Personal identification system based on multidimensional electroencephalographic signals

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data.For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.

<p><b>Metric Learning has proved valuable in information retrieval and classification problems, with many algorithms using statistical formulations to their advantage. Optimal Transport, a powerful framework for computing distances between probability distributions, has seen significant uptake in Machine Learning and some applications in Metric Learning. The Bures-Wasserstein distance, a particular formulation of Optimal Transport, has seen limited application in Metric Learning despite being well suited to the field. In this thesis Linear Metric Learning algorithms incorporating the Bures-Wasserstein distance are developed, utilising its novel properties. The first set of algorithms we contribute use the Bures-Wasserstein distance for learning linear metrics using Cyclic Projections, Riemannian barycenters and gradient-based algorithms. The convergence properties and classification performance of these algorithms are then compared to benchmark Linear Metric Learning algorithms. Our algorithms achieve competitive classification performance on feature and image datasets and converge reliability.</b></p> <p>The second set of contributions extend Linear Metric Learning with the Bures-Wasserstein distance to a low-rank context to address issues related to scalability. An extension of the previous Cyclic Projections algorithm and a Riemannian optimisation method are developed. Convergence and classification experiments analogous to the full-rank case are conducted to examine how the reduced rank affects both of these performance metrics. Both algorithms converge reliably under a variety of synthetic conditions. Reduction in rank generally decreased the training time for algorithms until effects caused by the size of the training data dominated. Reducing rank either left classification error unchanged or increased it. With respect to other low-rank Linear Metric Learning algorithms our algorithms again performed competitively with respect to classification error. </p> <p>The last set of contributions consider Linear Metric Learning on Symmetric Positive Definite (SPD) matrices. Some datasets are expressed as or are suited to a SPD representation. As such, Metric Learning algorithms that respect the structure of these matrices have found success when adapted to this kind of data. Another extension of the Cyclic Projections algorithm is developed to use the Generalised Bures-Wasserstein distance on SPD matrices. Two other methods based on a ground metric formulation of the Bures-Wasserstein distance for learning linear metrics on SPD data are also introduced. One ground metric formulation uses an approximation (inspired by the Sinkhorn distance) to increase its scalability. Convergence experiments on synthetic problems adapted to SPD matrices are conducted on the ground metric algorithms to establish their convergence properties. Classification experiments are also conducted with respect to several types of SPD data. While the Cyclic Projections method is competitive, the ground metric algorithms have poor performance. Despite their poor classification performance, the approximation method does evaluate faster than the Generalised Bures-Wasserstein distance, potentially offering some scalability improvements.</p>

A cross-session motor imagery classification method based on Riemannian geometry and deep domain adaptation

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices -especially of high-dimensional ones- comes at a high cost that limits the applicability of existing techniques. In this paper, we introduce algorithms able to handle high-dimensional SPD matrices by constructing a lower-dimensional SPD manifold. To this end, we propose to model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal projection. This lets us formulate dimensionality reduction as the problem of finding a projection that yields a low-dimensional manifold either with maximum discriminative power in the supervised scenario, or with maximum variance of the data in the unsupervised one. We show that learning can be expressed as an optimization problem on a Grassmann manifold and discuss fast solutions for special cases. Our evaluation on several classification tasks evidences that our approach leads to a significant accuracy gain over state-of-the-art methods.

