Proximity Graphs Research Articles

Improving cyber risk governance through storytelling

This paper addresses the critical challenge of cyber risk governance faced by executives, security committees and boards of directors in the rapidly changing digital landscape. Cyber security complexity, characterised by data deluges and the translational gap between technical jargon and business risk, significantly hinders effective cyber risk messaging and governance. Drawing on five years of research and interviews with chief information security officers (CISOs), the paper highlights the struggle in establishing trust and confidence in governance bodies due to these complexities. It introduces three constructs that aim to simplify cyber security messaging to enhance cyber risk governance: the intelligence to risk (I2R) pyramid, five risk impacts, and resilience and proximity graph. Each construct, illustrated with practical examples, is designed to provide clarity and foster understanding between cyber security professionals and governance bodies, ensuring a cohesive approach to cyber risk management. Readers can expect to gain valuable insights into overcoming the limitations of traditional risk communication tools such as risk registers. By adopting the presented storytelling approach, the paper promises strategies for building trust through transparency and accountability, bridging the communication gap between technical and executive levels, and facilitating informed decision making for improved governance outcomes in the face of cyber security threats.

Optics-free reconstruction of 2D images via DNA barcode proximity graphs.

Spatial genomic technologies include imaging- and sequencing-based methods ( 1-3 ). An emerging subcategory of sequencing-based methods relies on a surface coated with coordinate-associated DNA barcodes, which are leveraged to tag endogenous nucleic acids or cells in an overlaid tissue section ( 4-7 ). However, the physical registration of DNA barcodes to spatial coordinates is challenging, necessitating either high density printing of coordinate-specific oligonucleotides or in situ sequencing/probing of randomly deposited, oligonucleotide-bearing beads. As a consequence, the surface areas available to sequencing-based spatial genomic methods are constrained by the time, labor, cost, and instrumentation required to either print, synthesize or decode a coordinate-tagged surface. To address this challenge, we developed SCOPE (Spatial reConstruction via Oligonucleotide Proximity Encoding), an optics-free, DNA microscopy ( 8 ) inspired method. With SCOPE, the relative positions of randomly deposited beads on a 2D surface are inferred from the ex situ sequencing of chimeric molecules formed from diffusing "sender" and tethered "receiver" oligonucleotides. As a first proof-of-concept, we apply SCOPE to reconstruct an asymmetric "swoosh" shape resembling the Nike logo (16.75 × 9.25 mm). Next, we use a microarray printer to encode a "color" version of the Snellen eye chart for visual acuity (17.18 × 40.97 mm), and apply SCOPE to achieve optics-free reconstruction of individual letters. Although these are early demonstrations of the concept and much work remains to be done, we envision that the optics-free, sequencing-based quantitation of the molecular proximities of DNA barcodes will enable spatial genomics in constant experimental time, across fields of view and at resolutions that are determined by sequencing depth, bead size, and diffusion kinetics, rather than the limitations of optical instruments or microarray printers.

Leader-Following Connectivity Preservation and Collision Avoidance Control for Multiple Spacecraft with Bounded Actuation

This paper investigates the distributed formation control of a group of leader-following spacecraft with bounded actuation and limited communication ranges. In particular, connectivity-preserving and collision-avoidance controllers are proposed for the leader with constant or time-varying velocity, respectively. The communication graph between the spacecraft is modeled via a distance-induced proximity graph. By designing a virtual proxy for each spacecraft, the spacecraft–proxy couplings address the actuator saturation constraints. The inter-proxy dynamics incorporated with a bounded artificial potential function fulfill the coordination of all proxies. In addition, the bounded potential function can simultaneously tackle connectivity preservation and collision avoidance problems. The distributed formation controllers are proposed for multiple spacecraft with constant or time-varying velocities relative to the leader. A sliding mode control approach and the proxies’ dynamics are used in the design of a distributed cooperative controller for spacecraft to address the cooperative problem between the followers and the leader. Numerical simulations confirm the effectiveness of the anti-saturation distributed connectivity preservation controller.

Proximity Graph Networks: Predicting Ligand Affinity with Message Passing Neural Networks.

