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Efficient 3D Spatial Queries for Complex Objects. 复杂对象的高效3D空间查询。
IF 1.9 Q1 Mathematics Pub Date : 2022-06-01 Epub Date: 2022-02-12 DOI: 10.1145/3502221
Dejun Teng, Yanhui Liang, Hoang Vo, Jun Kong, Fusheng Wang

3D spatial data has been generated at an extreme scale from many emerging applications, such as high definition maps for autonomous driving and 3D Human BioMolecular Atlas. In particular, 3D digital pathology provides a revolutionary approach to map human tissues in 3D, which is highly promising for advancing computer-aided diagnosis and understanding diseases through spatial queries and analysis. However, the exponential increase of data at 3D leads to significant I/O, communication, and computational challenges for 3D spatial queries. The complex structures of 3D objects such as bifurcated vessels make it difficult to effectively support 3D spatial queries with traditional methods. In this article, we present our work on building an efficient and scalable spatial query system, iSPEED, for large-scale 3D data with complex structures. iSPEED adopts effective progressive compression for each 3D object with successive levels of detail. Further, iSPEED exploits structural indexing for complex structured objects in distance-based queries. By querying with data represented in successive levels of details and structural indexes, iSPEED provides an option for users to balance between query efficiency and query accuracy. iSPEED builds in-memory indexes and decompresses data on-demand, which has a minimal memory footprint. iSPEED provides a 3D spatial query engine that can be invoked on-demand to run many instances in parallel implemented with, but not limited to, MapReduce. We evaluate iSPEED with three representative queries: 3D spatial joins, 3D nearest neighbor query, and 3D spatial proximity estimation. The extensive experiments demonstrate that iSPEED significantly improves the performance of existing spatial query systems.

3D空间数据已经从许多新兴应用中以极端规模生成,例如用于自动驾驶的高清地图和3D人体生物分子图谱。特别是,3D数字病理学提供了一种革命性的方法来绘制人体组织的3D图,这对于通过空间查询和分析来推进计算机辅助诊断和理解疾病非常有希望。然而,3D数据的指数级增长给3D空间查询带来了巨大的I/O、通信和计算挑战。由于分叉血管等三维物体结构复杂,传统方法难以有效支持三维空间查询。在本文中,我们介绍了我们的工作,建立一个高效和可扩展的空间查询系统,iSPEED,具有复杂结构的大规模三维数据。iSPEED对每个具有连续细节级别的3D对象采用有效的渐进式压缩。此外,iSPEED在基于距离的查询中利用复杂结构化对象的结构索引。通过使用连续的细节级别和结构索引表示的数据进行查询,iSPEED为用户提供了在查询效率和查询准确性之间进行平衡的选项。iSPEED在内存中构建索引并按需解压缩数据,这具有最小的内存占用。iSPEED提供了一个3D空间查询引擎,可以按需调用,以并行运行许多实例,但不限于MapReduce。我们使用三种代表性查询来评估iSPEED: 3D空间连接、3D最近邻查询和3D空间接近估计。大量的实验表明,iSPEED显著提高了现有空间查询系统的性能。
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引用次数: 0
Laser Range Scanners for Enabling Zero-overhead WiFi-based Indoor Localization System 用于实现零开销wifi室内定位系统的激光测距扫描仪
IF 1.9 Q1 Mathematics Pub Date : 2022-06-01 DOI: 10.1145/3539659
Hamada Rizk, H. Yamaguchi, Maged A. Youssef, T. Higashino
Robust and accurate indoor localization has been the goal of several research efforts over the past decade. Toward achieving this goal, WiFi fingerprinting-based indoor localization systems have been proposed. However, fingerprinting involves significant effort—especially when done at high density—and needs to be repeated with any change in the deployment area. While a number of recent systems have been introduced to reduce the calibration effort, these still trade overhead with accuracy. This article presents LiPhi++, an accurate system for enabling fingerprinting-based indoor localization systems without the associated data collection overhead. This is achieved by leveraging the sensing capability of transportable laser range scanners to automatically label WiFi scans, which can subsequently be used to build (and maintain) a fingerprint database. As part of its design, LiPhi++ leverages this database to train a deep long short-term memory network utilizing the signal strength history from the detected access points. LiPhi++ also has provisions for handling practical deployment issues, including the noisy wireless environment, heterogeneous devices, among others. Evaluation of LiPhi++ using Android phones in two realistic testbeds shows that it can match the performance of manual fingerprinting techniques under the same deployment conditions without the overhead associated with the traditional fingerprinting process. In addition, LiPhi++ improves upon the median localization accuracy obtained from crowdsourcing-based and fingerprinting-based systems by 284% and 418%, respectively, when tested with data collected a few months later.
