Multiview Graph Learning with Consensus Graph

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.

Optimal Graph Filters for Clustering Attributed Graphs

Many real-world systems can be represented as graphs where the different entities are presented by nodes and their interactions by edges. An important task in studying large datasets is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on graph convolutional networks and graph convolutional filters to combine structural and content information. However, these methods are mostly limited to lowpass filtering and do not explicitly optimize the filters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we design polynomial graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem where graph filters that are interpretable and optimal for the given data are learned while maximizing the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art graph convolutional network approaches.

From Nano to Macro: Overview of the IEEE Bio Image and Signal Processing Technical Committee

The Bio Image and Signal Processing (BISP) Technical Committee (TC) of the IEEE Signal Processing Society (SPS) promotes activities within the broad technical field of biomedical image and signal processing. Areas of interest include medical and biological imaging, digital pathology, molecular imaging, microscopy, and associated computational imaging, image analysis, and image-guided treatment, alongside physiological signal processing, computational biology, and bioinformatics. BISP has 40 members and covers a wide range of EDICS, including CIS-MI: Medical Imaging, BIO-MIA: Medical Image Analysis, BIO-BI: Biological Imaging, BIO: Biomedical Signal Processing, BIO-BCI: Brain/Human-Computer Interfaces, and BIO-INFR: Bioinformatics. BISP plays a central role in the organization of the IEEE International Symposium on Biomedical Imaging (ISBI) and contributes to the technical sessions at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), and the IEEE International Conference on Image Processing (ICIP). In this paper, we provide a brief history of the TC, review the technological and methodological contributions its community delivered, and highlight promising new directions we anticipate.

Community Detection in Multi-frequency EEG Networks

Objective: In recent years, the functional connectivity of the human brain has been studied with graph theoretical tools. One such approach is community detection which is fundamental for uncovering the localized networks. Existing methods focus on networks constructed from a single frequency band while ignoring multi-frequency nature of functional connectivity. Therefore, there is a need to study multi-frequency functional connectivity to be able to capture the full view of neuronal connectivity. Methods: In this paper, we use multilayer networks to model multi-frequency functional connectivity. In the proposed model, each layer corresponds to a different frequency band. We then extend the definition of modularity to multilayer networks to develop a new community detection algorithm. Results} The proposed approach is applied to electroencephalogram data collected during a study of error monitoring in the human brain. The differences between the community structures within and across different frequency bands for two response types, i.e. error and correct, are studied. Conclusion: The results indicate that following an error response, the brain organizes itself to form communities across frequencies, in particular between theta and gamma bands while a similar cross-frequency community formation is not observed for the correct response. Moreover, the community structures detected for the error response were more consistent across subjects compared to the community structures for correct response. Significance: The multi-frequency functional connectivity network models combined with multilayer community detection algorithms can reveal changes in cross-frequency functional connectivity network formation across different tasks and response types.

Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization

Networks provide a powerful tool to model complex systems where the different entities in the system are presented by nodes and their interactions by edges. Recently, there has been a growing interest in multiplex networks as they can represent the interactions between a pair of nodes through multiple types of links, each reflecting a distinct type of interaction. One of the important tools in understanding network topology is community detection. Although there are numerous works on community detection in single layer networks, existing work on multiplex community detection mostly focuses on learning a common community structure across layers without taking the heterogeneity of the different layers into account. In this paper, we introduce a new multiplex community detection approach that can identify communities that are common across layers as well as those that are unique to each layer. The proposed algorithm employs Orthogonal Nonnegative Matrix Tri-Factorization to model each layer's adjacency matrix as the sum of two low-rank matrix factorizations, corresponding to the common and private communities, respectively. The proposed algorithm is evaluated on both synthetic and real multiplex networks and compared to state-of-the-art techniques.