Message passing neural networks (MPNNs) on molecular graphs generate continuous and differentiable encodings of small molecules with state-of-the-art performance on protein-ligand complex scoring tasks. Here, we describe the proximity graph network (PGN) package, an open-source toolkit that constructs ligand-receptor graphs based on atom proximity and allows users to rapidly apply and evaluate MPNN architectures for a broad range of tasks. We demonstrate the utility of PGN by introducing benchmarks for affinity and docking score prediction tasks. Graph networks generalize better than fingerprint-based models and perform strongly for the docking score prediction task. Overall, MPNNs with proximity graph data structures augment the prediction of ligand-receptor complex properties when ligand-receptor data are available.

Probabilistic Nearest Neighbors Based Locality Preserving Projections for Unsupervised Metric Learning

Dimensionality reduction based unsupervised metric learning consists in finding meaningful compact data representations previously to clustering and classification problems. One of the major aspects of these algorithms is the approximation of the underlying manifold by a weighted graph. A limitation with most manifold learning algorithms is that edge weights in the proximity graph rely heavily on the Euclidean distance, which is known to be quite sensitive to the presence of outliers. In this paper, we propose to improve the Locality Preserving Projections (LPP) algorithm by incorporating a recently proposed graph inference method called Probabilistic Nearest Neighbors (PNN), an extension of the Clustering with Adaptive Neighbors (CAN) approach, used with success in graph-based semi-supervised learning. The proposed PNN-LPP algorithm is able to achieve better classification results than regular LPP, showing competitive performance against state-of-the-art approaches for dimensionality reduction, such as the UMAP algorithm, especially in datasets with a limited number of samples.

On Reporting Durable Patterns in Temporal Proximity Graphs

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist over a long time. While there has been work on finding durable simple patterns, existing algorithms do not have provable guarantees and run in strictly super-linear time. The paper leverages the observation that many graphs arising in practice are naturally proximity graphs or can be approximated as such, where nodes are embedded as points in some high-dimensional space, and two nodes are connected by an edge if they are close to each other. We work with an implicit representation of the proximity graph, where nodes are additionally annotated by time intervals, and design near-linear-time algorithms for finding (approximately) durable patterns above a given durability threshold. We also consider an interactive setting where a client experiments with different durability thresholds in a sequence of queries; we show how to compute incremental changes to result patterns efficiently in time near-linear to the size of the changes.

Enhancing building pattern recognition through multi-scale data and knowledge graph: a case study of C-shaped patterns

ABSTRACT Building pattern recognition is important for understanding urban forms, automating map generalization, and visualizing 3D city models. However, current approaches based on object-independent methods have limitations in capturing all visually aware patterns due to the part-based nature of human vision. Moreover, these approaches also suffer from inefficiencies when applying proximity graph models. To address these limitations, we propose a framework that leverages multi-scale data and a knowledge graph, focusing on recognizing C-shaped building patterns. We first employ a specialized knowledge graph to represent the relationships between buildings within and across various scales. Subsequently, we convert the rules for C-shaped pattern recognition and enhancement into query conditions, where the enhancement refers to using patterns recognized at one scale to enhance pattern recognition at other scales. Finally, rule-based reasoning is applied within the constructed knowledge graph to recognize and enrich C-shaped building patterns. We verify the effectiveness of our method using multi-scale data with three levels of detail (LODs) collected from AMap, and our method achieves a higher recall rate of 26.4% for LOD1, 20.0% for LOD2, and 9.1% for LOD3 compared to existing methods with similar precision rates. We also achieve recognition efficiency improvements of 0.91, 1.37, and 9.35 times, respectively.

