Proximity Queries Research Articles

Stochastic Computation of Barycentric Coordinates

This paper presents a practical and general approach for computing barycentric coordinates through stochastic sampling. Our key insight is a reformulation of the kernel integral defining barycentric coordinates into a weighted least-squares minimization that enables Monte Carlo integration without sacrificing linear precision. Our method can thus compute barycentric coordinates directly at the points of interest, both inside and outside the cage, using just proximity queries to the cage such as closest points and ray intersections. As a result, we can evaluate barycentric coordinates for a large variety of cage representations (from quadrangulated surface meshes to parametric curves) seamlessly, bypassing any volumetric discretization or custom solves. To address the archetypal noise induced by sample-based estimates, we also introduce a denoising scheme tailored to barycentric coordinates. We demonstrate the efficiency and flexibility of our formulation by implementing a stochastic generation of harmonic coordinates, mean-value coordinates, and positive mean-value coordinates.

Proximity Queries on Point Clouds using Rapid Construction Path Oracle

The prevalence of computer graphics technology boosts the developments of point clouds in recent years, which offer advantages over terrain surfaces (represented by Triangular Irregular Networks, i.e., TINs) in proximity queries, including the shortest path query, the k-Nearest Neighbor (kNN) query and the range query. Since (1) all existing on-the-fly and oracle-based shortest path query algorithms on a TIN are very expensive, (2) all existing on-the-fly shortest path query algorithms on a point cloud are still not efficient, and (3) there are no oracle-based shortest path query algorithms on a point cloud, we propose an efficient (1+ε)-approximate shortest path oracle that answers the shortest path query for a set of Points-Of-Interests (POIs) on the point cloud, which has a good performance (in terms of the oracle construction time, oracle size and shortest path query time) due to the concise information about the pairwise shortest paths between any pair of POIs stored in the oracle. Our oracle can be easily adapted to answering the shortest path query for any points on the point cloud if POIs are not given as input, and also achieve a good performance. Then, we propose efficient algorithms for answering the (1+ε)-approximate kNN and range query with the assistance of our oracle. Our experimental results show that when POIs are given (resp. not given) as input, our oracle is up to 390 times, 30 times and 6 times (resp. 500 times, 140 times and 50 times) better than the best-known oracle on a TIN in terms of the oracle construction time, oracle size and shortest path query time, respectively. Our algorithms for the other two proximity queries are both up to 100 times faster than the best-known algorithms.

Development of a 3D Navigation System for Virtual Reality Using a Physically-Based 3D Game Engine with Haptic Feedback and Proximity Queries

Development of a 3D Navigation System for Virtual Reality Using a Physically-Based 3D Game Engine with Haptic Feedback and Proximity Queries

P2M: A Fast Solver for Querying Distance from Point to Mesh Surface

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables one to eliminate the vast majority of triangles that do not help find the closest point. In this paper, we develop a totally different algorithmic paradigm, named P2M , to speed up point-to-mesh distance queries. Our original intention is to precompute a KD tree (KDT) of mesh vertices to approximately encode the geometry of a mesh surface containing vertices, edges and faces. However, it is very likely that the closest primitive to the query point is an edge e (resp., a face f ), but the KDT reports a mesh vertex υ instead. We call υ an interceptor of e (resp., f ). The main contribution of this paper is to invent a simple yet effective interception inspection rule and an efficient flooding interception inspection algorithm for quickly finding out all the interception pairs. Once the KDT and the interception table are precomputed, the query stage proceeds by first searching the KDT and then looking up the interception table to retrieve the closest geometric primitive. Statistics show that our query algorithm runs many times faster than the state-of-the-art solvers.

