RESUMEN

An increasingly common viewpoint is that protein dynamics datasets reside in a nonlinear subspace of low conformational energy. Ideal data analysis tools should therefore account for such nonlinear geometry. The Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich mathematical structure to account for a wide range of geometries that can be modeled after an energy landscape. Second, many standard data analysis tools developed for data in Euclidean space can be generalized to Riemannian manifolds. In the context of protein dynamics, a conceptual challenge comes from the lack of guidelines for constructing a smooth Riemannian structure based on an energy landscape. In addition, computational feasibility in computing geodesics and related mappings poses a major challenge. This work considers these challenges. The first part of the paper develops a local approximation technique for computing geodesics and related mappings on Riemannian manifolds in a computationally feasible manner. The second part constructs a smooth manifold and a Riemannian structure that is based on an energy landscape for protein conformations. The resulting Riemannian geometry is tested on several data analysis tasks relevant for protein dynamics data. In particular, the geodesics with given start- and end-points approximately recover corresponding molecular dynamics trajectories for proteins that undergo relatively ordered transitions with medium-sized deformations. The Riemannian protein geometry also gives physically realistic summary statistics and retrieves the underlying dimension even for large-sized deformations within seconds on a laptop.

Asunto(s)

RESUMEN

Brain-computer interfaces (BCIs), representing a transformative form of human-computer interaction, empower users to interact directly with external environments through brain signals. In response to the demands for high accuracy, robustness, and end-to-end capabilities within BCIs based on motor imagery (MI), this paper introduces STaRNet, a novel model that integrates multi-scale spatio-temporal convolutional neural networks (CNNs) with Riemannian geometry. Initially, STaRNet integrates a multi-scale spatio-temporal feature extraction module that captures both global and local features, facilitating the construction of Riemannian manifolds from these comprehensive spatio-temporal features. Subsequently, a matrix logarithm operation transforms the manifold-based features into the tangent space, followed by a dense layer for classification. Without preprocessing, STaRNet surpasses state-of-the-art (SOTA) models by achieving an average decoding accuracy of 83.29% and a kappa value of 0.777 on the BCI Competition IV 2a dataset, and 95.45% accuracy with a kappa value of 0.939 on the High Gamma Dataset. Additionally, a comparative analysis between STaRNet and several SOTA models, focusing on the most challenging subjects from both datasets, highlights exceptional robustness of STaRNet. Finally, the visualizations of learned frequency bands demonstrate that temporal convolutions have learned MI-related frequency bands, and the t-SNE analyses of features across multiple layers of STaRNet exhibit strong feature extraction capabilities. We believe that the accurate, robust, and end-to-end capabilities of the STaRNet will facilitate the advancement of BCIs.

Asunto(s)

RESUMEN

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

Asunto(s)

RESUMEN

The pathogenesis of carcinoma is believed to come from the combined effect of polygenic variation, and the initiation and progression of malignant tumors are closely related to the dysregulation of biological pathways. Quantifying the alteration in pathway activation and identifying coordinated patterns of pathway dysfunction are the imperative part of understanding the malignancy process and distinguishing different tumor stages or clinical outcomes of individual patients. In this study, we have conducted in silico pathway activation analysis using Riemannian manifold (RiePath) toward pan-cancer personalized characterization, which is the first attempt to apply the Riemannian manifold theory to measure the extent of pathway dysregulation in individual patient on the tangent space of the Riemannian manifold. RiePath effectively integrates pathway and gene expression information, not only generating a relatively low-dimensional and biologically relevant representation, but also identifying a robust panel of biologically meaningful pathway signatures as biomarkers. The pan-cancer analysis across 16 cancer types reveals the capability of RiePath to evaluate pathway activation accurately and identify clinical outcome-related pathways. We believe that RiePath has the potential to provide new prospects in understanding the molecular mechanisms of complex diseases and may find broader applications in predicting biomarkers for other intricate diseases.

