Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

GCNs-Net: A Graph Convolutional Neural Network Approach for Decoding Time-resolved EEG Motor Imagery Signals

Towards developing effective and efficient brain-computer interface (BCI) systems, precise decoding of brain activity measured by electroencephalogram (EEG), is highly demanded. Traditional works classify EEG signals without considering the topological relationship among electrodes. However, neuroscience research has increasingly emphasized network patterns of brain dynamics. Thus, the Euclidean structure of electrodes might not adequately reflect the interaction between signals. To fill the gap, a novel deep learning framework based on the graph convolutional neural networks (GCNs) was presented to enhance the decoding performance of raw EEG signals during different types of motor imagery (MI) tasks while cooperating with the functional topological relationship of electrodes. Based on the absolute Pearson's matrix of overall signals, the graph Laplacian of EEG electrodes was built up. The GCNs-Net constructed by graph convolutional layers learns the generalized features. The followed pooling layers reduce dimensionality, and the fully-connected softmax layer derives the final prediction. The introduced approach has been shown to converge for both personalized and group-wise predictions. It has achieved the highest averaged accuracy, 93.056% and 88.57% (PhysioNet Dataset), 96.24% and 80.89% (High Gamma Dataset), at the subject and group level, respectively, compared with existing studies, which suggests adaptability and robustness to individual variability. Moreover, the performance was stably reproducible among repetitive experiments for cross-validation. To conclude, the GCNs-Net filters EEG signals based on the functional topological relationship, which manages to decode relevant features for brain motor imagery

EEG-Based Emotion Recognition Using Regularized Graph Neural Networks

Electroencephalography (EEG) measures the neuronal activities in different brain regions via electrodes. Many existing studies on EEG-based emotion recognition do not fully exploit the topology of EEG channels. In this paper, we propose a regularized graph neural network (RGNN) for EEG-based emotion recognition. RGNN considers the biological topology among different brain regions to capture both local and global relations among different EEG channels. Specifically, we model the inter-channel relations in EEG signals via an adjacency matrix in a graph neural network where the connection and sparseness of the adjacency matrix are inspired by neuroscience theories of human brain organization. In addition, we propose two regularizers, namely node-wise domain adversarial training (NodeDAT) and emotion-aware distribution learning (EmotionDL), to better handle cross-subject EEG variations and noisy labels, respectively. Extensive experiments on two public datasets, SEED and SEED-IV, demonstrate the superior performance of our model than state-of-the-art models in most experimental settings. Moreover, ablation studies show that the proposed adjacency matrix and two regularizers contribute consistent and significant gain to the performance of our RGNN model. Finally, investigations on the neuronal activities reveal important brain regions and inter-channel relations for EEG-based emotion recognition

A Topological Deep Learning Framework for Neural Spike Decoding

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. One of the ways brains encode spatial information is through grid cells, layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single grid. We want to capture this firing structure and use it to decode grid cell data. Understanding, representing, and decoding these neural structures require models that encompass higher order connectivity than traditional graph-based models may provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network (SCRNN). Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the SCRNN is demonstrated on head direction data to test its performance and then applied to grid cell datasets with the task to automatically predict trajectories

Adaptive and Topological Deep Learning with applications to Neuroscience

Deep Learning and neuroscience have developed a two way relationship with each informing the other. Neural networks, the main tools at the heart of Deep Learning, were originally inspired by connectivity in the brain and have now proven to be critical to state-of-the-art computational neuroscience methods. This dissertation explores this relationship, first, by developing an adaptive sampling method for a neural network-based partial different equation solver and then by developing a topological deep learning framework for neural spike decoding. We demonstrate that our adaptive scheme is convergent and more accurate than DGM -- as long as the residual mirrors the local error -- at the same number of training steps and using the same or less number of training points. We present a multitude of tests applied to selected PDEs discussing the robustness of our scheme. Next, we further illustrate the partnership between deep learning and neuroscience by decoding neural activity using a novel neural network architecture developed to exploit the underlying connectivity of the data by employing tools from Topological Data Analysis. Neurons encode information like external stimuli or allocentric location by generating firing patterns where specific ensembles of neurons fire simultaneously for one value. Understanding, representing, and decoding these neural structures require models that encompass higher order connectivity than traditional graph-based models may provide. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network (SCRNN). Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. The effectiveness and versatility of the SCRNN is demonstrated on head direction data to test its performance and then applied to grid cell datasets with the task to automatically predict trajectories

Graph Convolutional Network with Connectivity Uncertainty for EEG-based Emotion Recognition

Automatic emotion recognition based on multichannel Electroencephalography (EEG) holds great potential in advancing human-computer interaction. However, several significant challenges persist in existing research on algorithmic emotion recognition. These challenges include the need for a robust model to effectively learn discriminative node attributes over long paths, the exploration of ambiguous topological information in EEG channels and effective frequency bands, and the mapping between intrinsic data qualities and provided labels. To address these challenges, this study introduces the distribution-based uncertainty method to represent spatial dependencies and temporal-spectral relativeness in EEG signals based on Graph Convolutional Network (GCN) architecture that adaptively assigns weights to functional aggregate node features, enabling effective long-path capturing while mitigating over-smoothing phenomena. Moreover, the graph mixup technique is employed to enhance latent connected edges and mitigate noisy label issues. Furthermore, we integrate the uncertainty learning method with deep GCN weights in a one-way learning fashion, termed Connectivity Uncertainty GCN (CU-GCN). We evaluate our approach on two widely used datasets, namely SEED and SEEDIV, for emotion recognition tasks. The experimental results demonstrate the superiority of our methodology over previous methods, yielding positive and significant improvements. Ablation studies confirm the substantial contributions of each component to the overall performance.Comment: 10 page