Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Machine learning for cardiac ultrasound time series data

We consider the problem of identifying frames in a cardiac ultrasound video associated with left ventricular chamber end-systolic (ES, contraction) and end-diastolic (ED, expansion) phases of the cardiac cycle. Our procedure involves a simple application of non-negative matrix factorization (NMF) to a series of frames of a video from a single patient. Rank-2 NMF is performed to compute two end-members. The end members are shown to be close representations of the actual heart morphology at the end of each phase of the heart function. Moreover, the entire time series can be represented as a linear combination of these two end-member states thus providing a very low dimensional representation of the time dynamics of the heart. Unlike previous work, our methods do not require any electrocardiogram (ECG) information in order to select the end-diastolic frame. Results are presented for a data set of 99 patients including both healthy and diseased examples.UCLA through the Physical Sciences Division; Entrepreneurship and Innovation Fund; Department of Mathematics; NSF [DMS-1045536, DMS-1417674]; ONR [N00014-16-1-2119]; Cross-disciplinary Scholars in Science and Technology (CSST) program at UCLACPCI-S(ISTP)1013

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Topic time series analysis of microblogs

Social media data tends to cluster in time and space around events, such as sports competitions and local news-worthy phenomena. However, transforming raw, free-form, real time text into meaningful in-formation remains a challenging task. Confounding factors include the massive volume of posted data, lack of reliable event information, hidden temporal trends, and the vastly diverse nature of content. In the present work, we examine spatio-temporal topic distributions and self-exciting time series models as applied to social media microblog data. We apply topic modeling using non-negative matrix factorization with sparsity constraints to discover prevalent topics as well as latent thematic word associations within topics. We then present two methods for mining interesting spatio-temporal dynamics and relations among topics, one that compares the topic distributions directly, and another that models topics over time as temporal or spatio-temporal Hawkes process with exponential trig-ger functions. This second method allows identification of self-exciting topics and reveals unique temporal and spatial relationships among them

Mitral Valve Segmentation Using Robust Nonnegative Matrix Factorization.

Analyzing and understanding the movement of the mitral valve is of vital importance in cardiology, as the treatment and prevention of several serious heart diseases depend on it. Unfortunately, large amounts of noise as well as a highly varying image quality make the automatic tracking and segmentation of the mitral valve in two-dimensional echocardiographic videos challenging. In this paper, we present a fully automatic and unsupervised method for segmentation of the mitral valve in two-dimensional echocardiographic videos, independently of the echocardiographic view. We propose a bias-free variant of the robust non-negative matrix factorization (RNMF) along with a window-based localization approach, that is able to identify the mitral valve in several challenging situations. We improve the average f1-score on our dataset of 10 echocardiographic videos by 0.18 to a f1-score of 0.56