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Nodes of large degree in random trees and forests

Bernhard Gittenberger
2006 Random structures & algorithms (Print)  
We study the asymptotic behaviour of the number N k,n of nodes of given degree k in unlabeled random trees, when the tree size n and the node degree k both tend to infinity.  ...  The same holds for rooted, unlabeled trees and forests.  ...  The author thanks two anonymous referees for pointing out some references and several imprecisions in the manuscript.  ... 
doi:10.1002/rsa.20119 fatcat:f65gva3xfzailk3v2j4av23jcm

Network science applied to forest megaplots: tropical tree species coexist in small-world networks

Julia Sabine Schmid, Franziska Taubert, Thorsten Wiegand, I-Fang Sun, Andreas Huth
2020 Scientific Reports  
The species networks show the common small-world property and constant node degree distributions not yet described and explained by network science.  ...  We find remarkably similar tree and species networks among tropical forests in Panama, Sri Lanka and Taiwan.  ...  who tirelessly contributed in the repeated censuses of this plot.  ... 
doi:10.1038/s41598-020-70052-8 pmid:32764650 fatcat:6rlodawbfrepxgzy5sfjzme64u


2008 Natural Resource Modeling  
We use three common graph-theoretic measures of network structure to quantify the effect of understory tree size on the spatial association of understory species with trees in the canopy: the node degree  ...  Here, we investigate the ability of network analysis to detect spatial patterns of species association in a tropical forest.  ...  This manuscript is based in part on Dr.  ... 
doi:10.1111/j.1939-7445.2008.00004.x fatcat:xjnvopd45rguxbzyzionps6mji

Architecture of the wood-wide web: Rhizopogon spp. genets link multiple Douglas-fir cohorts

Kevin J. Beiler, Daniel M. Durall, Suzanne W. Simard, Sheri A. Maxwell, Annette M. Kretzer
2009 New Phytologist  
an efficient and robust network, where large trees play a foundational role in facilitating conspecific regeneration and stabilizing the ecosystem.  ...  The role of mycorrhizal networks in forest dynamics is poorly understood because of the elusiveness of their spatial structure.  ...  This project was funded by the Province of British Columbia through the Forest Investment Account-Forest Science Program, a University Graduate Fellowship from the University of British Columbia, and the  ... 
doi:10.1111/j.1469-8137.2009.03069.x pmid:19878460 fatcat:foz7xrf22zgwzdhzhnzvjmc7wq

Financial Data Anomaly Detection Method Based on Decision Tree and Random Forest Algorithm

Qingyang Zhang, Miaochao Chen
2022 Journal of Mathematics  
In this paper, the random forest algorithm is introduced into the detection of abnormal samples, and the concept of abnormal point scale is proposed to measure the abnormal degree of the sample based on  ...  With the emergence of machine learning and data mining in recent years, new ideas and methods have emerged in the detection of abnormal network flows.  ...  Acknowledgments is study was supported by Hangzhou Vocational and Technical College.  ... 
doi:10.1155/2022/9135117 fatcat:ci5mjbwlyngzvb4s2v2emdja2e

Surveying the Forests and Sampling the Trees: An overview of Classification and Regression Trees and Random Forests with applications in Survey Research

Trent D. Buskirk
2018 Survey Practice  
CART models can be estimated in the presence of missing data and random forest methods can adapt to the complexity of the dataset and can be estimated when the number of predictors is large relative to  ...  Classification and regression trees (CARTs) and random forests represent two of the methods that are being applied more commonly within the survey research context for creating nonresponse adjustments  ...  Splitting each tree in the forest occurs one node at a time, and each tree is grown as large as possible.  ... 
doi:10.29115/sp-2018-0003 fatcat:6dnm7gv4rnfffegsuddbx6zswu

Fragmentation of random trees

Z Kalay, E Ben-Naim
2014 Journal of Physics A: Mathematical and Theoretical  
We study fragmentation of a random recursive tree into a forest by repeated removal of nodes.  ...  We study statistical properties of trees and nodes in this heterogeneous forest, and find that the fraction of remaining nodes m characterizes the system in the limit N --> infty.  ...  Acknowledgments We acknowledge support by the World Premier International Research Center (WPI) Initiative of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and by  ... 
doi:10.1088/1751-8113/48/4/045001 fatcat:ggv74atvqzdo7fj4yty6ypi3qq

Guidelines for Developing and Reporting Machine Learning Predictive Models in Biomedical Research: A Multidisciplinary View

Wei Luo, Dinh Phung, Truyen Tran, Sunil Gupta, Santu Rana, Chandan Karmakar, Alistair Shilton, John Yearwood, Nevenka Dimitrova, Tu Bao Ho, Svetha Venkatesh, Michael Berk
2016 Journal of Medical Internet Research  
Common pitfalls of applying random forest include not optimizing the number of trees and insufficient randomization during the construction of base trees.  ...  We recommend the number of trees in the randomForest should be at least 25 and ideally 500 or more. The minimum number of observations in each splitting node and leaf node should be 20 or more.  ...  Gradient boosting is generally considered to have performance comparable to Random forest. Compared to random forest, it has more tuning parameters.  ... 
doi:10.2196/jmir.5870 pmid:27986644 pmcid:PMC5238707 fatcat:wmfxuxuw7rh47mn7bwwmm63vbm

