The subgraph matching problem arises in a variety of domains including pattern recognition for segmented images , meshes of 3D objects, biochemical reactions, and security applications. Large and complex solution spaces are common for this graph-based problem, especially when the world graph contains many more nodes and edges in comparison to the template graph. Researchers have focused on the task of finding one match or many matches, however a real use-case scenario can necessitate identifying specific matches from a combinatorially complex solution space. Our work directly addresses this challenge. We propose to introduce additional queries to the subgraph that iteratively reduce the size of the solution space, and consider the optimal strategy for doing so. We formalize this problem and demonstrate that it is NP-complete. We compare different quantitative criteria for choosing nodes to query. We introduce a new method based on a spanning tree that outperforms other graph-based criteria for the multichannel datasets. Finally, we present numerical experiments for single channel and multichannel subgraph matching problems created from both synthetic and real world datasets.

Graphs are powerful analytic tools for modeling adversarial activities across a wide range of domains and applications. Examples include identifying and responding to cybersecurity systems' threats and vulnerabilities, strengthening critical infrastructure's resilience and robustness, and combating covert illicit activities that span various domains like finance, communication, and transportation. With the rapid development of generative AI, the lifecycle and throughput of adversarial activities, such as generating attacks or synthesizing deceptive signals, have accelerated significantly. For instance, a malicious actor can generate a large number of malware variants to flood defense systems or create agents to disseminate misleading signals, obscuring their activities. Consequently, there is a pressing need for novel and effective technology to autonomously handle these adversarial activities and keep pace with the evolving threats. The purpose of this workshop is to provide a forum to discuss emerging research problems and novel approaches in graph analysis for modeling adversarial activities in the age of generative AI.

Theoretical and empirical comparisons have been made to assess the expressive power and performance of invariant and equivariant GNNs. However, there is currently no theoretical result comparing the expressive power of $k$-hop invariant GNNs and equivariant GNNs. Additionally, little is understood about whether the performance of equivariant GNNs, employing steerable features up to type-$L$, increases as $L$ grows -- especially when the feature dimension is held constant. In this study, we introduce a key lemma that allows us to analyze steerable features by examining their corresponding invariant features. The lemma facilitates us in understanding the limitations of $k$-hop invariant GNNs, which fail to capture the global geometric structure due to the loss of geometric information between local structures. Furthermore, we investigate the invariant features associated with different types of steerable features and demonstrate that the expressiveness of steerable features is primarily determined by their dimension -- independent of their irreducible decomposition. This suggests that when the feature dimension is constant, increasing $L$ does not lead to essentially improved performance in equivariant GNNs employing steerable features up to type-$L$. We substantiate our theoretical insights with numerical evidence.

This study explores the dynamic relationship between online discourse, as observed in tweets, and physical hate crimes, focusing on marginalized groups. Leveraging natural language processing techniques, including keyword extraction and topic modeling, we analyze the evolution of online discourse after events affecting these groups. Examining sentiment and polarizing tweets, we establish correlations with hate crimes in Black and LGBTQ+ communities. Using a knowledge graph, we connect tweets, users, topics, and hate crimes, enabling network analyses. Our findings reveal divergent patterns in the evolution of user communities for Black and LGBTQ+ groups, with notable differences in sentiment among influential users. This analysis sheds light on distinctive online discourse patterns and emphasizes the need to monitor hate speech to prevent hate crimes, especially following significant events impacting marginalized communities.

Traditional methods of linking large language models (LLMs) to knowledge bases via the semantic similarity search often fall short of capturing complex relational dynamics. To address these limitations, we introduce AutoKG, a lightweight and efficient approach for automated knowledge graph (KG) construction. For a given knowledge base consisting of text blocks, AutoKG first extracts keywords using a LLM and then evaluates the relationship weight between each pair of keywords using graph Laplace learning. We employ a hybrid search scheme combining vector similarity and graph-based associations to enrich LLM responses. Preliminary experiments demonstrate that AutoKG offers a more comprehensive and interconnected knowledge retrieval mechanism compared to the semantic similarity search, thereby enhancing the capabilities of LLMs in generating more insightful and relevant outputs.