Asunto(s)

RESUMEN

Brain network analyses have exploded in recent years and hold great potential in helping us understand normal and abnormal brain function. Network science approaches have facilitated these analyses and our understanding of how the brain is structurally and functionally organized. However, the development of statistical methods that allow relating this organization to phenotypic traits has lagged behind. Our previous work developed a novel analytic framework to assess the relationship between brain network architecture and phenotypic differences while controlling for confounding variables. More specifically, this innovative regression framework related distances (or similarities) between brain network features from a single task to functions of absolute differences in continuous covariates and indicators of difference for categorical variables. Here we extend that work to the multitask and multisession context to allow for multiple brain networks per individual. We explore several similarity metrics for comparing distances between connection matrices and adapt several standard methods for estimation and inference within our framework: standard F test, F test with scan-level effects (SLE), and our proposed mixed model for multitask (and multisession) BrAin NeTwOrk Regression (3M_BANTOR). A novel strategy is implemented to simulate symmetric positive-definite (SPD) connection matrices, allowing for the testing of metrics on the Riemannian manifold. Via simulation studies, we assess all approaches for estimation and inference while comparing them with existing multivariate distance matrix regression (MDMR) methods. We then illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project (HCP) data.

RESUMEN

How to use the characteristics of EEG signals to obtain more complementary and discriminative data representation is an issue in EEG-based emotion recognition. Many studies have tried spatio-temporal or spatio-spectral feature fusion to obtain higher-level representations of EEG data. However, these studies ignored the complementarity between spatial, temporal and spectral domains of EEG signals, thus limiting the classification ability of models. This study proposed an end-to-end network based on ManifoldNet and BiLSTM networks, named STSNet. The STSNet first constructed a 4-D spatio-temporal-spectral data representation and a spatio-temporal data representation based on EEG signals in manifold space. After that, they were fed into the ManifoldNet network and the BiLSTM network respectively to calculate higher-level features and achieve spatio-temporal-spectral feature fusion. Finally, extensive comparative experiments were performed on two public datasets, DEAP and DREAMER, using the subject-independent leave-one-subject-out cross-validation strategy. On the DEAP dataset, the average accuracy of the valence and arousal are 69.38% and 71.88%, respectively; on the DREAMER dataset, the average accuracy of the valence and arousal are 78.26% and 82.37%, respectively. Experimental results show that the STSNet model has good emotion recognition performance.

RESUMEN

Multiple sclerosis (MS) is a neurological condition characterized by severe structural brain damage and by functional reorganization of the main brain networks that try to limit the clinical consequences of structural burden. Resting-state (RS) functional connectivity (FC) abnormalities found in this condition were shown to be variable across different MS phases, according to the severity of clinical manifestations. The article describes a system exploiting machine learning on RS FC matrices to discriminate different MS phenotypes and to identify relevant functional connections for MS stage characterization. To this end, the system exploits some mathematical properties of covariance-based RS FC representation, which can be described by a Riemannian manifold. The classification performance of the proposed framework was significantly above the chance level for all MS phenotypes. Moreover, the proposed system was successful in identifying relevant RS FC alterations contributing to an accurate phenotype classification.

Asunto(s)

RESUMEN

Introduction: Affective computing is the core for Human-computer interface (HCI) to be more intelligent, where electroencephalogram (EEG) based emotion recognition is one of the primary research orientations. Besides, in the field of brain-computer interface, Riemannian manifold is a highly robust and effective method. However, the symmetric positive definiteness (SPD) of the features limits its application. Methods: In the present work, we introduced the Laplace matrix to transform the functional connection features, i.e., phase locking value (PLV), Pearson correlation coefficient (PCC), spectral coherent (COH), and mutual information (MI), to into semi-positive, and the max operator to ensure the transformed feature be positive. Then the SPD network is employed to extract the deep spatial information and a fully connected layer is employed to validate the effectiveness of the extracted features. Particularly, the decision layer fusion strategy is utilized to achieve more accurate and stable recognition results, and the differences of classification performance of different feature combinations are studied. What's more, the optimal threshold value applied to the functional connection feature is also studied. Results: The public emotional dataset, SEED, is adopted to test the proposed method with subject dependent cross-validation strategy. The result of average accuracies for the four features indicate that PCC outperform others three features. The proposed model achieve best accuracy of 91.05% for the fusion of PLV, PCC, and COH, followed by the fusion of all four features with the accuracy of 90.16%. Discussion: The experimental results demonstrate that the optimal thresholds for the four functional connection features always kept relatively stable within a fixed interval. In conclusion, the experimental results demonstrated the effectiveness of the proposed method.

