Publications

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There are numerous applications that combine data collected from sensors with machine-learning based classification models to predict the type of event or objects observed. Both the collection of the data itself and the classification models can be tuned for optimal performance, but we hypothesize that additional gains can be realized by jointly assessing both factors together. Through this research, we used a seismic event dataset and two neural network classification models that issued probabilistic predictions on each event to determine whether it was an earthquake or a quarry blast. Real world applications will have constraints on data collection, perhaps in terms of a budget for the number of sensors or on where, when, or how data can be collected. We mimicked such constraints by creating subnetworks of sensors with both size and locational constraints. We compare different methods of determining the set of sensors in each subnetwork in terms of their predictive accuracy and the number of events that they observe overall. Additionally, we take the classifiers into account, treating them both as black-box models and testing out various ways of combining predictions among models and among the set of sensors that observe any given event. We find that comparable overall performance can be seen with less than half the number of sensors in the full network. Additionally, a voting scheme that uses the average confidence across the sensors for a given event shows improved predictive accuracy across nearly all subnetworks. Lastly, locational constraints matter, but sometimes in unintuitive ways, as better-performing sensors may be chosen instead of the ones excluded based on location. This being a short-term research effort, we offer a lengthy discussion on interesting next-steps and ties to other ongoing research efforts that we did not have time to pursue. These include a detailed analysis of the subnetwork performance broken down by event type, specific location, and model confidence. This project also included a Campus Executive research partnership with Texas A&M University. Through this, we worked with a professor and student to study information gain for UAV routing. This was an alternative way of looking at the similar problem space that includes sensor operation for data collection and the resulting benefit to be gained from it. This work is described in an Appendix.

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We consider the problem of selecting a small set (mosaic) of sensor images (footprints) whose union covers a two-dimensional Region Of Interest (ROI) on Earth. We take the approach of modeling the mosaic problem as a Mixed-Integer Linear Program (MILP). This allows solutions to this subproblem to feed into a larger remote-sensor collection-scheduling MILP. This enables the scheduler to dynamically consider alternative mosaics, without having to perform any new geometric computations. Our approach to set up the optimization problem uses maximal disk sampling and point-in-polygon geometric calculations. Footprints may be of any shape, even non-convex, and we show examples using a variety of shapes that may occur in practice. The general integer optimization problem can become computationally expensive for large problems. In practice, the number of placed footprints is within an order of magnitude of ten, making the time to solve to optimality on the order of minutes. This is fast enough to make the approach relevant for near real-time mission applications. We provide open source software for all our methods, "GeoPlace."

We consider heuristic and optimal solutions to a discrete geometric bin packing problem that arises in a resource allocation problem. An imaging sensor is assigned to collect data over a large area, but some subregions are more valuable than others. To capture these high-value regions with higher fidelity, we can assign some number of non-overlapping rectangular subsets, called “subfootprints.” The sensor image is partitioned into squares called “chips”, and each chip is further partitioned into pixels. Pixels may have different values. Subfootprints are restricted to rectangular collections of chips, but we are free to choose different rectangle heights, widths, and areas. We seek the optimal arrangement over the family of possible rectangle shapes and sizes. We provide a mixed-integer linear program optimization formulation, as well as a greedy heuristic, to solve this problem. For the meta-problem, we have some freedom to align the chip boundaries to different pixels. However, it is too expensive to solve the optimization formulation for each alignment. However, we show that the greedy heuristic can inform which pixel alignments are worth solving the optimization over. We use a variant of k-means clustering to group greedy solutions by their transport shape-similarity. For each cluster, we run the optimization problem over the greedy layout with the highest value. In practice this efficiently explores the geometric configuration space, and produces solutions close to the global optimum. We show a contrived example using surveillance of the Mississippi River. Our software is available as open-source in the Github repository “GeoPlace .

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Remote sensing systems have firmly established a role in providing immense value to commercial industry, scientific exploration, and national security. Continued maturation of sensing technology has reduced the cost of deploying highly-capable sensors while at the same time increased reliance on the information these sensors can provide. The demand for time on these sensors is unlikely to diminish. Coordination of next-generation sensor systems, larger constellations of satellites, unmanned aerial vehicles, ground telescopes, etc. is prohibitively complex for existing heuristics-based scheduling techniques. The project was a two-year collaboration spanning multiple Sandia centers and included a partnership with Texas A&M University. We have developed algorithms and software for collection scheduling, remote sensor field-of-view pointing models, and bandwidth-constrained prioritization of sensor data. Our approach followed best practices from the operations research and computational geometry communities. These models provide several advantages over state of the art techniques. In particular, our approach is more flexible compared to heuristics that tightly couple models and solution techniques. First, our mixed-integer linear models afford a rigorous analysis so that sensor planners can quantitatively describe a schedule relative to the best possible. Optimal or near-optimal schedules can be produced with commercial solvers in operational run-times. These models can be modified and extended to incorporate different scheduling and resource constraints and objective function definitions. Further, we have extended these models to proactively schedule sensors under weather and ad hoc collection uncertainty. This approach stands in contrast to existing deterministic schedulers which assume a single future weather or ad hoc collection scenario. The field-of-view pointing algorithm produces a mosaic with the fewest number of images required to fully cover a region of interest. The bandwidth-constrained algorithms find the highest priority information that can be transmitted. All of these are based on mixed-integer linear programs so that, in the future, collection scheduling, field-of-view, and bandwidth prioritization can be combined into a single problem. Experiments conducted using the developed models, commercial solvers, and benchmark datasets have demonstrated that proactively scheduling against uncertainty regularly and significantly outperforms deterministic schedulers.

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We present here an example of how a large,multi-dimensional unstructured data set, namely aircraft trajectories over the United States, can be analyzed using relatively straightforward unsupervised learning techniques. We begin by adding a rough structure to the trajectory data using the notion of distance geometry. This provides a very generic structure to the data that allows it to be indexed as an n-dimensional vector. We then do a clustering based on the HDBSCAN algorithm to both group flights with similar shapes and find outliers that have a relatively unique shape. Next, we expand the notion of geometric features to more specialized features and demonstrate the power of these features to solve specific problems. Finally, we highlight not just the power of the technique but also the speed and simplicity of the implementation by demonstrating them on very large data sets.

We want to organize a body of trajectories in order to identify, search for, classify and predict behavior among objects such as aircraft and ships. Existing compari- son functions such as the Fr'echet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as total distance traveled and distance be- tween start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generally be mapped easily to behaviors of interest to humans that are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to iden- tify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories, predict destination and apply unsupervised machine learning algorithms.

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