Functional data analysis for BCI and biomedical signals - Revision history

Vs at 19:21, 11 February 2024

2024-02-11T19:21:31Z

Vs at 18:56, 11 February 2024

2024-02-11T18:56:47Z

Wiki: /* References */

2022-10-27T19:22:43Z

References

Wiki: /* Functional data analysis */

2022-10-27T01:07:42Z

Functional data analysis

Wiki: /* Functional data analysis */

2022-10-27T01:06:43Z

Functional data analysis

Wiki: /* Heterogeneous data and multi-modeling */

2022-10-24T22:01:16Z

Heterogeneous data and multi-modeling

Wiki at 14:25, 16 October 2022

2022-10-16T14:25:12Z

Wiki: /* Functional data analysis */

2022-10-16T14:16:32Z

Functional data analysis

Wiki: /* Functional data analysis */

2022-10-16T14:07:03Z

Functional data analysis

Wiki: /* Continous-time physical activity recognition */

2022-10-16T14:00:34Z

Continous-time physical activity recognition

@@ Line 1: / Line 1: @@
 {{#seo:
   |title=BCI forecasting models
-  |titlemode=append
+  |titlemode=replace
   |keywords=BCI
   |description=My research focuses on the construction of BCI forecasting models. I use deep learning models. The main challenges of the study are phase space construction, dimensionality reduction, manifold learning, heterogeneous modeling, and knowledge transfer.

← Older revision		Revision as of 18:56, 11 February 2024
Line 1:		Line 1:
		+	{{#seo:
		+	\|title=BCI forecasting models
		+	\|titlemode=append
		+	\|keywords=BCI
		+	\|description=My research focuses on the construction of BCI forecasting models. I use deep learning models. The main challenges of the study are phase space construction, dimensionality reduction, manifold learning, heterogeneous modeling, and knowledge transfer.
		+	}}
	''[[Vadim]]'', 2023		''[[Vadim]]'', 2023

