Classification of BCI-EEG based on augmented covariance matrix

• URL: http://arxiv.org/abs/2302.04508v1
• Date: Thu, 9 Feb 2023 09:04:25 GMT
• Title: Classification of BCI-EEG based on augmented covariance matrix
• Authors: Igor Carrara (UCA, CRISAM, Inria - Cronos Team), Th\'eodore Papadopoulo (UCA, CRISAM, Inria - Cronos Team)
• Abstract summary: We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. We will test our approach on several datasets and several subjects using the MOABB framework.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Related papers

• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Regularized Projection Matrix Approximation with Applications to Community Detection [1.3761665705201904]
  This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. Numerical experiments conducted on both synthetic and real-world datasets reveal that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering performance.
  arXiv  Detail & Related papers  (2024-05-26T15:18:22Z)
• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model [13.082805815235975]
  We introduce a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data. The effectiveness and practical merits of the proposed framework are demonstrated through experiments on both simulated and real datasets.
  arXiv  Detail & Related papers  (2023-07-02T13:59:47Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• High-Dimensional Sparse Bayesian Learning without Covariance Matrices [66.60078365202867]
  We introduce a new inference scheme that avoids explicit construction of the covariance matrix. Our approach couples a little-known diagonal estimation result from numerical linear algebra with the conjugate gradient algorithm. On several simulations, our method scales better than existing approaches in computation time and memory.
  arXiv  Detail & Related papers  (2022-02-25T16:35:26Z)
• Optimal Variable Clustering for High-Dimensional Matrix Valued Data [3.1138411427556445]
  We propose a new latent variable model for the features arranged in matrix form. Under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. We identify the optimal weight in the sense that using this weight guarantees our algorithm to be minimax rate-optimal.
  arXiv  Detail & Related papers  (2021-12-24T02:13:04Z)
• Multi-Objective Matrix Normalization for Fine-grained Visual Recognition [153.49014114484424]
  Bilinear pooling achieves great success in fine-grained visual recognition (FGVC) Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features. We propose an efficient Multi-Objective Matrix Normalization (MOMN) method that can simultaneously normalize a bilinear representation.
  arXiv  Detail & Related papers  (2020-03-30T08:40:35Z)
• A Block Coordinate Descent-based Projected Gradient Algorithm for Orthogonal Non-negative Matrix Factorization [0.0]
  This article utilizes the projected gradient method (PG) for a non-negative matrix factorization problem (NMF) We penalise the orthonormality constraints and apply the PG method via a block coordinate descent approach.
  arXiv  Detail & Related papers  (2020-03-23T13:24:43Z)
• Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach [2.8021833233819486]
  We analyze an algorithm for approximate inference with large Gaussian latent variable models in a student-trivial scenario. For the case of perfect data-model matching, the knowledge of static order parameters derived from the replica method allows us to obtain efficient algorithmic updates.
  arXiv  Detail & Related papers  (2020-01-14T17:22:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.