We analyze the impact of group activities targeting Social-Emotional Learning (SEL) and peer effects on the risk and protective factors associated with gang involvement among youth participating in the Los Angeles Mayor’s Office of Gang Reduction and Youth Development (GRYD) Prevention program. We compare the impact of targeted and non-targeted activities in decreasing Internal Risk, External Risk, and Family Norms Risk, as measured by a standardized questionnaire. We show that targeted activities are effective in decreasing Internal Risk and that activities focusing on Emotional Management are the most beneficial. Since targeted activities involve group interactions, we investigate the impact of peer network effects on outcomes using both a linear-in-means model and dynamic mode decomposition with control (DMDc). Our analysis suggests that peer network effects contribute to beneficial changes in risk and protective factors above and beyond the skill-building content of the activities.

Pretraining neural networks with massive unlabeled datasets has become popular as it equips the deep models with a better prior to solve downstream tasks. However, this approach generally assumes that the downstream tasks have access to annotated data of sufficient size. In this work, we propose ALOE, a novel system for improving the data- and label-efficiency of non-semantic speech tasks with active learning (AL). ALOE uses pretrained models in conjunction with active learning to label data incrementally and learn classifiers for downstream tasks, thereby mitigating the need to acquire labeled data beforehand. We demonstrate the effectiveness of ALOE on a wide range of tasks, uncertainty-based acquisition functions, and model architectures. Training a linear classifier on top of a frozen encoder with ALOE is shown to achieve performance similar to several baselines that utilize the entire labeled data.

Wind velocity estimation is a critical component of weather prediction, but accurately estimating atmospheric winds with in-place instruments is expensive, inefficient, and provides only sparse coverage. Consequently, methods which can extract wind patterns from remote sensing data would offer significant benefits—satellites and satellite-derived data in particular, provide comprehensive coverage of global weather phenomena. In this paper, we develop an optical flow method which successfully extracts dense wind velocity estimates from water vapor data, a commonly estimated quantity by satellites equipped with infrared or microwave instruments. The test-data comes from direct numerical simulations of a mesoscale convective system over the eastern Pacific and provides accompanying ground truth wind velocities, allowing us to quantitatively measure the performance of our methods.

We develop a graph active learning pipeline (GAP) to detect surface water and in-river sediment pixels in satellite images. The active learning approach is applied within the training process to optimally select specific pixels to generate a hand-labeled training set. Our method obtains higher accuracy with far fewer training pixels than both standard and deep learning models. According to our experiments, our GAP trained on a set of 3270 pixels reaches a better accuracy than the neural network method trained on 2.1 million pixels.

Hyperspectral unmixing is an effective tool to ascertain the material composition of each pixel in a hyperspectral image with typically hundreds of spectral channels. In this paper, we propose two graph-based semi-supervised unmixing methods. The first one directly applies graph learning to the unmixing problem, while the second one solves an optimization problem that combines the linear unmixing model and a graph-based regularization term. Following a semi-supervised framework, our methods require a very small number of training pixels that can be selected by a graph-based active learning method. We assume to obtain the ground truth information at these selected pixels, which can be either the exact abundance value or the one-hot pseudo label. In practice, the latter is much easier to obtain, which can be achieved by minimally involving a human in the loop. Compared to other popular blind unmixing methods, our methods significantly improve performance with minimal supervision. Specifically, the experiments demonstrate that the proposed methods improve the state-of-the-art blind unmixing approaches by 50% or more using only 0.4% of training pixels.

Using Knowledge Graphs to understand noisy naturalistic data has gained significant prominence in recent years. In this paper, we apply Knowledge Graphs to a new dataset of tweets of an ideologically far-right Twitter network by sourcing tweet histories of users who discussed QAnon in the summer of 2018 [1]. We further develop a new method that arms topic models with relational information from Knowledge Graphs and apply the new technique to study this dataset. Our analysis shows that users do not form a monolithic belief or social network, but rather comprise many smaller interlinking communities which discuss unique key political events (e.g., the January 6thCapitol riots).

We analyze the impact of the Los Angeles Mayor’s Office of Gang Reduction Youth Development (GRYD) prevention programming using quasi-experimental data. We model the evolution of questionnaire scores and apply Dynamic Mode Decomposition (DMD) to describe the asymptotic behavior of the dynamical system. The analysis indicates that risk decreased for youth who enrolled in GRYD prevention services, while it increased or remained the same for those who were in the control group. We augment these observations using a difference-in-differences (DID) model, showing that the decrease in risk can be attributed to enrolment in prevention services. We draw a connection between DMD and DID using both mathematical analysis and empirical evidence from the questionnaire data. Combining DMD and DID with factor analysis, we investigate the effectiveness of prevention services with respect to different attitudinal domains. We conclude that gang prevention is most effective in impacting attitudes towards negative peer obedience and least effective in impacting attitudes towards violence for self defense. Our analytical approach can be extended to other types of repeated questionnaires.