On reverse shortest paths in geometric proximity graphs

Let S be a set of n geometric objects of constant complexity (e.g., points, line segments, disks, ellipses) in R2, and let ϱ:S×S→R≥0 be a distance function on S. For a parameter r≥0, we define the proximity graphG(r)=(S,E) where E={(e1,e2)∈S×S|e1≠e2,ϱ(e1,e2)≤r}. Given S, s,t∈S, and an integer k≥1, the reverse-shortest-path (RSP) problem asks for computing the smallest value r⁎≥0 such that G(r⁎) contains a path from s to t of length at most k.In this paper we present a general randomized technique that solves the RSP problem efficiently for a large family of geometric objects and distance functions. Using standard, and sometimes more involved, semi-algebraic range-searching techniques, we first give an efficient algorithm for the decision problem, namely, given a value r≥0, determine whether G(r) contains a path from s to t of length at most k. Next, we adapt our decision algorithm and combine it with a random-sampling method to compute r⁎, by efficiently performing a binary search over an implicit set of O(n2) candidate ‘critical’ values that contains r⁎.We illustrate the versatility of our general technique by applying it to a variety of geometric proximity graphs. For example, we obtain (i) an O⁎(n4/3) expected-time randomized algorithm (where O⁎(⋅) hides polylog(n) factors) for the case where S is a set of (possibly intersecting) line segments in R2 and ϱ(e1,e2)=minx∈e1,y∈e2⁡‖x−y‖ (where ‖⋅‖ is the Euclidean distance), and (ii) an O⁎(n+m4/3) expected-time randomized algorithm for the case where S is a set of m points lying on an x-monotone polygonal chain T with n vertices, and ϱ(p,q), for p,q∈S, is the smallest value h such that the points p′:=p+(0,h) and q′:=q+(0,h) are visible to each other, i.e., all points on the segment p′q′ lie above or on the polygonal chain T.

The role of Abeta and Tau proteins in Alzheimer’s disease: a mathematical model on graphs

In this Note we study a mathematical model for the progression of Alzheimer’s Disease in the human brain. The novelty of our approach consists in the representation of the brain as two superposed graphs where toxic proteins diffuse, the connectivity graph which represents the neural network, and the proximity graph which takes into account the extracellular space. Toxic proteins such as beta amyloid and Tau play in fact a crucial role in the development of Alzheimer’s disease and, separately, have been targets of medical treatments. Recent biomedical literature stresses the potential impact of the synergetic action of these proteins. We numerically test various modelling hypotheses which confirm the relevance of this synergy.

Connectivity-preserving rendezvous in discrete-time multi-agent systems via relative neighborhood proximity graph

In this paper, we focus on the rendezvous problem of discrete-time multi-agent systems. Each agent is equipped with the same sensing, computing, and motion-control capabilities to achieve rendezvous based on the neighbors’ states. First, a convex hull combination algorithm (CHCA) is designed, in which each agent solves a convex problem composed of perceived neighbors in the sensing region and chooses an optimal control strategy to move to the next position with guaranteed connectivity under low-density network topologies. Second, the relative neighborhood graph is incorporated into the CHCA (RNCHCA) as the constraint set to adapt to the high-density network topologies. The convergence and connectivity of the proposed algorithms are proved based on the geometric concept and case analyses. Finally, a large number of simulation results show that under the initially connected topologies with different densities, the RNCHCA can achieve a higher rendezvous speed than that achieved by the traditional circumcenter algorithm, particularly under high-density network topologies.

Efficient Approximate Nearest Neighbor Search in Multi-dimensional Databases

Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.

Elastic beam algorithm for generating circular cartograms

ABSTRACT The circular cartogram, also known as the Dorling map, is a widely used tool for visualizing statistical data. It represents regions as circles with their areas in proportion to the statistical values and requires circle displacement to avoid overlap and maintain spatial relationships. In this paper, we propose a new approach for circular cartogram production that utilizes the elastic beam displacement algorithm in cartographic generalization. First, the initial circles are generated with their areas in proportion to the statistical values. Second, an elastic beam structure is built as a proximity graph based on the spatial relations between the circles. Third, the circles violating the quality requirements are considered to have a force on the nodes of a beam. Fourth, the elastic beam algorithm is applied to assign forces for each node to determine the new positions of the circles. Steps two through four are repeated until a circular cartogram that meets the defined quality requirements is obtained. The experiments indicate that the proposed approach can successfully generate circular cartograms without overlaps while maintaining topology and relative relationships with higher quality than existing approaches. Project website: https://github.com/TrentonWei/DorlingMap

Towards Efficient Index Construction and Approximate Nearest Neighbor Search in High-Dimensional Spaces