@@ Line 19: / Line 19: @@
 The Deep Learning methods give immediate results in modeling. They bring forecasts to compare with and develop. A promising ﬁeld of research is Functional Data Analysis. It works with objects and spaces of inﬁnite dimensionality. Geometric Deep Learning [19] connects the physical nature of measurements and the axioms to construct forecasting models. It brings physics-informed neural networks [20]. I believe combining modern Deep Learning techniques with Advanced Calculus and Physics delivers fruitful results in practical applications of BCI and biomedical signal analysis.
 ==References==
-# Maryam Bijanzadeh, Ankit N. Khambhati, Maansi Desai, Deanna L. Wallace, Alia Shafi, Heather E. Dawes, Virginia E. Sturm, and Ed- ward F. Chang. Decoding naturalistic affective behaviour from spectro-spatial features in multi-day human iEEG. Nature Human Behaviour, 6(6):823–836, mar 2022.
+# Maryam Bijanzadeh, Ankit N. Khambhati, Maansi Desai, Deanna L. Wallace, Alia Shafi, Heather E. Dawes, Virginia E. Sturm, and Ed- ward F. Chang. Decoding naturalistic affective behaviour from spectro-spatial features in multi-day human iEEG. Nature Human Behaviour, 6(6):823–836, 2022.
 # A. P. Motrenko and V. V. Strijov. Multi-way feature selection for Ecog-based brain-computer interface. Expert Systems with Applications, 114(30):402–413, 2018.
 # A. M. Katrutsa and V. V. Strijov. Stresstest procedure for feature selection algorithms. Chemometrics and Intelligent Laboratory Systems, 142:172–183, 2015.
-# Tamara G. Kolda and Brett W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455–500, aug 2009.
+# Tamara G. Kolda and Brett W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455–500, 2009.
 # A. M. Katrutsa and V. V. Strijov. Comprehensive study of feature selection methods to solve multicollinearity problem according to evaluation criteria. Expert Systems with Applications, 76:1–11, 2017.
-# Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Du- venaud. Neural ordinary differential equations. Advances in Neural Information Processing Systems 31 (NeurIPS 2018), 2018.
+# Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural ordinary differential equations. Advances in Neural Information Processing Systems 31, 2018.
-# Qibin Zhao, C. F. Caiafa, D. P. Mandic, Z. C. Chao, Y. Nagasaka, N. Fujii, Liqing Zhang, and A. Cichocki. Higher order partial least squares (HOPLS): A generalized multilinear regression method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(7):1660– 1673, jul 2013.
+# Qibin Zhao, C. F. Caiafa, D. P. Mandic, Z. C. Chao, Y. Nagasaka, N. Fujii, Liqing Zhang, and A. Cichocki. Higher order partial least squares (HOPLS): A generalized multilinear regression method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(7):1660–1673, 2013.
-# R. V. Isachenko and V. V. Strijov. Quadratic programming feature selection for multicorrelated signal decoding with partial least squares. Expert Systems with Applications, 207:117967, nov 2022.
+# R. V. Isachenko and V. V. Strijov. Quadratic programming feature selection for multicorrelated signal decoding with partial least squares. Expert Systems with Applications, 207:117967, 2022.
 # R. V. Isachenko and V. V. Strijov. Quadratic programming optimization with feature selection for non-linear models. Lobachevskii Journal of Mathematics, 39(9):1179–1187, 2018.
-# Jiequn Han, Arnulf Jentzen, and Weinan E. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34):8505–8510, aug 2018.
+# Jiequn Han, Arnulf Jentzen, and Weinan E. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018.
-# Julia Berezutskaya, Mariska J. Vansteensel, Erik J. Aarnoutse, Zachary V. Freudenburg, Giovanni Piantoni, Mariana P. Branco, and Nick F. Ramsey. Open multimodal iEEG-fMRI dataset from naturalistic stimulation with a short audiovisual film. Scientific Data, 9(1), mar 2022.
+# Julia Berezutskaya, Mariska J. Vansteensel, Erik J. Aarnoutse, Zachary V. Freudenburg, Giovanni Piantoni, Mariana P. Branco, and Nick F. Ramsey. Open multimodal iEEG-fMRI dataset from naturalistic stimulation with a short audiovisual film. Scientific Data, 9(1), 2022.
 # A. V. Grabovoy and V. V. Strijov. Prior distribution selection for a mixture of experts. Computational Mathematics and Mathematical Physics, 61(7):1149–1161, 2021.
 # O. Y. Bakhteev and V. V. Strijov. Comprehensive analysis of gradient-based hyper-parameter optimization algorithms. Annals of Operations Research, pages 1–15, 2020.
-# A. P. Motrenko and V. V. Strijov. Extracting fundamental periods to segment human motion time series. IEEE Journal of Biomedical and Health Informatics, 20(6):1466 – 1476, 2016.
+# A. P. Motrenko and V. V. Strijov. Extracting fundamental periods to segment human motion time series. IEEE Journal of Biomedical and Health Informatics, 20(6):1466–1476, 2016.
 # A. Motrenko et. al. Continuous physical activity recognition for intelligent labour monitoring. Multimedia Tools and Applications, 81(4):4877–4895, 2021.
 # A. V. Grabovoy and V. V. Strijov. Quasi-periodic time series clustering for human activity recognition. Lobachevskii Journal of Mathematics, 41:333–339, 2020.
-# Alim Louis Benabid et al. An exoskeleton controlled by an epidural wireless brain–machine interface in a tetraplegic patient: a proof-of-concept demonstration. The Lancet Neurology, 18(12):1112– 1122, dec 2019.
+# Alim Louis Benabid et al. An exoskeleton controlled by an epidural wireless brain–machine interface in a tetraplegic patient: a proof-of-concept demonstration. The Lancet Neurology, 18(12):1112–1122, 2019.
-# David K. Duvenaud Yulia Rubanova, Ricky T. Q. Chen. Latent ordinary differential equations for irregularly-sampled time series. Advances in Neural Information Processing Systems 32 (NeurIPS 2019), 2019.
+# David K. Duvenaud Yulia Rubanova, Ricky T. Q. Chen. Latent ordinary differential equations for irregularly-sampled time series. Advances in Neural Information Processing Systems 32, 2019.
 # Michael M. Bronstein, Joan Bruna, Taco Cohen, and Petar Veliˇckovi ́c. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges, 2021.
-# M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, feb 2019.
+# M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, 2019.