在过去的十年中,稳健和准确的室内定位一直是一些研究工作的目标。为了实现这一目标,已经提出了基于WiFi指纹的室内定位系统。但是,指纹识别需要大量的工作—特别是在高密度的情况下—并且需要在部署区域发生任何变化时重复进行。虽然最近已经引入了许多系统来减少校准工作,但这些系统仍然以准确性为代价。本文介绍了LiPhi++,这是一个精确的系统,可以实现基于指纹的室内定位系统,而不需要相关的数据收集开销。这是通过利用便携式激光测距扫描仪的传感能力来自动标记WiFi扫描,随后可用于建立(和维护)指纹数据库来实现的。作为其设计的一部分,LiPhi++利用这个数据库来训练一个深度的长短期记忆网络,利用来自检测到的接入点的信号强度历史。LiPhi++还提供了处理实际部署问题的规定,包括嘈杂的无线环境、异构设备等。使用Android手机在两个实际测试平台上对LiPhi++进行的评估表明,在相同的部署条件下,它可以匹配手动指纹识别技术的性能,而不会产生与传统指纹识别过程相关的开销。此外,在使用几个月后收集的数据进行测试时,LiPhi++在基于众包系统和基于指纹系统的定位精度中值基础上分别提高了284%和418%。
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引用次数: 10
Planning Wireless Backhaul Links by Testing Line of Sight and Fresnel Zone Clearance 通过测试视线和菲涅耳区间隙来规划无线回程链路
IF 1.9 Q1 Mathematics Pub Date : 2022-04-14 DOI: 10.1145/3517382
Philip E. Brown, Krystian Czapiga, Arun Jotshi, Y. Kanza, Velin Kounev, Poornima Suresh
Microwave backhaul links are often used as wireless connections between telecommunication towers, in places where deploying optical fibers is impossible or too expensive. The relatively high frequency of microwaves increases their ability to transfer information at a high rate, but it also makes them susceptible to spatial obstructions and interference. Hence, when deploying wireless links, there are two conflicting considerations. First, the antennas height, selected from the available slots on each tower, should be as low as possible. Second, there should be a line of sight (LoS) between the antennas, and a buffer around the LoS defined by the first Fresnel zone should be clear of obstacles. To compute antenna heights, a planning system for wireless links has to maintain an elevation model, efficiently discover obstacles between towers, and execute Fresnel-zone clearance tests over a 3D model of the deployment area. In this article we present a system and algorithms for computing the height of antennas, by testing LoS and clearance of Fresnel zones. The system handles the following requirements: (1) the need to cover large areas, e.g., all of the USA, (2) big distance between towers, e.g., 100 kilometers, and (3) computing batches of thousands of pairs within a few minutes. We introduce three novel algorithms for efficient computation of antenna heights, we show how to effectively model and manage the large-scale geospatial data needed for the planning, and we present the results of tests over real-world settings.