Symmetric positive-definite (SPD) matrices are ubiquitous in Computer Vision, Machine Learning and Medical Image Analysis. Finding the center/average of a population of such matrices is a common theme in many algorithms such as clustering, segmentation, principal geodesic analysis, etc. The center of a population of such matrices can be defined using a variety of distance/divergence measures as the minimizer of the sum of squared distances/divergences from the unknown center to the members of the population. It is well known that the computation of the Karcher mean for the space of SPD matrices which is a negatively-curved Riemannian manifold is computationally expensive. Recently, the LogDet divergence-based center was shown to be a computationally attractive alternative. However, the LogDet-based mean of more than two matrices can not be computed in closed form, which makes it computationally less attractive for large populations. In this paper we present a novel recursive estimator for center based on the Stein distance - which is the square root of the LogDet divergence - that is significantly faster than the batch mode computation of this center. The key theoretical contribution is a closed-form solution for the weighted Stein center of two SPD matrices, which is used in the recursive computation of the Stein center for a population of SPD matrices. Additionally, we show experimental evidence of the convergence of our recursive Stein center estimator to the batch mode Stein center. We present applications of our recursive estimator to K-means clustering and image indexing depicting significant time gains over corresponding algorithms that use the batch mode computations. For the latter application, we develop novel hashing functions using the Stein distance and apply it to publicly available data sets, and experimental results have shown favorable comparisons to other competing methods.

The electroencephalography (EEG) signals are easily contaminated by various artifacts and noise, which induces a domain shift in each subject and significant pattern variability among different subjects. Therefore, it hinders the improvement of EEG classification accuracy in the cross-subject learning scenario. Convolutional neural networks (CNNs) have been extensively applied to EEG-based Brain-Computer Interfaces (BCIs) by virtue of the capability of performing automatic feature extraction and classification. However, they have been mainly applied to the within-subject classification which would consume lots of time for training and calibration. Thus, it limits the further applications of CNNs in BCIs. In order to build a robust classification algorithm for a calibration-less BCI system, we propose an end-to-end model that transforms the EEG signals into symmetric positive definite (SPD) matrices and captures the features of SPD matrices by using a CNN. To avoid the time-consuming calibration and ensure the application of the proposed model, we use the meta-transfer-learning (MTL) method to learn the essential features from different subjects. We validate our model by making extensive experiments on three public motor-imagery datasets. The experimental results demonstrate the effectiveness of our proposed method in the cross-subject learning scenario.

Physical principles of brain–computer interfaces and their applications for rehabilitation, robotics and control of human brain states

Machine learning has achieved remarkable success across diverse domains. Nevertheless, concerns about interpretability in black-box models, especially within Deep Neural Networks (DNNs), have become pronounced in safety-critical fields like healthcare and finance. Classical machine learning (ML) classifiers, known for their higher interpretability, are preferred in these domains. Similar to DNNs, classical ML classifiers can exhibit bugs that could lead to severe consequences in practice. Test input prioritization has emerged as a promising approach to ensure the quality of an ML system, which prioritizes potentially misclassified tests so that such tests can be identified earlier with limited manual labeling costs. However, when applying to classical ML classifiers, existing DNN test prioritization methods are constrained from three perspectives: 1) Coverage-based methods are inefficient and time-consuming; 2) Mutation-based methods cannot be adapted to classical ML models due to mismatched model mutation rules; 3) Confidence-based methods are restricted to a single dimension when applying to binary ML classifiers, solely depending on the model’s prediction probability for one class. To overcome the challenges, we propose MLPrior, a test prioritization approach specifically tailored for classical ML models. MLPrior leverages the characteristics of classical ML classifiers (i.e., interpretable models and carefully engineered attribute features) to prioritize test inputs. The foundational principles are: 1) tests more sensitive to mutations are more likely to be misclassified, and 2) tests closer to the model’s decision boundary are more likely to be misclassified. Building on the first concept, we design mutation rules to generate two types of mutation features (i.e., <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model mutation features</b> and <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">input mutation features</b> ) for each test. Drawing from the second notion, MLPrior generates <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">attribute features</b> of each test based on its attribute values, which can indirectly reveal the proximity between the test and the decision boundary. For each test, MLPrior combines all three types of features of it into a final vector. Subsequently, MLPrior employs a pre-trained ranking model to predict the misclassification probability of each test based on its final vector and ranks tests accordingly. We conducted an extensive study to evaluate MLPrior based on 185 subjects, encompassing natural datasets, mixed noisy datasets, and fairness datasets. The results demonstrate that MLPrior outperforms all the compared test prioritization approaches, with an average improvement of 14.74%∼66.93% on natural datasets, 18.55%∼67.73% on mixed noisy datasets, and 15.34%∼62.72% on fairness datasets.

