to boost the behavioral classification quality by decision-rejecting 
# '''The principle''' if a generated pattern does not belong to one of the expected patterns (one-class classification) we reject the decision
# '''The plan''' 
## Create the simplest generative model for selected data
## apply SSM (state-space model) principles to make CCA (canonic-correlation analysis)
## Introduce classification model and decision-rejecting criterion
## compare quality 

===References===
# Direct Discriminative Decoder Models for Analysis of High-Dimensional Dynamical Neural Data by M.R. Rezaei et al. 2022 [DOI https://doi.org/10.1162/neco_a_01491]
# Deep Direct Discriminative Decoders for High-dimensional Time-series Data Analysis by M.R. Rezaei 2023 (NTDB)
# Decoding Hidden Cognitive States From Behavior and Physiology Using a Bayesian Approach by Ali Yousefi et al. [https://doi.org/10.1162/neco_a_01196 DOI]
# Bayesian Decoder Models with a Discriminative Observation Process by M.R. Rezaei et al. 2020 [https://doi.org/10.1101/2020.07.11.198564 DOI]
# Deep Discriminative Direct Decoders for High-dimensional Time-series Analysis by M.R. Rezaei 2020 [https://arxiv.org/abs/2205.10947 ArXiv]
# Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models by M.R. Rezaei 2020 [https://doi.org/10.1016/j.jneumeth.2020.109006 DOI]
# [https://github.com/vadim-vic/Deep_Direct_Discriminative_Decoder-D4- Basic code D4]
# Variational auto-encoded deep gaussian processes by Z. Dai et al. 2021 [https://arxiv.org/abs/1511.06455 ArXiv]
# Parametric Gaussian process regressors by M. Jankowiak et al. 2020 [https://arxiv.org/abs/1910.07123 ArXiv]
# A Tutorial on Gaussian Processes by Z. Ghahramani 2010 [http://learning.eng.cam.ac.uk/zoubin PDF]
# An Intuitive Tutorial to Gaussian Processes Regression by J. Wang 2021 [https://arxiv.org/abs/2009.10862 ArXiv]

==Riemannian Geometry and Graph Laplacian metric models==

# '''The goal''' is to create a metric '''behavioral''' forecasting model for BCI
# '''The impact'''  is to construct time-embedding metric space so that it is compatible with the generative models 
# '''The principle''' a dynamic system changes its state consequently, so we construct a metric state space that could be decomposed with one of diffusion models
# '''The plan''' 
## select a metric model with continuous time
## use Riemannian geometry and Graph-Laplacian approaches
## make diffusion decomposition
## boost decoding models with metric space


===References===
# Classification of covariance matrices using a Riemannian-based kernel for BCI applications by A. Barachant et al. 2013 (Neurocomputing)
# Multi-class Brain-Computer Interface Classification by Riemannian Geometry by A. Barachant et al. 
# Riemannian Geometry for EEG-based Brain-Computer Interfaces by M. Congedo et al.
# Online SSVEP-based BCI using Riemannian geometry by E. K. Kalunga 2016 [http://dx.doi.org/10.1016/j.neucom.2016.01.007 DOI]
# A Plug&Play P300 BCI Using Information Geometry by A. Barachant 2014 [https://arxiv.org/abs/1409.0107 ArXiv]
# Longitudinal predictive modeling of tau progression along the structural connectome by J.Dutta et al. 2021 [https://doi.org/10.1016/j.neuroimage.2021.118126 DOI]
# Grand: Graph neural diffusion by M.M. Bronstein et al. ICML, 2021.
# (inspiring) The inverse problem in electroencephalography using the bidomain model of electrical activity by A.L. Rincon and S. Shimoda, 2016 [http://dx.doi.org/10.1016/j.jneumeth.2016.09.011 DOI]
# (inverse)  High-Resolution EEG Source Reconstruction with Boundary Element Fast Multipole Method, N. Makaroff et al. 2022 [https://doi.org/10.1101/2022.10.30.514418 DOI]

==Data==
Any data that has
# timeline with a behavioral pattern, synchronous both for source and target data
# source time series with 
#* probabilistic assumptions for diffusion probabilistic models
# target time series with
#* behavioral pattern to make a decision

To select from
* [[BCI|List of datasets and tools]] 
* Scientific lessons from a catalog of 6674 brain recordings by A.D.J. Makin

==The problem==
# To make a classification decision or to reject it
# To forecast a system behavior (system state) and generate variants
# The rejection criterion is a mismatch observation from generated scenarios

==Assumptions==
# Short time series (relatively, hundreds or thousands of samples)
# Time series have big variances and systematic errors
# Time series could be significantly correlated
# Time series have origins
## exogenous, no one can control
## control signals 
## and decisions
## behavioral 
# Timeline has structure
## periods (seasonal or quasi)
## events (forced or selected)
## including decision timestamps

==Examples==
# Any sports game (exogenous, behavior to model, decisions)
# Brain computer interfaces
# Risk management, stock market

==The challenge is to put==
* generative models 
* of time series graph Laplacian
* into seq2seq framework
* to make quality decisions.