微波回程链路通常用作电信塔之间的无线连接,在这些地方部署光纤是不可能的或过于昂贵。相对较高的微波频率提高了它们高速传输信息的能力,但也使它们容易受到空间障碍和干扰。因此,在部署无线链路时,有两个相互冲突的考虑因素。首先,从每个塔的可用插槽中选择的天线高度应尽可能低。其次,天线之间应该有一条视线(LoS),并且由第一菲涅尔区定义的LoS周围的缓冲区应该没有障碍物。为了计算天线高度,无线链路的规划系统必须维护高程模型,有效地发现塔之间的障碍物,并在部署区域的3D模型上执行菲涅耳区域间隙测试。在本文中,我们提出了一个计算天线高度的系统和算法,通过测试LoS和菲涅耳区的间隙。该系统处理以下要求:(1)需要覆盖大面积,例如整个美国,(2)塔之间的大距离,例如100公里,以及(3)在几分钟内计算数千对。我们介绍了三种有效计算天线高度的新算法,展示了如何有效地建模和管理规划所需的大规模地理空间数据,并展示了在真实世界环境中的测试结果。
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引用次数: 3
A Grid-Based Two-Stage Parallel Matching Framework for Bi-Objective Euclidean Traveling Salesman Problem 基于网格的双目标欧氏旅行商问题的两阶段并行匹配框架
IF 1.9 Q1 Mathematics Pub Date : 2022-04-07 DOI: 10.1145/3526025
Fandel Lin, Hsun-Ping Hsieh
Traveling salesman problem (TSP) is one of the most studied combinatorial optimization problems; several exact, heuristic or even learning-based strategies have been proposed to solve this challenging issue. Targeting on the research problem of bi-objective non-monotonic Euclidean TSP and based on the concept of the multi-agent-based approach, we propose a two-stage parallel matching approaching for solving TSP. Acting as a divide-and-conquer strategy, the merit lies in the simultaneously clustering and routing in the dividing process. Precisely, we first propose the Two-Stage Parallel Matching algorithm (TSPM) to deal with the bi-objective TSP. We then formulate the Grid-Based Two-Stage Parallel Matching (GRAPE) framework, which can synergize with TSPM, exact method, or other state-of-the-art TSP solvers, for solving large-scale Euclidean TSP. According to this framework, the original problem space is divided into smaller regions and then computed in parallel, which helps to tackle and derive solutions for larger-scale Euclidean TSP within reasonable computational resources. Preliminary evaluation based on TSPLIB testbed shows that our proposed GRAPE framework holds a decent quality of solutions in especially runtime for large-scale Euclidean TSP. Meanwhile, experiments conducted on two real-world datasets demonstrate the efficacy and adaptability of our proposed TSPM in solving the bi-objective non-monotonic TSP.
旅行商问题(TSP)是研究最多的组合优化问题之一;已经提出了几种精确的、启发式的甚至基于学习的策略来解决这个具有挑战性的问题。针对双目标非单调欧氏TSP的研究问题,基于多智能体方法的概念,提出了一种求解TSP的两阶段并行匹配方法。作为一种分而治之的策略,其优点在于在划分过程中同时进行聚类和路由。准确地说,我们首先提出了两阶段并行匹配算法(TSPM)来处理双目标TSP。然后,我们制定了基于网格的两阶段并行匹配(GRAPE)框架,该框架可以与TSPM、精确方法或其他最先进的TSP求解器协同求解大规模欧几里得TSP。根据该框架,将原始问题空间划分为较小的区域,然后并行计算,这有助于在合理的计算资源范围内解决和导出更大规模欧几里得TSP的解。基于TSPLIB测试台的初步评估表明,我们提出的GRAPE框架在运行时尤其是在大规模欧几里得TSP的情况下具有良好的解质量。同时,在两个真实世界的数据集上进行的实验证明了我们提出的TSPM在解决双目标非单调TSP方面的有效性和适应性。
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引用次数: 0
A Review of Bayesian Networks for Spatial Data 空间数据贝叶斯网络研究进展
IF 1.9 Q1 Mathematics Pub Date : 2022-03-30 DOI: 10.1145/3516523
C. Krapu, R. Stewart, A. Rose
Bayesian networks are a popular class of multivariate probabilistic models as they allow for the translation of prior beliefs about conditional dependencies between variables to be easily encoded into their model structure. Due to their widespread usage, they are often applied to spatial data for inferring properties of the systems under study and also generating predictions for how these systems may behave in the future. We review published research on methodologies for representing spatial data with Bayesian networks and also summarize the application areas for which Bayesian networks are employed in the modeling of spatial data. We find that a wide variety of perspectives are taken, including a GIS-centric focus on efficiently generating geospatial predictions, a statistical focus on rigorously constructing graphical models controlling for spatial correlation, as well as a range of problem-specific heuristics for mitigating the effects of spatial correlation and dependency arising in spatial data analysis. Special attention is also paid to potential future directions for the integration of Bayesian networks with spatial processes.