Proximity Queries on Terrain Surface

Due to the advance of the geo-spatial positioning and the computer graphics technology, digital terrain data has become increasingly popular nowadays. Query processing on terrain data has attracted considerable attention from both the academic and the industry communities. Proximity queries such as the shortest path/distance query, k nearest/farthest neighbor query, and top- k closest/farthest pairs query are fundamental and important queries in the context of the terrain surfaces, and they have a lot of applications in Geographical Information System, 3D object feature vector construction, and 3D object data mining. In this article, we first study the most fundamental type of query, namely, shortest distance and path query, which is to find the shortest distance and path between two points of interest on the surface of the terrain. As observed by existing studies, computing the exact shortest distance/path is very expensive. Some existing studies proposed ϵ -approximate distance and path oracles, where ϵ is a non-negative real-valued error parameter. However, the best-known algorithm has a large oracle construction time, a large oracle size, and a large query time. Motivated by this, we propose a novel ϵ -approximate distance and path oracle called the S pace E fficient distance and path oracle (SE), which has a small oracle construction time, a small oracle size, and a small distance and path query time, thanks to its compactness of storing concise information about pairwise distances between any two points-of-interest. Then, we propose several algorithms for the k nearest/farthest neighbor and top- k closest/farthest pairs queries with the assistance of our distance and path oracle SE . Our experimental results show that the oracle construction time, the oracle size, and the distance and path query time of SE are up to two, three, and five orders of magnitude faster than the best-known algorithm, respectively. Besides, our algorithms for other proximity queries including k nearest/farthest neighbor queries and top- k closest/farthest pairs queries significantly outperform the state-of-the-art algorithms by up to two orders of magnitude.

Construction of rhombic triacontahedron discrete global grid systems

ABSTRACT Discrete Global Grid System (DGGS) is a new multi-resolution geospatial data modeling and processing scheme for the digital earth. The icosahedron is commonly regarded as an ideal polyhedron for constructing DGGSs with small distortions; however, the shape of its face is triangular, making it difficult to incorporate the matrix structure used for geospatial data storage and parallel computing. To overcome this limitation, this study utilizes the rhombic triacontahedron (RT) as the basic polyhedron to construct DGGSs. An equal-area projection between the surface of RT and the sphere is developed and used to design a grid-generation algorithm for the aperture 4 hexagonal DGGS based on RT. Compared with the equal-area DGGS based on the icosahedron, the proposed scheme results in smaller angular projection distortions, with the mean and standard deviation decreasing by 41.6% and 30.9%, respectively. The grid cells of the RT DGGS also achieve more optimized geometric characteristics in shape compactness, length deviation, and angle deviation than those in the icosahedron DGGS. Additionally, the cross-surface computation efficiency provides advantages in code conversion to latitude and longitude and proximity queries. Furthermore, the use of RT offers a new and better framework within the context of DGGS research and application.

GPU-based Real-time Contact Tracing at Scale.

Contact tracing is gaining its importance in controlling the spread of COVID-19. However, the enormous volume of the frequently sampled tracing data brings major challenges for real-time processing. In this paper, we propose a GPU-based real-time contact tracing system based on spatial proximity queries with temporal constraints using location data. We provide dynamic indexing of moving objects using an adaptive partitioning schema on GPU with extremely low overhead. Our system optimizes the retrieval of contacted pairs to match both the requirements of contact tracing scenarios and GPU centered parallelism. We propose an efficient contacts evaluation mechanism to keep only the spatially and temporally valid contacts. Our experiments demonstrate that the system can achieve sub-second level response for large-scale contact tracing of tens of millions of people, with two magnitudes of performance boost over CPU based approach.

A Unified Approach to Spatial Proximity Query Processing in Dynamic Spatial Networks.

