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.