贝叶斯网络是一类流行的多变量概率模型,因为它们允许将变量之间的条件依赖关系的先验信念转换为容易编码到它们的模型结构中。由于它们的广泛使用,它们经常被应用于空间数据,以推断所研究系统的性质,并对这些系统未来的行为产生预测。我们回顾了用贝叶斯网络表示空间数据的方法,并总结了贝叶斯网络在空间数据建模中的应用领域。我们发现采用了各种各样的视角,包括以gis为中心的高效生成地理空间预测,以统计学为中心的严格构建控制空间相关性的图形模型,以及一系列针对特定问题的启发式方法,以减轻空间数据分析中产生的空间相关性和依赖性的影响。特别关注贝叶斯网络与空间过程整合的潜在未来方向。
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引用次数: 1
Automated Urban Planning for Reimagining City Configuration via Adversarial Learning: Quantification, Generation, and Evaluation 通过对抗性学习重塑城市配置的自动化城市规划:量化、生成和评估
IF 1.9 Q1 Mathematics Pub Date : 2021-12-26 DOI: 10.1145/3524302
Dongjie Wang, Yanjie Fu, Kunpeng Liu, Fanglan Chen, Pengyang Wang, Chang-Tien Lu
Urban planning refers to the efforts of designing land-use configurations given a region. However, to obtain effective urban plans, urban experts have to spend much time and effort analyzing sophisticated planning constraints based on domain knowledge and personal experiences. To alleviate the heavy burden of them and produce consistent urban plans, we want to ask that can AI accelerate the urban planning process, so that human planners only adjust generated configurations for specific needs? The recent advance of deep generative models provides a possible answer, which inspires us to automate urban planning from an adversarial learning perspective. However, three major challenges arise: (1) how to define a quantitative land-use configuration? (2) how to automate configuration planning? (3) how to evaluate the quality of a generated configuration? In this article, we systematically address the three challenges. Specifically, (1) We define a land-use configuration as a longitude-latitude-channel tensor. (2) We formulate the automated urban planning problem into a task of deep generative learning. The objective is to generate a configuration tensor given the surrounding contexts of a target region. In particular, we first construct spatial graphs using geographic and human mobility data crawled from websites to learn graph representations. We then combine each target area and its surrounding context representations as a tuple, and categorize all tuples into positive (well-planned areas) and negative samples (poorly-planned areas). Next, we develop an adversarial learning framework, in which a generator takes the surrounding context representations as input to generate a land-use configuration, and a discriminator learns to distinguish between positive and negative samples. (3) We provide quantitative evaluation metrics and conduct extensive experiments to demonstrate the effectiveness of our framework.
城市规划是指在给定区域内设计土地利用配置的努力。然而,为了获得有效的城市规划,城市专家必须花费大量时间和精力,基于领域知识和个人经验分析复杂的规划约束。为了减轻他们的沉重负担并制定一致的城市规划,我们想问,人工智能能否加速城市规划过程,让人类规划者只根据特定需求调整生成的配置?深度生成模型的最新进展提供了一个可能的答案,它激励我们从对抗性学习的角度自动化城市规划。然而,出现了三大挑战:(1)如何定义定量的土地利用配置?(2) 如何自动化配置规划?(3) 如何评估生成配置的质量?在这篇文章中,我们系统地解决了这三个挑战。具体而言,(1)我们将土地利用配置定义为经纬度通道张量。(2) 我们将自动化城市规划问题转化为深度生成学习的任务。目标是在给定目标区域的周围上下文的情况下生成配置张量。特别是,我们首先使用从网站抓取的地理和人类流动数据来构建空间图,以学习图的表示。然后,我们将每个目标区域及其周围的上下文表示组合为一个元组,并将所有元组分类为正样本(规划良好的区域)和负样本(规划不良的区域)。接下来,我们开发了一个对抗性学习框架,其中生成器将周围的上下文表示作为输入来生成土地使用配置,鉴别器学习区分正样本和负样本。(3) 我们提供了定量评估指标,并进行了广泛的实验来证明我们的框架的有效性。
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引用次数: 7
Geographic-Region Monitoring by Drones in Adversarial Environments 无人机在对抗环境中的地理区域监测
IF 1.9 Q1 Mathematics Pub Date : 2021-11-02 DOI: 10.1145/3611009
O. Wolfson, Prabin Giri, S. Jajodia, Goce Trajcevski
We consider surveillance of a geographic region by a collaborative system of drones. The drones assist each other in identifying and managing activities of interest on the ground. We also consider an adversary who can create both genuine and fake activities on the ground. The objective of the adversary is to use fake activities to maximize the response time to genuine activities. We present two collaboration algorithms and analyze their response times, as well as the adversary’s efforts in terms of the number of fake activities required to achieve a certain response time.