Nearest neighbor (NN) and range (RN) queries are basic query types in spatial databases. In this study, we refer to collections of NN and RN queries as spatial proximity (SP) queries. At peak times, location-based services (LBS) need to quickly process SP queries that arrive simultaneously. Timely processing can be achieved by increasing the number of LBS servers; however, this also increases service costs. Existing solutions evaluate SP queries sequentially; thus, such solutions involve unnecessary distance calculations. This study proposes a unified batch algorithm (UBA) that can effectively process SP queries in dynamic spatial networks. With the proposed UBA, the distance between two points is indicated by the travel time on the shortest path connecting them. The shortest travel time changes frequently depending on traffic conditions. The goal of the proposed UBA is to avoid unnecessary distance calculations for nearby SP queries. Thus, the UBA clusters nearby SP queries and exploits shared distance calculations for query clusters. Extensive evaluations using real-world roadmaps demonstrated the superiority and scalability of UBA compared with state-of-the-art sequential solutions.

A Practical Index Structure Supporting Fréchet Proximity Queries among Trajectories

We present a scalable approach for range and k nearest neighbor queries under computationally expensive metrics, like the continuous Fréchet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree structure whose size is linear in the number of trajectories, regardless of the trajectory’s individual sizes or the spatial dimension, which allows one to exploit low “intrinsic dimensionality” of datasets for effective search space pruning. Since the distance computation is expensive, generic metric indexing methods are rendered impractical. We present strategies that (i) improve on known upper and lower bound computations, (ii) build cluster trees without any or very few distance calls, and (iii) search using bounds for metric pruning, interval orderings for reduction, and randomized pivoting for reporting the final results. We analyze the efficiency and effectiveness of our methods with extensive experiments on diverse synthetic and real-world datasets. The results show improvement over state-of-the-art methods for exact queries, and even further speedups are achieved for queries that may return approximate results. Surprisingly, the majority of exact nearest-neighbor queries on real datasets are answered without any distance computations.

Query filtering using two-dimensional local embeddings

In high dimensional data sets, exact indexes are ineffective for proximity queries, and a sequential scan over the entire data set is unavoidable. Accepting this, here we present a new approach employing two-dimensional embeddings. Each database element is mapped to the XY plane using the four-point property. The caveat is that the mapping is local: in other words, each object is mapped using a different mapping.The idea is that each element of the data is associated with a pair of reference objects that is well-suited to filter that particular object, in cases where it is not relevant to a query. This maximises the probability of excluding that object from a search. At query time, a query is compared with a pool of reference objects which allow its mapping to all the planes used by data objects. Then, for each query/object pair, a lower bound of the actual distance is obtained. The technique can be applied to any metric space that possesses the four-point property, therefore including Euclidean, Cosine, Triangular, Jensen–Shannon, and Quadratic Form distances.Our experiments show that for all the data sets tested, of varying dimensionality, our approach can filter more objects than a standard metric indexing approach. For low dimensional data this does not make a good search mechanism in its own right, as it does not scale with the size of the data: that is, its cost is linear with respect to the data size. However, we also show that it can be added as a post-filter to other mechanisms, increasing efficiency with little extra cost in space or time. For high-dimensional data, we show related approximate techniques which, we believe, give the best known compromise for speeding up the essential sequential scan. The potential uses of our filtering technique include pure GPU searching, taking advantage of the tiny memory footprint of the mapping.

Fast computation of Katz index for efficient processing of link prediction queries

Network proximity computations are among the most common operations in various data mining applications, including link prediction and collaborative filtering. A common measure of network proximity is Katz index, which has been shown to be among the best-performing path-based link prediction algorithms. With the emergence of very large network databases, such proximity computations become an important part of query processing in these databases. Consequently, significant effort has been devoted to developing algorithms for efficient computation of Katz index between a given pair of nodes or between a query node and every other node in the network. Here, we present LRC-Katz, an algorithm based on indexing and low rank correction to accelerate Katz index based network proximity queries. Using a variety of very large real-world networks, we show that LRC-Katzoutperforms the fastest existing method, Conjugate Gradient, for a wide range of parameter values. Taking advantage of the acceleration in the computation of Katz index, we propose a new link prediction algorithm that exploits locality of networks that are encountered in practical applications. Our experiments show that the resulting link prediction algorithm drastically outperforms state-of-the-art link prediction methods based on the vanilla and truncated Katz.