We investigate multi-task learning (MTL), where multiple learning tasks are performed jointly rather than separately to leverage their similarities and improve performance. We focus on the federated multi-task linear regression setting, where each machine possesses its own data for individual tasks and sharing the full local data between machines is prohibited. Motivated by graph regularization, we propose a novel fusion framework that only requires a one-shot communication of local estimates. Our method linearly combines the local estimates to produce an improved estimate for each task, and we show that the ideal mixing weight for fusion is a function of task similarity and task difficulty. A practical algorithm is developed and shown to significantly reduce mean squared error (MSE) on synthetic data, as well as improve performance on an income prediction task where the real-world data is disaggregated by race.

Stochastic gradient descent (SGD) algorithms, with constant momentum and its variants such as Adam, are the optimization methods of choice for training deep neural networks (DNNs). There is great interest in speeding up the convergence of these methods due to their high computational expense. Nesterov accelerated gradient with a time-varying momentum (NAG) improves the convergence rate of gradient descent for convex optimization using a specially designed momentum; however, it accumulates error when the stochastic gradient is used, slowing convergence at best and diverging at worst. In this paper, we propose scheduled restart SGD (SRSGD), a new NAG-style scheme for training DNNs. SRSGD replaces the constant momentum in SGD by the increasing momentum in NAG but stabilizes the iterations by resetting the momentum to zero according to a schedule. Using a variety of models and benchmarks for image classification, we demonstrate that, in training DNNs, SRSGD significantly improves convergence and generalization; for instance, in training ResNet-200 for ImageNet classification, SRSGD achieves an error rate of 20.93% versus the benchmark of 22.13%. These improvements become more significant as the network grows deeper. Furthermore, on both CIFAR and ImageNet, SRSGD reaches similar or even better error rates with significantly fewer training epochs compared to the SGD baseline. Our implementation of SRSGD is available at https://github.com/minhtannguyen/SRSGD.

The construction and application of knowledge graphs have seen a rapid increase across many disciplines in re-cent years. Additionally, the problem of uncovering relationships between developments in the COVID-19 pandemic and social me-dia behavior is of great interest to researchers hoping to curb the spread of the disease. In this paper we present a knowledge graph constructed from COVID-19 related tweets in the Los Angeles area, supplemented with federal and state policy announcements and disease spread statistics. By incorporating dates, topics, and events as entities, we construct a knowledge graph that describes the connections between these useful information. We use natural language processing and change point analysis to extract tweet-topic, tweet-date, and event-date relations. Further analysis on the constructed knowledge graph provides insight into how tweets reflect public sentiments towards COVID-19 related topics and how changes in these sentiments correlate with real-world events.

The subgraph matching problem arises in a number of modern machine learning applications including segmented images and meshes of 3D objects for pattern recognition, bio-chemical reactions and security applications. This graph-based problem can have a very large and complex solution space especially when the world graph has many more nodes and edges than the template. In a real use-case scenario, analysts may need to query additional information about template nodes or world nodes to reduce the problem size and the solution space. Currently, this query process is done by hand, based on the personal experience of analysts. By analogy to the well-known active learning problem in machine learning classification problems, we present a machine-based active learning problem for the subgraph match problem in which the machine suggests optimal template target nodes that would be most likely to reduce the solution space when it is otherwise overly large and complex. The humans in the loop can then include additional information about those target nodes. We present some case studies for both synthetic and real world datasets for multichannel subgraph matching.

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two properties that imply practical advantages over NODEs: (i) The adjoint state of an HBNODE also satisfies an HBNODE, accelerating both forward and backward ODE solvers, thus significantly reducing the number of function evaluations (NFEs) and improving the utility of the trained models. (ii) The spectrum of HBNODEs is well structured, enabling effective learning of long-term dependencies from complex sequential data. We verify the advantages of HBNODEs over NODEs on benchmark tasks, including image classification, learning complex dynamics, and sequential modeling. Our method requires remarkably fewer forward and backward NFEs, is more accurate, and learns long-term dependencies more effectively than the other ODE-based neural network models. Code is available at \url{https://github.com/hedixia/HeavyBallNODE}.

Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this article, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nyström method to approximate a fully connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a gray-scale image into a bitwise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.

In the past few years, graph-based methods have proven to be a useful tool in a wide variety of energy minimization problems. In this article, we propose a graph-based algorithm for feature extraction and segmentation of multimodal images. By defining a notion of similarity that integrates information from each modality, we create a fused graph that merges the different data sources. The graph Laplacian then allows us to perform feature extraction and segmentation on the fused data set. We apply this method in a practical example, namely, the segmentation of optical and LiDAR images. The results obtained confirm the potential of the proposed method.

We introduce the isoperimetric loss as a regularization criterion for learning the map from a visual representation to a semantic embedding, to be used to transfer knowledge to unknown classes in a zero-shot learning setting. We use a pre-trained deep neural network model as a visual representation of image data, a Word2Vec embedding of class labels, and linear maps between the visual and semantic embedding spaces. However, the spaces themselves are not linear, and we postulate the sample embedding to be populated by noisy samples near otherwise smooth manifolds. We exploit the graph structure defined by the sample points to regularize the estimates of the manifolds by inferring the graph connectivity using a generalization of the isoperimetric inequalities from Riemannian geometry to graphs. Surprisingly, this regularization alone, paired with the simplest baseline model, outperforms the state-of-the-art among fully automated methods in zero-shot learning benchmarks such as AwA and CUB. This improvement is achieved solely by learning the structure of the underlying spaces by imposing regularity.

We present a preliminary study of a knowledge graph created from season one of the television show Veronica Mars, which follows the eponymous young private investigator as she attempts to solve the murder of her best friend Lilly Kane. We discuss various techniques for mining the knowledge graph for clues and potential suspects. We also discuss best practice for collaboratively constructing knowledge graphs from television shows.

We present an approach for inexact subgraph matching on attributed graphs optimizing the graph edit distance. By combining lower bounds on the cost of individual assignments, we obtain a heuristic for a backtracking tree search to identify optimal solutions. We evaluate our algorithm on a knowledge graph dataset derived from real-world data, and analyze the space of optimal solutions.

Koopman operator theory, applied via numerical techniques such as dynamic mode decomposition (DMD) and autoencoders, has recently emerged as an interesting mathematical framework for understanding how complex, high-dimensional dynamical systems evolve. In this paper, we apply several DMD and autoencoder algorithms to a dataset of gang involvement and activity to assess the effectiveness City of Los Angeles Mayor's Office of Gang Reduction and Youth Development's (GRYD) Intervention Family Case Management Program. We compare various subsets of the data to explore differences in sub-populations. We then control for different covariates in our analysis of dynamical changes in population characteristics over time. Statistically significant results suggest the efficacy of the GRYD FCM Program.

We study a recent dataset documenting the nature of gang involvement among 14-25 year-olds participating in the Los Angeles Mayor's Office of Gang Reduction and Youth Development (GRYD) Intervention Family Case Management Program. We use natural language processing techniques, including emotion classification and textual clustering, to perform quantitative analyses of free-form responses in the data. These analyses yield insights into the effectiveness of the program and provide a better understanding of its participants. We also compare several computational techniques and remark on their relative effectiveness in application to this dataset.

Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\em MomentumRNNs}. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance.

We address the problem of finding noisy subgraph isomorphisms on large multiplex networks. Our goal is to find as many subgraph matches as possible within a noise tolerance. We propose a novel approach based on the well-known A* search algorithm. Our approach employs new heuristics to estimate the number of missing edges of subgraph matches. This method is verified on one of the synthetic multiplex networks from the Modeling Adversarial Activity program of the Defense Advanced Research Projects Agency.

Structural Equivalence refers to the ability to exchange two vertices in a graph without changing the structure of the graph. We provide basic definitions and properties applicable to the subgraph isomorphism problem. We show examples of structural equivalence that reduce the size of the search tree for subgraph isomorphism counting and enumeration, applied to multichannel networks.