==Schedule 2023==
{|class="wikitable"        
|-
| '''Date'''
| 
| '''N'''
| '''Progress'''
| '''To discuss'''
| '''Result'''
|-  
|September
|16
|1	
|Introduction and planning
|Topics for the next week 
|Subscribed to the schedule
|-  
|
|23
|2
|Possible models
|Introductions to models 
|Slides, references, questions to reason
|-
|
|30
|3
|Model reasoning and selection
|Discussion of the questions, refined presentations of models
|Role of models in the system
|-
|October
|7
|4
|System description
|Variants of the system, code sources
|List of code references, toolbox(es) selection
|-
|
|14
|5
|Architecture planning
|Variants of the pipelines
|Collection of pipelines, executable 
|-
|
|21
|6
|Data collection
|Discussion of the applications 
|Links to the data and downloaders
|-
|
|28
|7
|Minimum value system
|Discussion of the tutorials
|Tutorial plan
|-
|November
|4
|8
|Examples and documents  
|Tutorial presentation
|List of new models and challenges
|-
|
|11
|9
|New directions
|Model presentation (week 2)
|List of challenges
|-
|
|18
|10
|Analysis, testing, and applications
|Decomposition of the system
|List of possible projects
|-
|
|25
|11
|Project proposals
|Project presentations
|Project descriptions
|-
|December
|2
|12
|Project description review
|Discussion of the messages
|Published descriptions
|-
|}

=== Week 2. Propedevtics === 
* [https://docs.google.com/document/d/1qBkJ3DBIYCL8M71B9ybeMkJwTzo9N-VcOt5KB_YL_kQ/edit?usp=sharing The goals and themes to select from]

=== Week 2. Topics to discuss === 
# CCA generative models 
# Continous models for graph Laplacian
# D4 and variants 
# Riemmanian model with time
# SSM generative models
# Generative models with time graph convolutions 
# (risky) RL for time series scenario generation
# (math) CCA Error functions and (tech) Autograd for seq2seq generative pipelines



== References by theme ==
=== CCA linear === 
#
#
#

=== CCA probabilistic === 
# DCCA: Deep Canonical Correlation Analysis by Galen Andrew et al., ICML, 2013,  [https://github.com/Michaelvll/DeepCCA/ GitHub] ''over-engineered''
# Deep Generalized Canonical Correlation Analysis by Adrian Benton et al., 2019, [https://github.com/arminarj/deepgcca-pytorch GitHub], [https://paperswithcode.com/paper/deep-generalized-canonical-correlation pwc]
# Deep Canonical Correlation Analysis by Galen Andrew, 2013,  [https://proceedings.mlr.press/v28/andrew13.pdf JMLR]
# On Deep Multi-View Representation Learning by Weiran Wang et al., 2015, [https://proceedings.mlr.press/v37/wangb15.pdf JMLR]

=== Generative === 
# Denoising Diffusion Probabilistic Models by Jonathan Ho, 2020, [https://arxiv.org/abs/2006.11239 ArXiv]
# Score-Based Generative Modeling through Stochastic Differential Equations by Yang Song et al.,  2020, [https://arxiv.org/abs/2011.13456 ArXiv], [https://github.com/yang-song/score_sde GitHub]
# Denoising Diffusion Probabilistic Model in Pytorch by Yannic Kilcher et al., 2023, [https://github.com/lucidrains/denoising-diffusion-pytorch/tree/main GitHub]
# Collection of Generative Models with PyTorch, 2022, [https://github.com/znxlwm/pytorch-generative-model-collections GitHub]
# DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting by Salva Rühling Cachay et al., 2023, [https://arxiv.org/pdf/2306.01984.pdf ArXiv]

=== CCA generative === 
# Deep Variational Canonical Correlation Analysis by Weiran Wang, 2016, [https://arxiv.org/pdf/1610.03454.pdf ArXiv]
# Deep Probabilistic Canonical Correlation Analysis by Mahdi Karami, 2021 [ AAAI]
#

=== Riemannian ===
# Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis by Ce Ju and Cuntai Guan, 2022, [https://arxiv.org/abs/2211.02641 ArXiv], [https://github.com/GeometricBCI/Tensor-CSPNet-and-Graph-CSPNet/tree/main GitHub], 'explanative figs'
# From canonical correlation analysis to self-supervised graph neural networks by  Hengrui Zhang et al., 2021, [https://arxiv.org/abs/2106.12484 NIPS],  [https://github.com/hengruizhang98/CCA-SSG/tree/main#neurips-2021-from-canonical-correlation-analysis-to-self-supervised-graph-neural-networks GitHub], [https://github.com/arminarj/DeepGCCA-pytorch/blob/master/DGCCA_loss_test.ipynb Github]

=== Generative Riemannian ===
# Riemannian Diffusion Models by Chin-Wei Huang et al., 2022, [https://arxiv.org/pdf/2208.07949.pdf ArXiv], nocode
#
#




<!--- === CCA Generative Riemannian === -->



===State space models ===
# Deep learning for universal linear embeddings of nonlinear dynamics by Bethany Lusch et al., 2018, [https://www.nature.com/articles/s41467-018-07210-0 Nature]
# Data-driven discovery of coordinates and governing equations by Kathleen Championa et al. 2019, [https://www.pnas.org/doi/full/10.1073/pnas.1906995116 PNAS]

=== Bayesian model selection ===