RESUMEN

We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve estimation performance over irreversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator.

RESUMEN

BACKGROUND: The EEG-based emotion recognition is one of the primary research orientations in the field of emotional intelligence and human-computer interaction (HCI). NEW METHOD: We proposed a novel model, denoted as ICRM-LSTM, for EEG-based emotion recognition by combining the independent component analysis (ICA), the Riemannian manifold (RM), and the long short-term memory network (LSTM). The SEED and MAHNOB-HCI dataset were employed to verify the performance of the proposed model. Firstly, ICA was used to perform blind source separation (BSS) for the preprocessed EEG signals provided by the two datasets. Then, a series of the covariance matrices according to time order were extracted from the blind source signals, and the symmetric positive definiteness of covariance matrix allowed us to project them from RM space to Euclid space by logarithmic mapping. Finally, the transformed covariance matrices were taken as inputs of the LSTM network to perform the emotion recognition. RESULTS: To validate the effect of the ICRM method on the performance of the proposed model, we designed three groups of comparative experiments. The average accuracy of the ICRM-LSTM model were 96.75 % and 98.09 % in SEED and MAHNOB-HCI, respectively. Then we compared our model with the models didn't perform the ICA or RM method, where we found that the proposed model had better performance. Furthermore, to verify the robustness, we added three groups of Gaussian noise with different signal-to-noise ratios (SNR) to the preprocessed EEG signals, and the proposed model achieved a good performance in both the two datasets. COMPARISON WITH EXISTING METHOD: The performance of our model was superior to most of existing methods which also employed the SEED or MAHNOB-HCI dataset. CONCLUSION: This paper demonstrated that the ICA and RM were helpful for EEG-based emotion recognition, and provided the evidence that the RM method could effectively alleviate the problem of the uncertain ordering of ICA.

Asunto(s)

RESUMEN

In the paper, we study a class of novel stochastic composition optimization problems over Riemannian manifold, which have been raised by multiple emerging machine learning applications such as distributionally robust learning in Riemannian manifold setting. To solve these composition problems, we propose an effective Riemannian compositional gradient (RCG) algorithm, which has a sample complexity of O(ϵ-4) for finding an ϵ-stationary point. To further reduce sample complexity, we propose an accelerated momentum-based Riemannian compositional gradient (M-RCG) algorithm. Moreover, we prove that the M-RCG obtains a lower sample complexity of Õ(ϵ-3) without large batches, which achieves the best known sample complexity for its Euclidean counterparts. Extensive numerical experiments on training deep neural networks (DNNs) over Stiefel manifold and learning principal component analysis (PCA) over Grassmann manifold demonstrate effectiveness of our proposed algorithms. To the best of our knowledge, this is the first study of the composition optimization problems over Riemannian manifold.

Asunto(s)

RESUMEN

Recently, Riemannian geometry-based pattern recognition has been widely employed to brain computer interface (BCI) researches, providing new idea for emotion recognition based on electroencephalogram (EEG) signals. Although the symmetric positive definite (SPD) matrix manifold constructed from the traditional covariance matrix contains large amount of spatial information, these methods do not perform well to classify and recognize emotions, and the high dimensionality problem still unsolved. Therefore, this paper proposes a new strategy for EEG emotion recognition utilizing Riemannian geometry with the aim of achieving better classification performance. The emotional EEG signals of 32 healthy subjects were from an open-source dataset (DEAP). The wavelet packets were first applied to extract the time-frequency features of the EEG signals, and then the features were used to construct the enhanced SPD matrix. A supervised dimensionality reduction algorithm was then designed on the Riemannian manifold to reduce the high dimensionality of the SPD matrices, gather samples of the same labels together, and separate samples of different labels as much as possible. Finally, the samples were mapped to the tangent space, and the K-nearest neighbors (KNN), Random Forest (RF) and Support Vector Machine (SVM) method were employed for classification. The proposed method achieved an average accuracy of 91.86%, 91.84% on the valence and arousal recognition tasks. Furthermore, we also obtained the superior accuracy of 86.71% on the four-class recognition task, demonstrated the superiority over state-of-the-art emotion recognition methods.