Stress is a common problem in modern life that can bring both psychological and physical disorder. Wearable sensors are commonly used to study the relationship between physical records and mental status. Although sensor data generated by wearable devices provides an opportunity to identify stress in people for predictive medicine, in practice, the data are typically complicated and vague and also often fragmented. In this paper, we propose DataCompletion with Diurnal Regularizers (DCDR) and TemporallyHierarchical Attention Network (THAN) to address the fragmented data issue and predict human stress level with recovered sensor data. We model fragmentation as a sparsity issue. The nuclear norm minimization method based on the low-rank assumption is first applied to derive unobserved sensor data with diurnal patterns of human behaviors. A hierarchical recurrent neural network with the attention mechanism then models temporally structural information in the reconstructed sensor data, thereby inferring the predicted stress level. Data for this study were from 75 undergraduate students (taken from a sample of a larger study) who provided sensor data from smart wristbands. They also completed weekly stress surveys as ground-truth labels about their stress levels. This survey lasted 12 weeks and the sensor records are also in this period. The experimental results demonstrate that our approach significantly outperforms conventional methods in both data completion and stress level prediction. Moreover, an in-depth analysis further shows the effectiveness and robustness of our approach.

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty, which simultaneously enforces group and within-group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well-chosen penalties can significantly improve the unmixing performance compared to classical sparse regression techniques or to the naive bundle approach.

We present filtering methods for finding all sub-graphs of a large multiplex network that are isomorphic to a smaller template network. These methods are shown to be effective on a set of synthetic transaction networks from the DARPA Modeling Adversarial Activity (MAA) program. In some cases, filtering allows us to identify and enumerate all possible isomorphisms. We observe that in some of the MAA networks, the number of subgraphs isomorphic to the template is orders of magnitude larger than the size of the network.

This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common strategy based on discretization, and unifies other continuous notions of coverage. We present two benchmarks against which to compare the error metric value of a given swarm configuration: non-trivial bounds on the error metric, and the probability density function of the error metric when robot positions are sampled at random from the target swarm distribution. We give rigorous results that this probability density function of the error metric obeys a central limit theorem, allowing for more efficient numerical approximation. For both of these benchmarks, we present supporting theory, computation methodology, examples, and MATLAB implementation code.

Gas plume detection is a challenging task in the field of remote sensing. Due to sensor development, it is now possible to detect and track chemical gas plumes with hyperspectral video sequences (HVS). For the purpose of high detection accuracy, it is important to explore spectral characteristic, and take full advantages of spatial continuity and temporal consistency in HVS. However, the high computational complexity and the large amount of data limit its application in time-critical scenarios. In this paper, we propose a GPU parallel implementation of gas plume detection in HVS, which properly exploits shared memory and intrinsic concurrency of the CUDA blocks, as well as parallel workload assignment and resource allocation. The experimental results demonstrate the proposed GPU parallel method has a considerable acceleration factor while retaining the same detection accuracy compared with the serial and multicore version.

Hyperspectral video sequences (HVSs) are well suited for gas plume detection (GPD). The high spectral resolution allows the detection of chemical clouds even when they are optically thin. Processing this new type of video sequences is challenging and requires advanced image and video analysis algorithms. In this paper, we propose a novel method for GPD recorded in HVSs. Based on the assumption that the background is stationary and the gas plume is moving, the proposed method separates the background from the gas plume via a low-rank and sparse decomposition. Furthermore, taking into consideration that the gas plume is continuous in both spatial and temporal dimensions, we include total variation regularization in the constrained minimization problem, which we solve using the augmented Lagrangian multiplier method. After applying the above process to each extracted feature, a novel fusion strategy is proposed to combine the information into a final detection result. Experimental results using real data sets indicate that the proposed method achieves very promising GPD performance.

We propose a semi-supervised algorithm for processing and classification of hyperspectral imagery. For initialization, we keep 20% of the data intact, and use Principal Component Analysis to discard voxels from noisier bands and pixels. Then, we use either an Accelerated Proximal Gradient algorithm (APGL), or a modified APGL algorithm with a penalty term for distance between inpainted pixels and endmembers (APGL Hyp), on the initialized datacube to inpaint the missing data. APGL and APGL Hyp are distinguished by performance on datasets with full pixels removed or extreme noise. This inpainting technique results in band-by-band datacube sharpening and removal of noise from individual spectral signatures. We can also classify the inpainted cube by assigning each pixel to its nearest endmember via Euclidean distance. We demonstrate improved accuracy in classification over data-mining techniques like k-means, unmixing techniques like Hierarchical Non-Negative Matrix Factorization, and graph-based methods like Non-Local Total Variation.