The approximate nearest neighbor (ANN) search in high-dimensional spaces is a fundamental but computationally very expensive problem. Many methods have been designed for solving the ANN problem, such as LSH-based methods and graph-based methods. The LSH-based methods can be costly to reach high query quality due to the hash-boundary issues, while the graph-based methods can achieve better query performance by greedy expansion in an approximate proximity graph (APG). However, the construction cost of these APGs can be one or two orders of magnitude higher than that for building hash-based indexes. In addition, they fail short in incrementally maintaining APGs as the underlying dataset evolves. In this paper, we propose a novel approach named LSH-APG to build APGs and facilitate fast ANN search using a lightweight LSH framework. LSH-APG builds an APG via consecutively inserting points based on their nearest neighbor relationship with an efficient and accurate LSH-based search strategy. A high-quality entry point selection technique and an LSH-based pruning condition are developed to accelerate index construction and query processing by reducing the number of points to be accessed during the search. LSH-APG supports fast maintenance of APGs in lieu of building them from scratch as dataset evolves. Its maintenance cost and query cost for a point is proven to be less affected by dataset cardinality. Extensive experiments on real-world and synthetic datasets demonstrate that LSH-APG incurs significantly less construction cost but achieves better query performance than existing graph-based methods.

Simultaneous control of combustion instabilities and NOx emissions in a lean premixed flame using linear genetic programming

Combustion instabilities have been a plaguing challenge in lean-conditioned propulsion systems. An open-loop control system was developed using machine learning to suppress pressure fluctuations and NOx emissions simultaneously. The open-loop control is realized by regulating the solenoid valve to modulate the methane supply. Control laws comprising the multi-frequency forcing are generated via the linear genetic programming (LGP), before being converted into square waves with different frequencies and duty cycles to activate the solenoid valve. The cost function is intended to evaluate and rank individuals of each generation, so as to select candidates for evolution. Optimized periodic forcing (OPF) with different duty cycles (d) and frequencies (fP) is set to provide a comparison with the superiority of multi-frequency forcing of LGP. Three stages of pressure oscillations and NOx emissions have been found as d increases from 0.5 to 1.0: high level, transition, and low level, revealing the transition of the combustion mode. After ten generations of development, the pressure amplitude and NOx emissions are reduced by 67.1% and 36.9% under the optimal control law identified by LGP, respectively. The flame structure images and Rayleigh index maps indicate that the convective movement of the flame, which may be the key factor driving combustion instabilities, can be suppressed by the optimal control law. Furthermore, the proximity graph of the similarity between control laws is introduced to depict the machine learning process, with the steepest descent lines visualizing its ridgeline topology. With the evolution process, individuals are found moving closer to the top right-hand corner of the map, and two main search pathways gradually become clear.

Jasmine and Iris: population-scale structural variant comparison and analysis.

The availability of long reads is revolutionizing studies of structural variants (SVs). However, because SVs vary across individuals and are discovered through imprecise read technologies and methods, they can be difficult to compare. Addressing this, we present Jasmine and Iris ( https://github.com/mkirsche/Jasmine/ ), for fast and accurate SV refinement, comparison and population analysis. Using an SV proximity graph, Jasmine outperforms six widely used comparison methods, including reducing the rate of Mendelian discordance in trio datasets by more than fivefold, and reveals a set of high-confidence de novo SVs confirmed by multiple technologies. We also present a unified callset of 122,813 SVs and 82,379 indels from 31 samples of diverse ancestry sequenced with long reads. We genotype these variants in 1,317 samples from the 1000 Genomes Project and the Genotype-Tissue Expression project with DNA and RNA-sequencing data and assess their widespread impact on gene expression, including within medically relevant genes.