MIS on trees

Christoph Lenzen, Roger Wattenhofer
2011 Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11  
In this paper, we present a solution with randomized running time O( √ log n log log n) on trees, improving roughly quadratically on the state-of-the-art bound.  ...  Our algorithm is uniform and nodes need to exchange merely O(log n) many bits with high probability.  ...  In order to bound the number of phases for which a node can have a significant chance to retain a large degree, we bound the depth of delay trees rooted at high-degree nodes. Proof.  ... 
doi:10.1145/1993806.1993813 dblp:conf/podc/LenzenW11 fatcat:nqaqwrvtlncu5ju62yhg2x3qpq

Financial Hazard Map: Financial Vulnerability Predicted by a Random Forests Classification Model

Katsuyuki Tanaka, Takuji Kinkyo, Shigeyuki Hamori
2018 Sustainability  
The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.  ...  Acknowledgments: We are grateful to four anonymous referees for their helpful comments and suggestions. This work is supported by JSPS KAKENHI Grant Number 17K18564 and 17H00983.  ...  First, random forests perform better in terms of classification accuracy by building a large number of trees instead of only a single tree.  ... 
doi:10.3390/su10051530 fatcat:6wzgxkxhbnhjddew3funl2y3uq

Constructing Maximum-Lifetime Data-Gathering Forests in Sensor Networks

Yan Wu, Zhoujia Mao, Sonia Fahmy, Ness B. Shroff
2010 IEEE/ACM Transactions on Networking  
We show that both the tree and forest construction algorithms terminate in polynomial time and are provably near optimal. We then verify the efficacy of our algorithms via numerical comparisons.  ...  We design an algorithm that starts from an arbitrary tree and iteratively reduces the load on bottleneck nodes (nodes likely to soon deplete their energy due to high degree or low remaining energy).  ...  For a forest with nodes and base stations, the sum of degrees of nodes in is at most .  ... 
doi:10.1109/tnet.2010.2045896 fatcat:sjfpmdah45htblq3wtwk5pk37e

Dual-stage constructed random graph algorithm to generate random graphs featuring the same topological characteristics with power grids

Shiqian MA, Yixin YU, Lei ZHAO
2017 Journal of Modern Power Systems and Clean Energy  
The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely.  ...  Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world  ...  The average degree of a tree denoted by \k T [ is: hk T i ¼ 2ðn À 1Þ=n ð5Þ 12) Spanning forest: A spanning forest is a forest that contains every node of G such that two nodes are in the same tree of the  ... 
doi:10.1007/s40565-017-0318-8 fatcat:4sqsnhakzvgidf3ymzsnlom23u

On the Integrality Gap of the Prize-Collecting Steiner Forest LP

Jochen Könemann, Neil Olver, Kanstantsin Pashkovich, R. Ravi, Chaitanya Swamy, Jens Vygen, Marc Herbstritt
2017 International Workshop on Approximation Algorithms for Combinatorial Optimization  
For the special case of prize-collecting Steiner tree (PCST), we prove that the natural LP relaxation admits basic feasible solutions with all coordinates of value at most 1/3 and all edge variables positive  ...  In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph G = (V, E), edge costs {c e ≥ 0} e∈E , terminal pairs {(s i , t i )} k i=1 , and penalties {π i } k i=1 for each  ...  Then for n and k chosen sufficiently large, there exists a degree-2 node u in G such thatP [u ∼ F r 0 ] ≤ α − 2 + ,where F is a uniformly random forest from F 1 , . . . , F q .Proof.  ... 
doi:10.4230/lipics.approx-random.2017.17 dblp:conf/approx/KonemannOP0SV17 fatcat:kis2fag6fndpfchfyslh7gkqau

Knowledge aggregation in decision-making process with C-fuzzy random forest using OWA operators

Łukasz Gadomer, Zenon A. Sosnowski
2018 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
The idea of knowledge aggregation contained in C-fuzzy decision tree nodes with OWA operators during the C-fuzzy random forest decision-making process is presented in this paper.  ...  C-fuzzy random forest is a new kind of ensemble classifier which consists of C-fuzzy decision trees.  ...  These operators aggregate the knowledge contained in C-fuzzy decision tree nodes which are part of C-fuzzy random forest.  ... 
doi:10.1007/s00500-018-3036-x fatcat:vh3rpvopsrbthe622ggpmnpdse

Combining random forest with multi-block local binary pattern feature selection for multiclass head pose estimation

Min-Joo Kang, Jung-Kyung Lee, Je-Won Kang, Yudong Zhang
2017 PLoS ONE  
The randomized tree aims to maximize the information gain at each node while random samples traverse the nodes in the tree.  ...  In the proposed technique a randomized tree with useful attributes is trained to improve estimation accuracy and tolerance of occlusions and illumination.  ...  a split function in each node of a randomized tree.  ... 
doi:10.1371/journal.pone.0180792 pmid:28715442 pmcid:PMC5513428 fatcat:jhuk7kuvljddfnupqhttanpk3i
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