Retracted] Using Wireless Sensor Network to Correct Posture in Sports Training Based on Hidden Markov Matching Algorithm

This paper combines the research of wireless sensor networks and sports training and proposes a wireless sensor network‐based intelligent sports training system. According to the requirements of the system, this design uses the wireless sensor network system as the platform for development and the ZigBee module for wireless communication. The advantage of this system is to transmit the obtained information to the ZigBee coordinator module, and after the processing of information and the resultant decision, a nonwearable unmonitored motion training model based on visual sensing is proposed. The motion terminal collects video data streams of user motion actions and extracts features to establish HMM motion recognition algorithm to achieve recognition of motion actions, automatic counting, and intelligent scoring functions. The template matching algorithm based on dynamic time regularization and weighted Euclidean distance realizes a universal real‐time motion recognition algorithm with high standard and low latency and can guide the user’s motion action based on similarity calculation. The intelligent sports training system is designed and developed to maintain a high‐quality human‐computer interaction experience with a real‐time feedback client and uploads sports data to a cloud server via the HTTP protocol, which supports real‐time sports proximity query and training plan development on the website. After practical application tests, the intelligent sports training system based on the wireless sensor network proposed in this paper is stable and reliable and adds fun and competitiveness to boring sports. The research of this paper has some reference value for the application of wireless sensor networks and the research of the motion recognition algorithm.

Site2Vec: a reference frame invariant algorithm for vector embedding of protein–ligand binding sites

Protein–ligand interactions are one of the fundamental types of molecular interactions in living systems. Ligands are small molecules that interact with protein molecules at specific regions on their surfaces called binding sites. Binding sites would also determine ADMET properties of a drug molecule. Tasks such as assessment of protein functional similarity and detection of side effects of drugs need identification of similar binding sites of disparate proteins across diverse pathways. To this end, methods for computing similarities between binding sites are still evolving and is an active area of research even today. Machine learning methods for similarity assessment require feature descriptors of binding sites. Traditional methods based on hand engineered motifs and atomic configurations are not scalable across several thousands of sites. In this regard, deep neural network algorithms are now deployed which can capture very complex input feature space. However, one fundamental challenge in applying deep learning to structures of binding sites is the input representation and the reference frame. We report here a novel algorithm, Site2Vec, that derives reference frame invariant vector embedding of a protein–ligand binding site. The method is based on pairwise distances between representative points and chemical compositions in terms of constituent amino acids of a site. The vector embedding serves as a locality sensitive hash function for proximity queries and determining similar sites. The method has been the top performer with more than 95% quality scores in extensive benchmarking studies carried over 10 data sets and against 23 other site comparison methods in the field. The algorithm serves for high throughput processing and has been evaluated for stability with respect to reference frame shifts, coordinate perturbations and residue mutations. We also provide the method as a standalone executable and a web service hosted at (http://services.iittp.ac.in/bioinfo/home).

Integrated querying and version control of context-specific biological networks.

MotivationBiomolecular data stored in public databases is increasingly specialized to organisms, context/pathology and tissue type, potentially resulting in significant overhead for analyses. These networks are often specializations of generic interaction sets, presenting opportunities for reducing storage and computational cost. Therefore, it is desirable to develop effective compression and storage techniques, along with efficient algorithms and a flexible query interface capable of operating on compressed data structures. Current graph databases offer varying levels of support for network integration. However, these solutions do not provide efficient methods for the storage and querying of versioned networks.ResultsWe present VerTIoN, a framework consisting of novel data structures and associated query mechanisms for integrated querying of versioned context-specific biological networks. As a use case for our framework, we study network proximity queries in which the user can select and compose a combination of tissue-specific and generic networks. Using our compressed version tree data structure, in conjunction with state-of-the-art numerical techniques, we demonstrate real-time querying of large network databases.ConclusionOur results show that it is possible to support flexible queries defined on heterogeneous networks composed at query time while drastically reducing response time for multiple simultaneous queries. The flexibility offered by VerTIoN in composing integrated network versions opens significant new avenues for the utilization of ever increasing volume of context-specific network data in a broad range of biomedical applications.Availability and Implementation VerTIoN is implemented as a C++ library and is available at http://compbio.case.edu/omics/software/vertion and https://github.com/tjcowman/vertionContacttyler.cowman@case.edu