In the past few years, graph-based methods have proven to be a useful tool in a wide variety of energy minimization problems [1]. In this paper, we propose a graph-based algorithm for feature extraction and segmentation of multimodal images. By defining a notion of similarity that integrates information from each modality, we merge the different sources at the data level. The graph Laplacian then allows us to perform feature extraction and segmentation on the fused dataset. We apply this method in a practical example, namely the segmentation of optical and lidar images. The results obtained confirm the potential of the proposed method.

This paper explores a stochastic approach for controlling swarms of independent robots toward a target distribution in a bounded domain. The robot swarm has no central controller, and individual robots lack both communication and localization capabilities. Robots can only measure a scalar field (e.g. concentration of a chemical) from the environment and from this deduce the desired local swarm density. Based on this value, each robot follows a simple control law that causes the swarm as a whole to diffuse toward the target distribution. Using a new holonomic drive robot, we present the first confirmation of this control law with physical experiment. Despite deviations from assumptions underpinning the theory, the swarm achieves the theorized convergence to the target distribution in both simulation and experiment. In fact, simulated and experimental performance agree with one another and with our hypothesis that the error from the target distribution is inversely proportional to the square root of the number of robots. This is evidence that the algorithm is both practical and easily scalable to large swarms.

It is now possible to collect hyperspectral video sequences at a near real-time frame rate. The wealth of spectral, spatial, and temporal information of those sequences is appealing for various applications, but classical video processing techniques must be adapted to handle the high dimensionality and huge size of the data to process. In this paper, we introduce a novel method based on the hierarchical analysis of hyperspectral video sequences to perform object tracking. This latter operation is tackled as a sequential object detection process, conducted on the hierarchical representation of the hyperspectral video frames. We apply the proposed methodology to the chemical gas plume tracking scenario and compare its performances with state-of-the-art methods, for two real hyperspectral video sequences, and show that the proposed approach performs at least equally well.

In this paper, a graph-based nonlocal total variation method is proposed for unsupervised classification of hyperspectral images (HSI). The variational problem is solved by the primal-dual hybrid gradient algorithm. By squaring the labeling function and using a stable simplex clustering routine, an unsupervised clustering method with random initialization can be implemented. The effectiveness of this proposed algorithm is illustrated on both synthetic and real-world HSI, and numerical results show that the proposed algorithm outperforms other standard unsupervised clustering methods, such as spherical K -means, nonnegative matrix factorization, and the graph-based Merriman-Bence-Osher scheme.

We apply social ℓ-norms for the first time to the problem of hyperspectral unmixing while modeling spectral variability. These norms are built with inter-group penalties which are combined in a global intra-group penalization that can enforce selection of entire endmember bundles; this results in the selection of a few representative materials even in the presence of large endmembers bundles capturing each material's variability. We demonstrate improvements quantitatively on synthetic data and qualitatively on real data for three cases of social norms: group, elitist, and a fractional social norm, respectively. We find that the greatest improvements arise from using either the group or fractional flavor.

Thanks to the fast development of sensors, it is now possible to acquire sequences of hyperspectral images. Those hyperspectral video sequences (HVS) are particularly suited for the detection and tracking of chemical gas plumes. In this paper, we present a novel gas plume detection method. It is based on the decomposition of the sequence into a low-rank and a sparse term, corresponding to the background and the plume, respectively, and incorporating temporal consistency. To introduce spatial continuity, a post processing is added using the Total Variation (TV) regularized model. Experimental results on real hyperspectral video sequences validate the effectiveness of the proposed method.

We consider the challenge of detection of chemical plumes in hyperspectral image data. Segmentation of gas is difficult due to the diffusive nature of the cloud. The use of hyperspectral imagery provides non-visual data for this problem, allowing for the utilization of a richer array of sensing information. In this paper, we present a method to track and classify objects in hyperspectral videos. The method involves the application of a new algorithm recently developed for high dimensional data. It is made efficient by the application of spectral methods and the Nyström extension to calculate the eigenvalues/eigenvectors of the graph Laplacian. Results are shown on plume detection in LWIR standoff detection.

We present two graph-based algorithms for multiclass segmentation of high-dimensional data on graphs. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, image labeling, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art in multiclass graph-based segmentation algorithms for high-dimensional data.