Coupled Support Tensor Machine Classification for Multimodal Neuroimaging Data

Multimodal data arise in various applications where information about the same phenomenon is acquired from multiple sensors and across different imaging modalities. Learning from multimodal data is of great interest in machine learning and statistics research as this offers the possibility of capturing complementary information among modalities. Multimodal modeling helps to explain the interdependence between heterogeneous data sources, discovers new insights that may not be available from a single modality, and improves decision-making. Recently, coupled matrix-tensor factorization has been introduced for multimodal data fusion to jointly estimate latent factors and identify complex interdependence among the latent factors. However, most of the prior work on coupled matrix-tensor factors focuses on unsupervised learning and there is little work on supervised learning using the jointly estimated latent factors. This paper considers the multimodal tensor data classification problem. A Coupled Support Tensor Machine (C-STM) built upon the latent factors jointly estimated from the Advanced Coupled Matrix Tensor Factorization (ACMTF) is proposed. C-STM combines individual and shared latent factors with multiple kernels and estimates a maximal-margin classifier for coupled matrix tensor data. The classification risk of C-STM is shown to converge to the optimal Bayes risk, making it a statistically consistent rule. C-STM is validated through simulation studies as well as a simultaneous EEG-fMRI analysis. The empirical evidence shows that C-STM can utilize information from multiple sources and provide a better classification performance than traditional single-mode classifiers.

Low-rank on Graphs plus Temporally Smooth Sparse Decomposition for Anomaly Detection in Spatiotemporal Data

Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited for point anomalies in sequence data and cannot deal with temporal and spatial dependencies that arise in spatiotemporal data. In recent years, tensor-based methods have been proposed for anomaly detection to address this problem. These methods rely on conventional tensor decomposition models, not taking the structure of the anomalies into account, and are supervised or semi-supervised. We introduce an unsupervised tensor-based anomaly detection method that takes the sparse and temporally continuous nature of anomalies into account. In particular, the anomaly detection problem is formulated as a robust lowrank + sparse tensor decomposition with a regularization term that minimizes the temporal variation of the sparse part, so that the extracted anomalies are temporally persistent. We also approximate rank minimization with graph total variation minimization to reduce the complexity of the optimization algorithm. The resulting optimization problem is convex, scalable, and is shown to be robust against missing data and noise. The proposed framework is evaluated on both synthetic and real spatiotemporal urban traffic data and compared with baseline methods.

Multi-Branch Tensor Network Structure for Tensor-Train Discriminant Analysis

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has been a lot of work in the area of tensor decomposition and low-rank tensor approximation, extensions to supervised learning, feature extraction and classification are still limited. Moreover, most of the existing supervised tensor learning approaches are based on the orthogonal Tucker model. However, this model has some limitations for large tensors including high memory and computational costs. In this paper, we introduce a supervised learning approach for tensor classification based on the tensor-train model. In particular, we introduce a multi-branch tensor network structure for efficient implementation of tensor-train discriminant analysis (TTDA). The proposed approach takes advantage of the flexibility of the tensor train structure to implement various computationally efficient versions of TTDA. This approach is then evaluated on image and video classification tasks with respect to computation time, storage cost and classification accuracy and is compared to both vector and tensor based discriminant analysis methods.

Identification of Dynamic functional brain network states Through Tensor Decomposition

With the advances in high resolution neuroimaging, there has been a growing interest in the detection of functional brain connectivity. Complex network theory has been proposed as an attractive mathematical representation of functional brain networks. However, most of the current studies of functional brain networks have focused on the computation of graph theoretic indices for static networks, i.e. long-time averages of connectivity networks. It is well-known that functional connectivity is a dynamic process and the construction and reorganization of the networks is key to understanding human cognition. Therefore, there is a growing need to track dynamic functional brain networks and identify time intervals over which the network is quasi-stationary. In this paper, we present a tensor decomposition based method to identify temporally invariant 'network states' and find a common topographic representation for each state. The proposed methods are applied to electroencephalogram (EEG) data during the study of error-related negativity (ERN).