Investigative Simulation: Towards Utilizing Graph Pattern Matching for Investigative Search

This paper proposes the use of graph pattern matching for investigative graph search, which is the process of searching for and prioritizing persons of interest who may exhibit part or all of a pattern of suspicious behaviors or connections. While there are a variety of applications, our principal motivation is to aid law enforcement in the detection of homegrown violent extremists. We introduce investigative simulation, which consists of several necessary extensions to the existing dual simulation graph pattern matching scheme in order to make it appropriate for intelligence analysts and law enforcement officials. Specifically, we impose a categorical label structure on nodes consistent with the nature of indicators in investigations, as well as prune or complete search results to ensure sensibility and usefulness of partial matches to analysts. Lastly, we introduce a natural top-k ranking scheme that can help analysts prioritize investigative efforts. We demonstrate performance of investigative simulation on a real-world large dataset.Comment: 8 pages, 6 figures. Paper to appear in the Fosint-SI 2016 conference proceedings in conjunction with the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining ASONAM 201

Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inapplicable. Accordingly, coordinate systems and characterizations based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian coordinates for many network algorithms. Herein, we present an approach to recover geometric and topological properties of a network with a small set of distance measurements. In particular, our approach is a combination of shortest path (often called geodesic) recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Results for sensor networks embedded in 2-D and 3-D spaces, as well as a social networks, indicates that the method can accurately capture the network connectivity with a small set of measurements. TPM generation can now also be based on various context appropriate measurements or VC systems, as long as they characterize different nodes by distances to small sets of random nodes (instead of a set of global anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph shortest paths, making it applicable in contexts such as social networks where VC generation may not be possible.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1712.1006

Link Dimension and Exact Construction of a Graph

Minimum resolution set and associated metric dimension provide the basis for unique and systematic labeling of nodes of a graph using distances to a set of landmarks. Such a distance vector set, however, may not be unique to the graph and does not allow for its exact construction. The concept of construction set is presented, which facilitates the unique representation of nodes and the graph as well as its exact construction. Link dimension is the minimum number of landmarks in a construction set. Results presented include necessary conditions for a set of landmarks to be a construction set, bounds for link dimension, and guidelines for transforming a resolution set to a construction set.Comment: 8pages, 1 figure, in revie

Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inappropriate. Accordingly, Topology Preserving Maps (TPMs) derived from a Virtual-Coordinate (VC) system representing the distance to a small set of anchors is an attractive alternative to physical coordinates for many network algorithms. Herein, we present an approach, based on the theory of low-rank matrix completion, to recover geometric properties of a network with only partial information about the VCs of nodes. In particular, our approach is a combination of geodesic recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Distortion evaluated using the change of distance among node pairs shows that even with up to 40% to 60% of random coordinates missing, accurate TPMs can be obtained. TPM generation can now also be based on different context appropriate VC systems or measurements as long as they characterize each node with distances to a small set of random nodes (instead of a global set of anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph geodesics, making it applicable in contexts such as social networks where VC generation may not be possible.Comment: A more recent version uploade

Conditional Random Fields as Recurrent Neural Networks

Pixel-level labelling tasks, such as semantic segmentation, play a central role in image understanding. Recent approaches have attempted to harness the capabilities of deep learning techniques for image recognition to tackle pixel-level labelling tasks. One central issue in this methodology is the limited capacity of deep learning techniques to delineate visual objects. To solve this problem, we introduce a new form of convolutional neural network that combines the strengths of Convolutional Neural Networks (CNNs) and Conditional Random Fields (CRFs)-based probabilistic graphical modelling. To this end, we formulate mean-field approximate inference for the Conditional Random Fields with Gaussian pairwise potentials as Recurrent Neural Networks. This network, called CRF-RNN, is then plugged in as a part of a CNN to obtain a deep network that has desirable properties of both CNNs and CRFs. Importantly, our system fully integrates CRF modelling with CNNs, making it possible to train the whole deep network end-to-end with the usual back-propagation algorithm, avoiding offline post-processing methods for object delineation. We apply the proposed method to the problem of semantic image segmentation, obtaining top results on the challenging Pascal VOC 2012 segmentation benchmark.Comment: This paper is published in IEEE ICCV 201

Optimizing Over Radial Kernels on Compact Manifolds

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition.Comment: Published in CVPR 201

Bringing an emphasis on technical writing to a freshman course in electrical engineering

Includes bibliographical references (page 41).We have recently added a strong writing component to one of our freshman courses in electrical engineering. The students prepared two kinds of reports—memoranda and formal engineering project reports. Our instructional objectives were to execute well these two forms: to write with a professional tone, and to make good choices about which technical material to include. To meet these objectives, model memos and engineering project reports were developed, lectures about these memos and reports were presented, a Web site for the course was developed, the technical aspects of the reports were graded by a student hourly grader, the writing aspects of the reports were evaluated by a professor, and followup debriefings were conducted at the lecture class meetings. We report on the development process and discuss student response to the course