Asunto(s)

RESUMEN

BACKGROUND: Brain computer interface (BCI) utilizes brain signals to help users interact with external devices directly. EEG is one of the most commonly used techniques for brain signal acquisition in BCI. However, it is notoriously difficult to build a generic EEG recognition model due to significant non-stationarity and subject-to-subject variations, and the requirement for long time training. Transfer learning (TL) is particularly useful because it can alleviate the calibration requirement in EEG-based BCI applications by transferring the calibration information from existing subjects to new subject. To take advantage of geometric properties in Riemann manifold and joint distribution adaptation, a manifold embedded transfer learning (METL) framework was proposed for motor imagery (MI) EEG decoding. NEW METHOD: First, the covariance matrices of the EEG trials are first aligned on the SPD manifold. Then the features are extracted from both the symmetric positive definite (SPD) manifold and Grassmann manifold. Finally, the classification model is learned by combining the structural risk minimization (SRM) of source domain and joint distribution alignment of source and target domains. RESULT: Experimental results on two MI EEG datasets verify the effectiveness of the proposed METL. In particular, when there are a small amount of labeled samples in the target domain, METL demonstrated a more accurate and stable classification performance than conventional methods. COMPARISON WITH EXISTING METHODS: Compared with several state-of-the-art methods, METL has achieved better classification accuracy, 71.81% and 69.06% in single-to-single (STS), 83.14% and 76.00% in multi-to-single (MTS) transfer tasks, respectively. CONCLUSIONS: METL can cope with single source domain or multi-source domains and compared with single-source transfer learning, multi-source transfer learning can improve the performance effectively due to the data expansion. It is effective enough to achieve superior performance for classification of EEG signals.

Asunto(s)

RESUMEN

Locally linear embedding (LLE) is an effective tool to extract the significant features from a dataset. However, most of the relevant existing algorithms assume that the original dataset resides on a Euclidean space, unfortunately nearly all the original data space is non-Euclidean. In addition, the original LLE does not use the discriminant information of the dataset, which will degrade its performance in feature extraction. To address these problems raised in the conventional LLE, we first employ the original dataset to construct a symmetric positive definite manifold, and then estimate the tangent space of this manifold. Furthermore, the local and global discriminant information are integrated into the LLE, and the improved LLE is operated in the tangent space to extract the important features. We introduce Iris dataset to analyze the capability of the proposed method to extract features. Finally, several experiments are performed on five machinery datasets, and experimental results indicate that our proposed method can extract the excellent low-dimensional representations of the original dataset. Compared with the state-of-the-art methods, the proposed algorithm shows a strong capability for fault diagnosis.

Asunto(s)

RESUMEN

Diffusion tensor imaging (DTI) data interpolation is important for DTI processing, which could affect the precision and computational complexity in the process of denoising, filtering, regularization, and DTI registration and fiber tracking. In this paper, we propose a novel DTI interpolation framework named with spectrum-sine (SS) focusing on tensor orientation variation in DTI processing. Compared with the state-of-the-art DTI interpolation method using Euler angles or quaternion to represent the orientation of DTI tensors, this method does not need to convert eigenvectors into Euler angles or quaternions, but interpolates each tensor's unit eigenvector directly. The prominent merit of this tensor interpolation method lies in tensor orientation information preservation, which is different from the existing DTI tensor interpolation methods that interpolating tensor's orientation information in a scalar way. The experimental results from both synthetic and real human brain DTI data demonstrated the proposed SS interpolation scheme not only maintains the advantages of Log-Euclidean and Riemannian interpolation frameworks, such as preserving the tensor's symmetric positive definiteness and the monotonic determinant variation, but also preserve the tensor's anisotropy property which was proposed in the spectral quaternion (SQ) method.

