Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data.

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or . For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (, walking, sitting, running).

Network Inference via the Time-Varying Graphical Lasso.

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of such data, it is essential to understand the relationships between the different entities and how these relationships evolve over time. In this paper, we introduce the , a method of inferring time-varying networks from raw time series data.

Learning the Network Structure of Heterogeneous Data via Pairwise Exponential Markov Random Fields.

Markov random fields (MRFs) are a useful tool for modeling relationships present in large and high-dimensional data. Often, this data comes from various sources and can have diverse distributions, for example a combination of numerical, binary, and categorical variables. Here, we define the (PE-MRF), an approach capable of modeling exponential family distributions in heterogeneous domains.

SnapVX: A Network-Based Convex Optimization Solver.

SnapVX is a high-performance solver for convex optimization problems defined on networks. For problems of this form, SnapVX provides a fast and scalable solution with guaranteed global convergence. It combines the capabilities of two open source software packages: Snap.

Network Lasso: Clustering and Optimization in Large Graphs.

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems.

Estimating the cumulative ecological effect of local scale landscape changes in south Florida.

Ecosystem restoration in south Florida is a state and national priority centered on the Everglades wetlands. However, urban development pressures affect the restoration potential and remaining habitat functions of the natural undeveloped areas. Land use (LU) planning often focuses at the local level, but a better understanding of the cumulative effects of small projects at the landscape level is needed to support ecosystem restoration and preservation.