A Low Arithmetic-Degree Algorithm for Computing Proximity Graphs

In this paper, we study the problem of designing robust algorithms for computing the minimum spanning tree, the nearest neighbor graph, and the relative neighborhood graph of a set of points in the plane, under the Euclidean metric. We use the term “robust” to denote an algorithm that can properly handle degenerate configurations of the input (such as co-circularities and collinearities) and that is not affected by errors in the flow of control due to round-off approximations. Existing asymptotically optimal algorithms that compute such graphs are either suboptimal in terms of the arithmetic precision required for the implementation, or cannot handle degeneracies, or are based on complex data structures. We present a unified approach to the robust computation of the above graphs. The approach is a variant of the general region approach for the computation of proximity graphs based on Yao graphs, first introduced in Ref. 43 (A. C.-C. Yao, On constructing minimum spanning trees in [Formula: see text]-dimensional spaces and related problems, SIAM J. Comput. 11(4) (1982) 721–736). We show that a sparse supergraph of these geometric graphs can be computed in asymptotically optimal time and space, and requiring only double precision arithmetic, which is proved to be optimal. The arithmetic complexity of the approach is measured by using the notion of degree, introduced in Ref. 31 (G. Liotta, F. P. Preparata and R. Tamassia, Robust proximity queries: An illustration of degree-driven algorithm design, SIAM J. Comput. 28(3) (1998) 864–889) and Ref. 3 (J. D. Boissonnat and F. P. Preparata, Robust plane sweep for intersecting segments, SIAM J. Comput. 29(5) (2000) 1401–1421). As a side effect of our results, we solve a question left open by Katajainen27 (J. Katajainen, The region approach for computing relative neighborhood graphs in the [Formula: see text] metric, Computing 40 (1987) 147–161) about the existence of a subquadratic algorithm, based on the region approach, that computes the relative neighborhood graph of a set of points [Formula: see text] in the plane under the [Formula: see text] metric.

Culling for Extreme-Scale Segmentation Volumes: A Hybrid Deterministic and Probabilistic Approach.

With the rapid increase in raw volume data sizes, such as terabyte-sized microscopy volumes, the corresponding segmentation label volumes have become extremely large as well. We focus on integer label data, whose efficient representation in memory, as well as fast random data access, pose an even greater challenge than the raw image data. Often, it is crucial to be able to rapidly identify which segments are located where, whether for empty space skipping for fast rendering, or for spatial proximity queries. We refer to this process as culling. In order to enable efficient culling of millions of labeled segments, we present a novel hybrid approach that combines deterministic and probabilistic representations of label data in a data-adaptive hierarchical data structure that we call the label list tree. In each node, we adaptively encode label data using either a probabilistic constant-time access representation for fast conservative culling, or a deterministic logarithmic-time access representation for exact queries. We choose the best data structures for representing the labels of each spatial region while building the label list tree. At run time, we further employ a novel query-adaptive culling strategy. While filtering a query down the tree, we prune it successively, and in each node adaptively select the representation that is best suited for evaluating the pruned query, depending on its size. We show an analysis of the efficiency of our approach with several large data sets from connectomics, including a brain scan with more than 13 million labeled segments, and compare our method to conventional culling approaches. Our approach achieves significant reductions in storage size as well as faster query times.