Reinforcement Routing on Proximity Graph for Efficient Recommendation

We focus on Maximum Inner Product Search (MIPS), which is an essential problem in many machine learning communities. Given a query, MIPS finds the most similar items with the maximum inner products. Methods for Nearest Neighbor Search (NNS) which is usually defined on metric space do not exhibit the satisfactory performance for MIPS problem since inner product is a non-metric function. However, inner products exhibit many good properties compared with metric functions, such as avoiding vanishing and exploding gradients. As a result, inner product is widely used in many recommendation systems, which makes efficient Maximum Inner Product Search a key for speeding up many recommendation systems. Graph-based methods for NNS problem show the superiorities compared with other class methods. Each data point of the database is mapped to a node of the proximity graph. Nearest neighbor search in the database can be converted to route on the proximity graph to find the nearest neighbor for the query. This technique can be used to solve MIPS problem. Instead of searching the nearest neighbor for the query, we search the item with a maximum inner product with query on the proximity graph. In this article, we propose a reinforcement model to train an agent to search on the proximity graph automatically for MIPS problem if we lack the ground truths of training queries. If we know the ground truths of some training queries, our model can also utilize these ground truths by imitation learning to improve the agent’s searchability. By experiments, we can see that our proposed mode which combines reinforcement learning with imitation learning shows the superiorities over the state-of-the-art methods.

Recovering cyclic tilings through β-skeletons

There is a class of proximity graphs parameterized by a real number β that are called β-skeletons and which are geometrical graphs whose vertex set V is a discrete set of points in the plane and two points p and q are adjacent if certain region luneβ(p, q) defined by them does not contain any other vertex. Special cases of β-skeletons are the Gabriel Graph (β = 1) and the Relative Neighborhood Graph (β = 2). Cyclic tilings are tilings of the plane whose tiles are convex cyclic polygons that contain the center of the circle in which they are inscribed. Up to our knowledge, this class of tilings has not been studied before. They generalize regular, Archimedean, and k-uniform tilings. We give sufficient conditions for the graph of a cyclic tiling to be a β-skeleton of its vertices. The result is particularly nice for the case of the Gabriel graph. The study of the relationship between tilings arises while studying street networks. This relationship is illustrated briefly.

TRUST: A Novel Framework for Vehicle Trajectory Recovery from Urban-Scale Videos.

We study a new type of path inference query against urban-scale video databases. Given a vehicle image query, our goal is to recover its historical trajectory from the footprints captured by surveillance cameras deployed across the road network. The problem is challenging because visual matching inherently suffers from object occlusion, low camera resolution, varying illumination conditions, and viewing angles. Furthermore, with limited computation resources, only a fraction of video frames can be ingested and indexed, causing severe data sparsity issues for visual matching. To support efficient and accurate trajectory recovery, we develop a select-and-refine framework in a heterogeneous hardware environment with both CPUs and GPUs. We construct a proximity graph from the top-k visually similar frames and propose holistic scoring functions based on visual and spatial-temporal coherence. To avoid enumerating all the paths, we also propose a coarse-grained scoring function with monotonic property to reduce search space. Finally, the derived path is refined by examining raw video frames to fill the missing cameras. For performance evaluation, we construct two largest-scale video databases generated from cameras deployed upon real road networks. Experimental results validate the efficiency and accuracy of our proposed trajectory recovery framework.

Corrigendum for “Fast and incremental loop closure detection with deep features and proximity graphs”

Corrigendum for “Fast and incremental loop closure detection with deep features and proximity graphs”

Network Rebalance and Operational Efficiency of Sharing Transportation System: Multi-Objective Optimization and Model Predictive Control Approaches

Sharing transportation systems can significantly promote travelers convenience and efficiency. As a vital part, bike-sharing system (BSS) has effectively solved “the-last-mile” problem during transportation interchange, but bike imbalance between docks severely deteriorates operational efficiency of BSS. In this paper, we present multi-objective optimization and predictive control approaches to tackle the bike rebalancing problem, where optimal redistributing strategies can maximize the operational efficiency of BSS with respects to equilibrium state and redistribution cost. A dock-based BSS dynamic network is modeled based on a proximity graph, in which connection relation, bike usage, and redistribution flow are formulated. To measure the operational efficiency, a performance metric is presented to consider both benefits of user and operator. To satisfy bike renting, returning, and redistributing requirements, model predictive control (MPC) is then employed to compute feasible and optimal redistribution strategies based on the network model. The effectiveness of multi-objective optimization and MPC is verified on different topologies of BSS. Experimental results show that when the BSS reaches the equilibrium state, the operational efficiency will be maximized in the proposed approaches.