New inequalities for network distance measures by using graph spectra

2019 ◽  
Vol 252 ◽  
pp. 17-27 ◽  
Author(s):  
Matthias Dehmer ◽  
Stefan Pickl ◽  
Yongtang Shi ◽  
Guihai Yu
Keyword(s):  
Distance Measures ◽  
Graph Spectra ◽  
Network Distance ◽  
New Inequalities

Context-aware Distance Measures for Dynamic Networks

2022 ◽  
Vol 16 (1) ◽  
pp. 1-34
Author(s):  
Yiji Zhao ◽  
Youfang Lin ◽  
Zhihao Wu ◽  
Yang Wang ◽  
Haomin Wen
Keyword(s):  
Large Scale ◽  
Dynamic Networks ◽  
Distance Measures ◽  
General Definition ◽  
Mathematical Representation ◽  
Network Clustering ◽  
Context Aware ◽  
Network Distance ◽  
Practical Applications ◽  
Spectral Distance

Dynamic networks are widely used in the social, physical, and biological sciences as a concise mathematical representation of the evolving interactions in dynamic complex systems. Measuring distances between network snapshots is important for analyzing and understanding evolution processes of dynamic systems. To the best of our knowledge, however, existing network distance measures are designed for static networks. Therefore, when measuring the distance between any two snapshots in dynamic networks, valuable context structure information existing in other snapshots is ignored. To guide the construction of context-aware distance measures, we propose a context-aware distance paradigm, which introduces context information to enrich the connotation of the general definition of network distance measures. A Context-aware Spectral Distance (CSD) is then given as an instance of the paradigm by constructing a context-aware spectral representation to replace the core component of traditional Spectral Distance (SD). In a node-aligned dynamic network, the context effectively helps CSD gain mainly advantages over SD as follows: (1) CSD is not affected by isospectral problems; (2) CSD satisfies all the requirements of a metric, while SD cannot; and (3) CSD is computationally efficient. In order to process large-scale networks, we develop a kCSD that computes top- k eigenvalues to further reduce the computational complexity of CSD. Although kCSD is a pseudo-metric, it retains most of the advantages of CSD. Experimental results in two practical applications, i.e., event detection and network clustering in dynamic networks, show that our context-aware spectral distance performs better than traditional spectral distance in terms of accuracy, stability, and computational efficiency. In addition, context-aware spectral distance outperforms other baseline methods.

scholarly journals Network Distance and Fatal Outcomes among Gunshot Wound Victims

2019 ◽  
Author(s):  
Giovanni Circo ◽  
Andrew Palmer Wheeler
Keyword(s):  
Predictive Accuracy ◽  
Distance Measures ◽  
Network Distance ◽  
Time Estimates ◽  
Level 1 ◽  
New Research ◽  
Level 1 Trauma Center ◽  
Practical Implications ◽  
Drive Time

Despite nation-wide decreases in crime, urban gun violence remains a serious and pressing issue in many cities. Victim survival in these incidents is often contingent on the speed and quality of care provided. Increasingly, new research has identified the role that specialized trauma care plays in victim survival from firearm-related injuries. Using nearly four years of data on shooting victimizations in Philadelphia we test whether distance to the nearest level 1 trauma center is associated with victim survival. We employ different distance measures based on street network distances, drive-time estimates, and Euclidean distance - comparing the predictive accuracy of each. Our results find that victims who are shot farther from trauma centers have an increased likelihood of death, and drive time distances provide the most accurate predictions. We discuss the practical implications of this research as it applies to urban public health.

scholarly journals Comparing two distance measures in the spatial mapping of food deserts: The case of Petržalka, Slovakia

2017 ◽  
Vol 25 (2) ◽  
pp. 95-103 ◽  
Author(s):  
Kristína Bilková ◽  
František Križan ◽  
Marcel Horňák ◽  
Peter Barlík ◽  
Pavol Kita
Keyword(s):  
Euclidean Distance ◽  
Large Scale ◽  
Food Deserts ◽  
Distance Measures ◽  
Spatial Mapping ◽  
Street Network ◽  
Network Distance ◽  
Food Stores ◽  
Gis Environment ◽  
Distance Approach

AbstractOver the last twenty years or so, researchers’ attention to the issue of food deserts has increased in the geographical literature. Accessibility to large-scale retail units is one of the essential and frequently-used indicators leading to the identification and mapping of food deserts. Numerous accessibility measures of various types are available for this purpose. Euclidean distance and street network distance rank among the most frequently-used approaches, although they may lead to slightly different results. The aim of this paper is to compare various approaches to the accessibility to food stores and to assess the differences in the results gained by these methods. Accessibility was measured for residential block centroids, with applications of various accessibility measures in a GIS environment. The results suggest a strong correspondence between Euclidean distance and a little more accurate street network distance approach, applied in the case of the urban environment of Bratislava-Petržalka, Slovakia.