Asunto(s)

RESUMEN

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices, which are inherently points that live on a curved Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, traditional Euclidean machine learning algorithms yield poor results on such data. In this paper, we generalize the probabilistic learning vector quantization algorithm for data points living on the manifold of symmetric positive definite matrices equipped with Riemannian natural metric (affine-invariant metric). By exploiting the induced Riemannian distance, we derive the probabilistic learning Riemannian space quantization algorithm, obtaining the learning rule through Riemannian gradient descent. Empirical investigations on synthetic data, image data , and motor imagery electroencephalogram (EEG) data demonstrate the superior performance of the proposed method.

Asunto(s)

RESUMEN

This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi-isometric classification with the bi-Lipschitz classification. On the other hand, we study the problem whether two quasi-isometrically equivalent Lie groups may be made isometric if equipped with suitable left-invariant Riemannian metrics. We show that this is the case for three-dimensional simply connected groups, but it is not true in general for multiply connected groups. The counterexample also demonstrates that 'may be made isometric' is not a transitive relation.

RESUMEN

Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure called Riemannian manifold. Due to its geometric properties, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space. Analysis of functional networks on the SPD space takes account of all the pairwise interactions (edges) as a whole, which differs from the conventional rationale of considering edges as independent from each other. Despite its geometric characteristics, only a few studies have been conducted for functional network analysis on the SPD manifold and inference methods specialized for connectivity analysis on the SPD manifold are rarely found. The current study aims to show the significance of connectivity analysis on the SPD space and introduce inference algorithms on the SPD manifold, such as regression analysis of functional networks in association with behaviors, principal geodesic analysis, clustering, state transition analysis of dynamic functional networks and statistical tests for network equality on the SPD manifold. We applied the proposed methods to both simulated data and experimental resting state fMRI data from the human connectome project and argue the importance of analyzing functional networks under the SPD geometry. All the algorithms for numerical operations and inferences on the SPD manifold are implemented as a MATLAB library, called SPDtoolbox, for public use to expediate functional network analysis on the right geometry.

Asunto(s)

RESUMEN

To achieve more appropriate fault feature representation for bearing, a statistical-enhanced covariance matrix (SECM) is proposed to extract the global-local features and the interaction of them. Besides, three statistical parameters are introduced to SECM to enhance its statistical characteristics. For fully mining the Riemannian geometric information embedded in SECMs, a Riemannian maximum margin flexible convex hull (RMMFCH) classifier with Log-Euclidean metric (LEM) is designed, where a set of Riemannian kernel mapping functions map SECMs to a higher-dimensional Hilbert space. In this space, the RMMFCH can be directly solved, which reduces the extra computation cost. Hence, we design a fault diagnosis scheme of bearing with SECM and RMMFCH. Experiment results prove the promising performance of our method for bearing fault diagnosis.

RESUMEN

Breast cancer is the most prevalent invasive type of cancer among women. The mortality rate of the disease can be reduced considerably through timely prognosis and felicitous treatment planning, by utilizing the computer aided detection and diagnosis techniques. With the advent of whole slide image (WSI) scanners for digitizing the histopathological tissue samples, there is a drastic increase in the availability of digital histopathological images. However, these samples are often unlabeled and hence they need labeling to be done through manual annotations by domain experts and experienced pathologists. But this annotation process required for acquiring high quality large labeled training set for nuclear atypia scoring is a tedious, expensive and time consuming job. Active learning techniques have achieved widespread acceptance in reducing this human effort in annotating the data samples. In this paper, we explore the possibilities of active learning on nuclear pleomorphism scoring over a non-Euclidean framework, the Riemannian manifold. Active learning technique adopted for the cancer grading is in the batch-mode framework, that adaptively identifies the apt batch size along with the batch of instances to be queried, following a submodular optimization framework. Samples for annotation are selected considering the diversity and redundancy between the pair of samples, based on the kernelized Riemannian distance measures such as log-Euclidean metrics and the two Bregman divergences - Stein and Jeffrey divergences. Results of the adaptive Batch Mode Active Learning on the Riemannian metric show a superior performance when compared with the state-of-the-art techniques for breast cancer nuclear pleomorphism scoring, as it makes use of the information from the unlabeled samples.

Asunto(s)