The region covariance descriptors have recently become a popular method for detection and tracking of objects in an image. However, these descriptors are not suitable for classification of images with heterogeneous contents. In this paper, we present an image-level descriptor obtained using an affine-invariant geodesic mean of region covariance descriptors on the Riemannian manifold of symmetric positive definite (SPD) matrices. The resulting image descriptors are also SPD matrices, lending themselves to tractable geodesic distance based k-nearest neighbour classification using efficient kernels. We show that the proposed descriptor yields high classification accuracy on a challenging problem of nuclear pleomorphism scoring in breast cancer histology images.

The growing dependence on mobile phones for communication has raised concerns regarding the neurological impact of radio-frequency electromagnetic fields, especially in audio and video calls. This research investigates the impact of WhatsApp audio and video calls on cognitive load and mental fatigue using non-invasive electroencephalography (EEG) signals. EEG signals were recorded from 28 healthy participants during baseline, 3-minute, and 4-minute call sessions, with participants equally distributed between audio and video call groups. The signals were preprocessed using bandpass filtering, continuous wavelet transform, and independent component analysis to isolate theta and alpha frequency bands. Cognitive load was assessed using the theta-alpha ratio (TAR), and mental fatigue was measured using Mahalanobis distance-based analysis of theta and alpha rhythms. The findings reveal that video calls impose significantly more cognitive load (e.g., TAR mean: 0.78 (SD: 0.36) for 3-minute video call and mean: 0.76 (SD: 0.37) for 3-minute audio call, p<0.05) and mental fatigue (e.g., 42.11 microvolts for 4-minute video call and 38.84 microvolts for 4-minute audio call) than audio calls, and both effects become stronger for prolonged durations. Machine learning (ML) classification also demonstrated high separability, with receiver operating characteristic analysis exhibiting area under the curve values above 0.90 for distinguishing call conditions. These results demonstrate that video communication places higher cognitive and fatigue demands as compared to audio communication. By integrating EEG indices, self-report measures, and ML classification, this study exhibits convergent evidence for the cognitive impact of mobile phone calls and illustrates the necessity to consider communication modality when assessing workload and fatigue in real-world contexts.

Symmetric Positive Definite (SPD) matrices have been used in many fields of medical data analysis. Many Riemannian metrics have been defined on this manifold but the choice of the Riemannian structure lacks a set of principles that could lead one to choose properly the metric. This drives us to introduce the principle of balanced metrics that relate the affine-invariant metric with the Euclidean and inverse-Euclidean metric, or the Bogoliubov-Kubo-Mori metric with the Euclidean and log-Euclidean metrics. We introduce two new families of balanced metrics, the mixed-power-Euclidean and the mixed-power-affine metrics and we discuss the relation between this new principle of balanced metrics and the concept of dual connections in information geometry.