@@ Line 14: / Line 14: @@
 ==Functional data analysis==
 The methods of functional brain mapping verify the signal diﬀusion hypothesis. It shows that activity zone changes over the cortical space control limb movements [17]. The model must consider the spatial structure of the signals. Neural networks do not consider information about the neighborhood on the brain surface. We proposed a graph representation of brain signals. It reveals interrelationships of diﬀerent areas and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that deﬁnes a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that deﬁnes a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model [18].
-[[File:BCI_graph.jpeg|class=img-responsive|left|alt Brain functional group reconstruction model]]
+[[File:BCI_graph.jpeg|class=img-responsive|left|Brain functional group reconstruction model]]
 ==Direction of future work==

@@ Line 14: / Line 14: @@
 ==Functional data analysis==
 The methods of functional brain mapping verify the signal diﬀusion hypothesis. It shows that activity zone changes over the cortical space control limb movements [17]. The model must consider the spatial structure of the signals. Neural networks do not consider information about the neighborhood on the brain surface. We proposed a graph representation of brain signals. It reveals interrelationships of diﬀerent areas and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that deﬁnes a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that deﬁnes a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model [18].
 ==Direction of future work==
 The Deep Learning methods give immediate results in modeling. They bring forecasts to compare with and develop. A promising ﬁeld of research is Functional Data Analysis. It works with objects and spaces of inﬁnite dimensionality. Geometric Deep Learning [19] connects the physical nature of measurements and the axioms to construct forecasting models. It brings physics-informed neural networks [20]. I believe combining modern Deep Learning techniques with Advanced Calculus and Physics delivers fruitful results in practical applications of BCI and biomedical signal analysis.

@@ Line 7: / Line 7: @@
 The BCI models are the signal decoding models [7]. It is a special class of models that includes canonical correlation analysis for multivariate and tensor variables. I plan to study the problem of model selection to restore hidden dependencies in the source and target spaces. For example, periodical limb movements cause multiple correlations in the target space. We proposed to reduce the dimension by projecting the source and target in the latent space [8]. Linear and non-linear methods match predictive models in high-dimensional spaces [9]. Recently we proposed a feature selection algorithm for linear models and tested it on ECoG signals [2]. I plan to develop this algorithm for tensor dimensionality reduction. The base method is the High-order partial least squares [7]. A good problem for development is manifold learning. The manifold is a solution to the neural partial diﬀerential equations [10]. The challenge is to ﬁnd an optimal dimensionality of the manifold.
 <!--~\citep{lauzon2018sequential,engel2017kernel,biancolillo2017extension,hervas2018sparse}-->
-==Heterogeneous data and multi-modeling==
+==Heterogeneous data and knowledge transfer==
 The new studies of brain activity fruitfully deliver a variety of measurements. For a group of patients, they contain audio, video, iEEEG-ECoG, ECG, fMRI, and hand or eye movements. These data sets require multi models. Each patient has its peculiarities. It requires a method to transfer knowledge from one patient's model to another. Knowledge transfer for heterogenous models is an important part of my investigation. I use Bayesian inference for multimodel selection to construct an ensemble of models and teacher-student pairs. The information, gained by the properly trained models serves as a prior distribution for a student model.
 == Continous-time physical activity recognition ==
 A forecast of limb motions stands on cycles of motion [14]. They form a phase trajectory [15]. Parameters of the trajectory deﬁne a class of motion. A sequence of these classes forms the physical human behavior pattern. Recently we proposed human activity recognition algorithm based on the data from wearable sensors [16]. The solution is based on the hierarchical representation of activities as sets of low-level motions. The hierarchical model provides an interpretable description of studied motions.