A wavelet analogue of the Ginzburg--Landau energy was recently designed and integrated in variational methods for image processing. In this paper we prove global well-posedness of the gradient descent equation (in the weak sense) and convergence to an extremum. We also develop further uses for this energy completed with an additional edge-preserving forcing term. We present examples including inpainting, superresolution, segmentation, denoising, and contour detection. Combining the spatial and the edge-preserving forcing terms gives an amazing flexibility of the model that is not only applicable to various image processing tasks but is also highly tunable.

In this paper we present a computationally efficient algorithm utilizing a fully or seminonlocal graph Laplacian for solving a wide range of learning problems in binary data classification and image processing. In their recent work [Multiscale Model. Simul., 10 (2012), pp. 1090--1118], Bertozzi and Flenner introduced a graph-based diffuse interface model utilizing the Ginzburg--Landau functional for solving problems in data classification. Here, we propose an adaptation of the classic numerical Merriman--Bence--Osher (MBO) scheme for minimizing graph-based diffuse interface functionals, like those originally proposed by Bertozzi and Flenner. We also make use of fast numerical solvers for finding eigenvalues and eigenvectors of the graph Laplacian. Various computational examples are presented to demonstrate the performance of our algorithm, which is successful on images with texture and repetitive structure due to its nonlocal nature. The results show that our method is multiple times more efficient than other well-known nonlocal models.

Earth-observing satellites usually not only take ordinary red-green-blue images but also provide several images including the near-infrared and infrared spectrum. These images are called multispectral, for about four to seven different bands, or hyperspectral, for higher dimensional images of up to 210 bands. The drawback of the additional spectral information is that each spectral band has rather low spatial resolution. In this paper we propose a new variational method for sharpening high dimensional spectral images with the help of a high resolution gray-scale image while preserving the spectral characteristics used for classification and identification tasks. We describe the application of split Bregman minimization to our energy, prove convergence speed, and compare the split Bregman method to a descent method based on the ideas of alternating directions minimization. Finally, we show results on Quickbird multispectral as well as on AVIRIS hyperspectral data.

In this paper we propose an active contour model for segmentation based on the Chan–Vese model. The new model can capture inherent sharp features, i.e., the sharp corners of objects, which are often smoothed by the regularization term in segmentation. Motivated by the snaked based method in [M. Droske and A. Bertozzi, SIAM J. Imaging Sci., 3 (2010), pp. 21–51] that emphasizes straight edges and corners without regard to orientation, we develop a region based method with a level set representation. The model combines the Chan–Vese model with the level set version of a higher order nonlinear term. We extend this model to multispectral images. Higher order methods can be very stiff, so we propose a splitting scheme to remove the stiffness and prove the model's stability and convergence. Finally we show numerical results on gray, color, and hyperspectral images. We can see that the model is robust to noise.

We introduce two fourth-order regularization methods that remove geometric noise without destroying significant geometric features. These methods leverage ideas from image denoising and simplification of high contrast images in which piecewise affine functions are preserved up to infinitesimally small transition zones. We combine the regularization techniques with active contour models and apply them to segmentation of polygonal objects in aerial images. To avoid loss of features during the computation of the external driving forces we use total variation–based inverse scale-space techniques on the input data. Furthermore, we use the models for feature-preserving removal of geometric texture on surfaces.

We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDE-based techniques involving the Ginzburg-Landau functional, but using more localized wavelet-based methods. We present results for both binary and grayscale images. Comparable speeds are achieved with better sharpness of edges in the reconstruction.

Most algorithms for reconstructing shape from defocus assume that the images are obtained with a camera that has been previously calibrated so that the aperture, focal plane, and focal length are known. In this manuscript we characterize the set of scenes that can be reconstructed from defocused images regardless of calibration parameters. In lack of knowledge about the camera or about the scene, reconstruction is possible only up to an equivalence class that is described analytically. When weak knowledge about the scene is available, however, we show how it can be exploited in order to auto-calibrate the imaging device. This includes imaging a slanted plane or generic assumptions on the restoration of the deblurred images.

In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set of interacting Dubins vehicles with fixed turning angle and speed. We perform simulations for a large number of agents and we show experimental realizations of the model on a testbed with a small number of vehicles. In both cases, critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.

Image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas. We outline here the use of a model for binary inpainting based on the Cahn-Hilliard equation, which allows for fast, efficient inpainting of degraded text, as well as super-resolution of high contrast images.

Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. We introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a 'stream function for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.