Indexed fast network proximity querying

Node proximity queries are among the most common operations on network databases. A common measure of node proximity is random walk based proximity, which has been shown to be less susceptible to noise and missing data. Real-time processing of random-walk based proximity queries poses significant computational challenges for larger graphs with over billions of nodes and edges, since it involves solution of large linear systems of equations. Due to the importance of this operation, significant effort has been devoted to developing efficient methods for random-walk based node proximity computations. These methods either aim to speed up iterative computations by exploiting numerical properties of random walks, or rely on computation and storage of matrix inverses to avoid computation during query processing. Although both approaches have been well studied, the speedup achieved by iterative approaches does not translate to real-time query processing, and the storage requirements of inversion-based approaches prohibit their use on very large graph databases. We present a novel approach to significantly reducing the computational cost of random walk based node proximity queries with scalable indexing. Our approach combines domain graph-partitioning based indexing with fast iterative computations during query processing using Chebyshev polynomials over the complex elliptic plane. This approach combines the query processing benefits of inversion techniques with the memory and storage benefits of iterative approache. Using real-world networks with billions of nodes and edges, and top- k proximity queries as the benchmark problem, we show that our algorithm, I-C hopper , significantly outperforms existing methods. Specifically, it drastically reduces convergence time of the iterative procedure, while also reducing storage requirements for indexing.

Geometry Helps to Compare Persistence Diagrams

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft-Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.

Efficient Proximity Queries for Continuum Robots on Parallel Computing Hardware

Surgical manipulators are increasingly capable of approaching deep-seated pathologies through convoluted pathways due to the advances in the field of continuum robotics. This class of robots can be, in most cases, accurately modeled as a chain of cylindrical shapes. In order to safely and seamlessly telemanipulate these robots, which have complex nonintuitive kinematics, haptic guidance schemes have been developed that rely on accurate proximity queries (PQ) to calculate the distance between the continuum robot and the anatomy. This letter introduces an approach to accurately model the continuum robots using cylindrical-shaped segments with spherical or flat caps and then efficiently calculate the shortest distance to a triangle mesh. Implementations of efficient, analytical narrow phase PQ calculations for simple and complex geometrical primitives suitable for parallel computing hardware are presented together with an experimental validation which show improved performance suitable for real-time robotic applications. An in silico experiment comparing various root-finding algorithms, which are commonly used in PQ calculation or other optimization tasks are compared to assess their suitability when executed on different hardware. The implications of these experimental results are discussed, in particular with regards to the selection of a suitable proximity query algorithm depending on the available parallel computing hardware. Finally, an outlook of future improvements for dense dynamic anatomies is presented.

Linearity of network proximity measures: implications for set-based queries and significance testing

In recent years, various network proximity measures have been proposed to facilitate the use of biomolecular interaction data in a broad range of applications. These applications include functional annotation, disease gene prioritization, comparative analysis of biological systems and prediction of new interactions. In such applications, a major task is the scoring or ranking of the nodes in the network in terms of their proximity to a given set of 'seed' nodes (e.g. a group of proteins that are identified to be associated with a disease, or are deferentially expressed in a certain condition). Many different network proximity measures are utilized for this purpose, and these measures are quite diverse in terms of the benefits they offer. We propose a unifying framework for characterizing network proximity measures for set-based queries. We observe that many existing measures are linear, in that the proximity of a node to a set of nodes can be represented as an aggregation of its proximity to the individual nodes in the set. Based on this observation, we propose methods for processing of set-based proximity queries that take advantage of sparse local proximity information. In addition, we provide an analytical framework for characterizing the distribution of proximity scores based on reference models that accurately capture the characteristics of the seed set (e.g. degree distribution and biological function). The resulting framework facilitates computation of exact figures for the statistical significance of network proximity scores, enabling assessment of the accuracy of Monte Carlo simulation based estimation methods. Implementations of the methods in this paper are available at https://bioengine.case.edu/crosstalker which includes a robust visualization for results viewing. stm@case.edu or mxk331@case.edu. Supplementary data are available at Bioinformatics online.