The geometry of mixed-Euclidean metrics on symmetric positive definite matrices

We present a distributed memory algorithm for the approximate hierarchical of symmetric positive definite (SPD) matrices. Our method is based on the distributed memory GOFMM, an algorithm that appeared in SC18 (doi:10.1109/SC.2018.00018). GOFMM constructs a hierarchical matrix approximation of an arbitrary SPD matrix that compresses the matrix by creating low-rank approximations of the off-diagonal blocks. GOFMM method has no guarantees of success for arbitrary SPD matrices. (This is similar to the SVD; not every matrix admits a good low-rank approximation.) But for many SPD matrices, GOFMM does enable compression that results in fast matrix-vector multiplication that can reach N logN time—as opposed to N2 required for a dense matrix. GOFMM supports shared and distributed memory parallelism. In this paper, we build an approximate based on the Hierarchically Semi-Separable (HSS) compression of the GOFMM. This requires O(N) work (given the compressed matrix) and O(N=p) + O(log p) time on p MPI processes (assuming a hypercube topology). The previous state-of-the-art required O(N logN) work. We present the algorithm, discuss its complexity, and present weak and strong scaling results for the factorization and phases of our algorithm. We also discuss the performance of the inexact ULV as a preconditioner for a few exemplary large dense linear systems. In our largest run, we were able to factorize a 67M-by-67M matrix in less than one second; and solve a system with 64 right-hand sides in less than one-tenth of a second. This run was on 6,144 Intel Skylake cores on the SKX partition of the Stampede2 system at the Texas Advanced Computing Center.

The evolution and improvements of deep learning are being used to tackle any research obstacles that could be converted into classification problems in all spheres of life. Each Deep convolutional neural network (DCNN) design's output is determined by the depth and value of the hyperparameters, which explains why so many of them have been proposed. These DCNN architectures must be created entirely from scratch, and they can only be used for the applications for which they were intended. Transfer learning may be used to modify these pre-trained networks so they are more appropriate for particular purposes. This article aims to evaluate the empirical performance of the applicability of pre-trained DCNN models to identify human face presentation threats (FPAD). Human FPAD is one of the most significant and crucial areas of research right now because of the introduction of ambient computing, which necessitates contact-free identification of persons with the help of their biometric traits. Six pre-trained DCNN models are taken into account for an experimental evaluation in human FPAD alias VGG19, VGG16, DensNet121, MobileNet, Xception, and InceptionV3. The investigation makes use of the NUAA and Replay-Attack benchmark FPAD datasets. Thepade's sorted block truncation coding (SBTC) 10-ary features are merged with deep learning features produced from the finest performing finetuned DCNNs to enhance the FPAD capabilities of analyzed machine learning (ML) classifiers. The integration of features of Thepade's SBTC 10-ary and DCNN has considerably increased the FPAD accuracy of ML classifiers with slightly more computations of feature extraction.

The decoding of motor imagery electroencephalography (MI-EEG) is constrained by core issues including low signal-to-noise ratio (SNR) and cross-session as well as cross-subject domain shift, which seriously impedes the practical deployment of brain-computer interfaces (BCIs). To address these challenges, this paper proposes a novel end-to-end MI-EEG decoding method named BARN-DA. Two innovative modules, Band-Aware Channel Attention (BACA) and Multi-Scale Kernel Perception (MSKP), are designed: one enhances discriminative channel features by modeling channel information fused with frequency band feature representation, and the other captures complex data correlations via multi-scale parallel convolutions to improve the discriminability of the network's feature extraction. Subsequently, the features are mapped onto the Riemannian manifold. For the source and target domain features residing on this manifold, a Riemannian Maximum Mean Discrepancy (R-MMD) loss is designed based on the log-Euclidean metric. This approach enables the effective embedding of Symmetric Positive Definite (SPD) matrices into the Reproducing Kernel Hilbert Space (RKHS), thereby reducing cross-domain discrepancies. Experimental results on four public datasets demonstrate that the BARN-DA method achieves average cross-session classification accuracies of 84.65% ± 8.97% (BCIC IV 2a), 89.19% ± 7.69% (BCIC IV 2b), and 61.76% ± 12.68% (SHU), as well as average cross-subject classification accuracies of 65.49% ± 11.64% (BCIC IV 2a), 78.78% ± 8.44% (BCIC IV 2b), and 78.14% ± 14.41% (BCIC III 4a). Compared with state-of-the-art methods, BARN-DA obtains higher classification accuracy and stronger cross-session and cross-subject generalization ability. These results confirm that BARN-DA effectively alleviates low SNR and domain shift problems in MI-EEG decoding, providing an efficient technical solution for practical BCI systems.