← Older revision		Revision as of 14:16, 16 October 2022
Line 24:		Line 24:
	==Functional data analysis==		==Functional data analysis==
	The methods of functional brain mapping verify the signal diﬀusion hypothesis. It shows that activity zone changes over the cortical space control limb movements [17]. The model must consider the spatial structure of the signals. Neural networks do not consider information about the neighborhood on the brain surface. We proposed a graph representation of brain signals. It reveals interrelationships of diﬀerent areas and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that deﬁnes a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that deﬁnes a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model [18].		The methods of functional brain mapping verify the signal diﬀusion hypothesis. It shows that activity zone changes over the cortical space control limb movements [17]. The model must consider the spatial structure of the signals. Neural networks do not consider information about the neighborhood on the brain surface. We proposed a graph representation of brain signals. It reveals interrelationships of diﬀerent areas and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that deﬁnes a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that deﬁnes a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model [18].
		+
		+	==Direction of future work==
		+	The Deep Learning methods give immediate results in modeling. They bring forecasts to compare with and develop. A promising ﬁeld of research is Functional Data Analysis. It works with objects and spaces of inﬁnite dimensionality. Geometric Deep Learning [19] connects the physical nature of measurements and the axioms to construct forecasting models. It brings physics-informed neural networks [20]. I believe combining modern Deep Learning techniques with Advanced Calculus and Physics delivers fruitful results in practical applications of BCI and biomedical signal analysis.
		+
		+	==References==
		+	# Maryam Bijanzadeh, Ankit N. Khambhati, Maansi Desai, Deanna L. Wallace, Alia Shafi, Heather E. Dawes, Virginia E. Sturm, and Ed- ward F. Chang. Decoding naturalistic affective behaviour from spectro-spatial features in multi-day human iEEG. Nature Human Behaviour, 6(6):823–836, mar 2022.
		+	# A. P. Motrenko and V. V. Strijov. Multi-way feature selection for Ecog-based brain-computer interface. Expert Systems with Applications, 114(30):402–413, 2018.
		+	# A. M. Katrutsa and V. V. Strijov. Stresstest procedure for feature selection algorithms. Chemometrics and Intelligent Laboratory Systems, 142:172–183, 2015.
		+	# Tamara G. Kolda and Brett W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455–500, aug 2009.
		+	# A. M. Katrutsa and V. V. Strijov. Comprehensive study of feature selection methods to solve multicollinearity problem according to evaluation criteria. Expert Systems with Applications, 76:1–11, 2017.
		+	# Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Du- venaud. Neural ordinary differential equations. Advances in Neural Information Processing Systems 31 (NeurIPS 2018), 2018.
		+	# Qibin Zhao, C. F. Caiafa, D. P. Mandic, Z. C. Chao, Y. Nagasaka, N. Fujii, Liqing Zhang, and A. Cichocki. Higher order partial least squares (HOPLS): A generalized multilinear regression method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(7):1660– 1673, jul 2013.
		+	# R. V. Isachenko and V. V. Strijov. Quadratic programming feature selection for multicorrelated signal decoding with partial least squares. Expert Systems with Applications, 207:117967, nov 2022.
		+	# R. V. Isachenko and V. V. Strijov. Quadratic programming optimization with feature selection for non-linear models. Lobachevskii Journal of Mathematics, 39(9):1179–1187, 2018.
		+	# Jiequn Han, Arnulf Jentzen, and Weinan E. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34):8505–8510, aug 2018.
		+	# Julia Berezutskaya, Mariska J. Vansteensel, Erik J. Aarnoutse, Zachary V. Freudenburg, Giovanni Piantoni, Mariana P. Branco, and Nick F. Ramsey. Open multimodal iEEG-fMRI dataset from naturalis- tic stimulation with a short audiovisual film. Scientific Data, 9(1), mar 2022.
		+	# A. V. Grabovoy and V. V. Strijov. Prior distribution selection for a mixture of experts. Computational Mathematics and Mathematical Physics, 61(7):1149–1161, 2021.
		+	# O. Y. Bakhteev and V. V. Strijov. Comprehensive analysis of gradient-based hyper-parameter optimization algorithms. Annals of Operations Research, pages 1–15, 2020.
		+	# A. P. Motrenko and V. V. Strijov. Extracting fundamental periods to segment human motion time series. IEEE Journal of Biomedical and Health Informatics, 20(6):1466 – 1476, 2016.
		+	# A. Motrenko et. al. Continuous physical activity recognition for intelligent labour monitoring. Multimedia Tools and Applications, 81(4):4877–4895, 2021.
		+	# A. V. Grabovoy and V. V. Strijov. Quasi-periodic time series clustering for human activity recognition. Lobachevskii Journal of Mathematics, 41:333–339, 2020.
		+	# Alim Louis Benabid et al. An exoskeleton controlled by an epidural wireless brain–machine interface in a tetraplegic patient: a proof-of-concept demonstration. The Lancet Neurology, 18(12):1112– 1122, dec 2019.
		+	# David K. Duvenaud Yulia Rubanova, Ricky T. Q. Chen. Latent ordinary differential equations for irregularly-sampled time series. Advances in Neural Information Processing Systems 32 (NeurIPS 2019), 2019.
		+	# Michael M. Bronstein, Joan Bruna, Taco Cohen, and Petar Veliˇckovi ́c. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges, 2021.
		+	# M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, feb 2019.