我们考虑通过无人机协作系统监视一个地理区域。无人机相互协助识别和管理地面上感兴趣的活动。我们还考虑到一个既能在地面上制造真实活动又能在地面上制造虚假活动的对手。攻击者的目标是使用虚假活动来最大化对真实活动的响应时间。我们提出了两种协作算法,并分析了它们的响应时间,以及对手在达到一定响应时间所需的虚假活动数量方面的努力。
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引用次数: 2
GloBiMapsAI: An AI-Enhanced Probabilistic Data Structure for Global Raster Datasets 全球栅格数据集的人工智能增强概率数据结构
IF 1.9 Q1 Mathematics Pub Date : 2021-06-21 DOI: 10.1145/3453184
M. Werner
In the last decade, more and more spatial data has been acquired on a global scale due to satellite missions, social media, and coordinated governmental activities. This observational data suffers from huge storage footprints and makes global analysis challenging. Therefore, many information products have been designed in which observations are turned into global maps showing features such as land cover or land use, often with only a few discrete values and sparse spatial coverage like only within cities. Traditional coding of such data as a raster image becomes challenging due to the sizes of the datasets and spatially non-local access patterns, for example, when labeling social media streams. This article proposes GloBiMap, a randomized data structure, based on Bloom filters, for modeling low-cardinality sparse raster images of excessive sizes in a configurable amount of memory with pure random access operations avoiding costly intermediate decompression. In addition, the data structure is designed to correct the inevitable errors of the randomized layer in order to have a fully exact representation. We show the feasibility of the approach on several real-world datasets including the Global Urban Footprint in which each pixel denotes whether a particular location contains a building at a resolution of roughly 10m globally as well as on a global Twitter sample of more than 220 million precisely geolocated tweets. In addition, we propose the integration of a denoiser engine based on artificial intelligence in order to reduce the amount of error correction information for extremely compressive GloBiMaps.
在过去的十年里,由于卫星任务、社交媒体和协调的政府活动,在全球范围内获得了越来越多的空间数据。这些观测数据存在巨大的存储足迹,使全球分析具有挑战性。因此,已经设计了许多信息产品,将观测结果转化为显示土地覆盖或土地利用等特征的全球地图,通常只有几个离散值,空间覆盖范围稀疏,就像只在城市内一样。例如,在标记社交媒体流时,由于数据集的大小和空间上的非本地访问模式,将这种数据编码为光栅图像变得具有挑战性。本文提出了GloBiMap,这是一种基于Bloom滤波器的随机数据结构,用于在可配置的内存量中建模过大的低基数稀疏光栅图像,采用纯随机访问操作,避免了昂贵的中间解压缩。此外,数据结构被设计为校正随机化层的不可避免的错误,以便具有完全精确的表示。我们在几个真实世界的数据集上展示了该方法的可行性,包括全球城市足迹,其中每个像素表示特定位置是否包含全球分辨率约为1000米的建筑,以及在超过2.2亿条精确地理定位推文的全球推特样本上。此外,我们建议集成基于人工智能的去噪器引擎,以减少极压缩GloBiMaps的纠错信息量。
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引用次数: 1
The Impact of Stationarity, Regularity, and Context on the Predictability of Individual Human Mobility 平稳性、规律性和环境对个体人类流动性可预测性的影响
IF 1.9 Q1 Mathematics Pub Date : 2021-06-21 DOI: 10.1145/3459625
D. Teixeira, A. C. Viana, J. Almeida, Mrio S. Alvim
Predicting mobility-related behavior is an important yet challenging task. On the one hand, factors such as one’s routine or preferences for a few favorite locations may help in predicting their mobility. On the other hand, several contextual factors, such as variations in individual preferences, weather, traffic, or even a person’s social contacts, can affect mobility patterns and make its modeling significantly more challenging. A fundamental approach to study mobility-related behavior is to assess how predictable such behavior is, deriving theoretical limits on the accuracy that a prediction model can achieve given a specific dataset. This approach focuses on the inherent nature and fundamental patterns of human behavior captured in that dataset, filtering out factors that depend on the specificities of the prediction method adopted. However, the current state-of-the-art method to estimate predictability in human mobility suffers from two major limitations: low interpretability and hardness to incorporate external factors that are known to help mobility prediction (i.e., contextual information). In this article, we revisit this state-of-the-art method, aiming at tackling these limitations. Specifically, we conduct a thorough analysis of how this widely used method works by looking into two different metrics that are easier to understand and, at the same time, capture reasonably well the effects of the original technique. We evaluate these metrics in the context of two different mobility prediction tasks, notably, next cell and next distinct cell prediction, which have different degrees of difficulty. Additionally, we propose alternative strategies to incorporate different types of contextual information into the existing technique. Our evaluation of these strategies offer quantitative measures of the impact of adding context to the predictability estimate, revealing the challenges associated with doing so in practical scenarios.