An Introduction to the Theory of Graph Spectra

2009 ◽  
Author(s):  
Dragos Cvetkovic ◽  
Peter Rowlinson ◽  
Slobodan Simic
Keyword(s):  
Graph Spectra

scholarly journals Deformable Models for Segmentation Based on Local Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Jimena Olveres ◽  
Erik Carbajal-Degante ◽  
Boris Escalante-Ramírez ◽  
Enrique Vallejo ◽  
Carla María García-Moreno
Keyword(s):  
Local Binary Patterns ◽  
Distance Measures ◽  
Local Analysis ◽  
Hermite Transform ◽  
Active Shape Models ◽  
Shape Models ◽  
Segmentation Methods ◽  
Segmentation Algorithms ◽  
Image Modality ◽  
New Algorithms

Segmentation tasks in medical imaging represent an exhaustive challenge for scientists since the image acquisition nature yields issues that hamper the correct reconstruction and visualization processes. Depending on the specific image modality, we have to consider limitations such as the presence of noise, vanished edges, or high intensity differences, known, in most cases, as inhomogeneities. New algorithms in segmentation are required to provide a better performance. This paper presents a new unified approach to improve traditional segmentation methods as Active Shape Models and Chan-Vese model based on level set. The approach introduces a combination of local analysis implementations with classic segmentation algorithms that incorporates local texture information given by the Hermite transform and Local Binary Patterns. The mixture of both region-based methods and local descriptors highlights relevant regions by considering extra information which is helpful to delimit structures. We performed segmentation experiments on 2D images including midbrain in Magnetic Resonance Imaging and heart’s left ventricle endocardium in Computed Tomography. Quantitative evaluation was obtained with Dice coefficient and Hausdorff distance measures. Results display a substantial advantage over the original methods when we include our characterization schemes. We propose further research validation on different organ structures with promising results.

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

Identifying longitudinal-growth patterns from infancy to childhood: a study comparing multiple clustering techniques

2021 ◽  
Author(s):  
Paraskevi Massara ◽  
Charles D G Keown-Stoneman ◽  
Lauren Erdman ◽  
Eric O Ohuma ◽  
Celine Bourdon ◽  
...  
Keyword(s):  
Latent Class ◽  
Growth Patterns ◽  
Pattern Detection ◽  
Distance Measures ◽  
Longitudinal Growth ◽  
Important Health ◽  
Modelling Techniques ◽  
Different Populations ◽  
Growth Features ◽  
Time Invariant

Abstract Background Most studies on children evaluate longitudinal growth as an important health indicator. Different methods have been used to detect growth patterns across childhood, but with no comparison between them to evaluate result consistency. We explored the variation in growth patterns as detected by different clustering and latent class modelling techniques. Moreover, we investigated how the characteristics/features (e.g. slope, tempo, velocity) of longitudinal growth influence pattern detection. Methods We studied 1134 children from The Applied Research Group for Kids cohort with longitudinal-growth measurements [height, weight, body mass index (BMI)] available from birth until 12 years of age. Growth patterns were identified by latent class mixed models (LCMM) and time-series clustering (TSC) using various algorithms and distance measures. Time-invariant features were extracted from all growth measures. A random forest classifier was used to predict the identified growth patterns for each growth measure using the extracted features. Results Overall, 72 TSC configurations were tested. For BMI, we identified three growth patterns by both TSC and LCMM. The clustering agreement was 58% between LCMM and TS clusters, whereas it varied between 30.8% and 93.3% within the TSC configurations. The extracted features (n = 67) predicted the identified patterns for each growth measure with accuracy of 82%–89%. Specific feature categories were identified as the most important predictors for patterns of all tested growth measures. Conclusion Growth-pattern detection is affected by the method employed. This can impact on comparisons across different populations or associations between growth patterns and health outcomes. Growth features can be reliably used as predictors of growth patterns.

TNDP: Tensor-based Network Distance Prediction with Confidence Intervals

2021 ◽  
pp. 1-1
Author(s):  
Haojun Huang ◽  
Li Li ◽  
Geyong Min ◽  
Wang Miao ◽  
Yingying Zhu ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Network Distance ◽  
Distance Prediction
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