← Older revision		Revision as of 14:07, 16 October 2022
Line 23:		Line 23:

	==Functional data analysis==		==Functional data analysis==
−	The brain ~~functional~~ mapping ~~methods~~ verify the signal ~~diffusion~~ hypothesis. It ~~tells~~ that changes ~~in cortical activity zones~~ over the ~~intracranial~~ space control limb movements. The model must consider the spatial structure of the signals. ~~Due to the lack of a common definition of~~ the neighborhood on the ~~spherical~~ surface ~~of the brain, convolutional neural networks cannot be effectively applied to account for spatial information~~. We proposed a graph representation of ~~the signal~~. It reveals interrelationships of ~~different~~ areas ~~of intracranial activity~~ and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that ~~defines~~ a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that ~~defines~~ a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model.	+	The methods of functional brain mapping verify the signal diﬀusion hypothesis. It shows that activity zone changes over the cortical space control limb movements [17]. The model must consider the spatial structure of the signals. Neural networks do not consider information about the neighborhood on the brain surface. We proposed a graph representation of brain signals. It reveals interrelationships of diﬀerent areas and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that deﬁnes a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that deﬁnes a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model [18].

@@ Line 17: / Line 17: @@
 == Continous-time physical activity recognition ==
-A forecast of limb motions stands on the precedents. These precedents, quasi-periodic time series, form a phase trajectory. It is a basic cycle of motion. This trajectory is a loop whose parameters define a class of movement. <!-- SLOPPY To construct the trajectory, we solved a time-series segmentation problem. Assume that each studied time series contains a fundamental periodic.--> A sequence of these classes forms the physical human behavior pattern. Recently we proposed human activity recognition algorithm based on the data from wearable sensors. The solution is based on the hierarchical representation of activities as sets of low-level actions. The hierarchical representation provides an interpretable description of studied activities in terms of actions.
+A forecast of limb motions stands on cycles of motion [14]. They form a phase trajectory [15]. Parameters of the trajectory deﬁne a class of motion. A sequence of these classes forms the physical human behavior pattern. Recently we proposed human activity recognition algorithm based on the data from wearable sensors [16]. The solution is based on the hierarchical representation of activities as sets of low-level motions. The hierarchical model provides an interpretable description of studied motions.
 <!-- == Wearable device mapping ==
 ==Hand movement recognition==  -->
 ==Functional data analysis==
 The brain functional mapping methods verify the signal diffusion hypothesis. It tells that changes in cortical activity zones over the intracranial space control limb movements. The model must consider the spatial structure of the signals. Due to the lack of a common definition of the neighborhood on the spherical surface of the brain, convolutional neural networks cannot be effectively applied to account for spatial information. We proposed a graph representation of the signal. It reveals interrelationships of different areas of intracranial activity and provides a neurobiological interpretation of the functional connections. I plan to develop various methods for constructing a connectivity matrix that defines a graph structure. Estimating connectivity relies on correlation, spectral analysis, and canonic correlation analysis. The matrix is a metric tensor that defines a Riemannian space. The forecasting model is a composition of a graph convolution for aggregating spatial information and a recurrent or neural ODE model.