预测与移动相关的行为是一项重要但具有挑战性的任务。一方面,一个人的日常生活或对几个最喜欢的地点的偏好等因素可能有助于预测他们的流动性。另一方面,一些环境因素,如个人偏好的变化、天气、交通,甚至一个人的社会联系,都会影响移动模式,使其建模更具挑战性。研究移动性相关行为的一个基本方法是评估这种行为的可预测性,在给定特定数据集的情况下,得出预测模型可以达到的精度的理论限制。该方法侧重于该数据集中捕获的人类行为的固有性质和基本模式,过滤掉依赖于所采用预测方法的特殊性的因素。然而,目前最先进的估计人类流动性可预测性的方法存在两个主要限制:低可解释性和难以纳入已知有助于流动性预测的外部因素(即上下文信息)。在本文中,我们将重新讨论这种最先进的方法,旨在解决这些限制。具体地说,我们通过研究两种更容易理解的不同度量,对这种广泛使用的方法是如何工作的进行了彻底的分析,同时,合理地捕获了原始技术的效果。我们在两种不同的移动性预测任务中评估这些指标,特别是具有不同难度的下一个细胞和下一个不同细胞预测。此外,我们提出了将不同类型的上下文信息合并到现有技术中的替代策略。我们对这些策略的评估提供了在可预测性评估中添加上下文的影响的定量度量,揭示了在实际场景中这样做所带来的挑战。
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引用次数: 6
Evaluating the Utility of High-Resolution Proximity Metrics in Predicting the Spread of COVID-19 评估高分辨率接近度指标在预测COVID-19传播中的效用
IF 1.9 Q1 Mathematics Pub Date : 2021-06-10 DOI: 10.1145/3531006
Zakaria Mehrab, A. Adiga, M. Marathe, S. Venkatramanan, S. Swarup
High resolution mobility datasets have become increasingly available in the past few years and have enabled detailed models for infectious disease spread including those for COVID-19. However, there are open questions on how such mobility data can be used effectively within epidemic models and for which tasks they are best suited. In this paper, we extract a number of graph-based proximity metrics from high resolution cellphone trace data from X-Mode and use it to study COVID-19 epidemic spread in 50 land grant university counties in the US. We present an approach to estimate the effect of mobility on cases by fitting an ordinary differential equation based model and performing multivariate linear regression to explain the estimated time varying transmissibility. We find that, while mobility plays a significant role, the contribution is heterogeneous across the counties, as exemplified by a subsequent correlation analysis. We also evaluate the metrics’ utility for case surge prediction defined as a supervised classification problem, and show that the learnt model can predict surges with 95% accuracy and an 87% F1-score.
在过去几年中,高分辨率流动性数据集越来越多,并使包括COVID-19在内的传染病传播的详细模型成为可能。然而,关于如何在流行病模型中有效地使用这种流动性数据以及它们最适合哪些任务,还存在一些悬而未决的问题。在本文中,我们从X-Mode的高分辨率手机追踪数据中提取了一些基于图形的接近度量,并使用它来研究美国50个赠地大学县的COVID-19流行病传播。我们提出了一种方法,通过拟合一个基于常微分方程的模型,并使用多元线性回归来解释估计的时变传播率,从而估计迁移率对情况的影响。我们发现,虽然流动性发挥了重要作用,但随后的相关分析表明,各县之间的贡献是异质性的。我们还评估了指标对定义为监督分类问题的病例浪涌预测的效用,并表明学习的模型可以以95%的准确率和87%的f1分数预测浪涌。
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引用次数: 3
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ACM Transactions on Spatial Algorithms and Systems
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