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Fast Sampling via Spectral Independence Beyond Bounded-degree Graphs
2024
ACM Transactions on Algorithms
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Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. ...
sets, matchings, and Ising-model configurations. ...
Reference [7] for the random-cluster model. ...
doi:10.1145/3631354
fatcat:3baxid45djgnnei44dfsmiryiy
Consistent Procedures for Cluster Tree Estimation and Pruning
2014
IEEE Transactions on Information Theory
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For a density f on R d , a high-density cluster is any connected component of {x : f (x) ≥ λ}, for some λ > 0. The set of all high-density clusters forms a hierarchy called the cluster tree of f . ...
We give finite-sample convergence rates for these algorithms which also imply consistency, and we derive lower bounds on the sample complexity of cluster tree estimation. ...
Let A n and A ′ n be the vertices of two separate connected components (potentially at different levels) in the cluster tree returned by an algorithm. ...
doi:10.1109/tit.2014.2361055
fatcat:exn5a5yyyjfmbdblljeldd2lse
A Regression Tree Method for Longitudinal and Clustered Data with Multivariate Responses
[article]
2023
arXiv
pre-print
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2022 pre-print arXiv:2206.03952v1 fatcat:sqfw2rt6qreyfhqpsl33ofmuw4
RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. ...
Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. ...
) component. ...
arXiv:2206.03952v2
fatcat:ozgsodm7jzdb5imjsobcyr35v4
Beyond independence: probabilistic models for query approximation on binary transaction data
2003
IEEE Transactions on Knowledge and Data Engineering
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, the Chow-Liu tree model, and the Bernoulli mixture model. ...
We focus in particular on probabilistic model-based approaches to this problem and develop a number of techniques that are significantly more accurate than a baseline independence model. ...
Acknowledgements The research described in this paper was supported in part by NSF awards IRI-9703120 and IIS-0083489 and by research gifts from IBM Research and Microsoft Research. ...
doi:10.1109/tkde.2003.1245281
fatcat:vxb5h6cuoze47orum3zkchgceq
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
2006
International Journal of Computer Vision
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We illustrate the new tree clustering framework on shock-graphs extracted from the silhouettes of 2D shapes. ...
This involves interleaved steps for updating the affinity matrix using an eigendecomposition method and updating the cluster membership indicators. ...
We connect the two nodes ( p, q) and (r, s) if and only if p and r are independent in t, and q and s are independent in t . ...
doi:10.1007/s11263-006-8929-y
fatcat:sxzdv3367zh2deith5hfqjmp7i
MC64-Cluster: Many-Core CPU Cluster Architecture and Performance Analysis in B-Tree Searches
2017
Computer journal
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MC64-Cluster architecture was outlined in terms of both hardware and software, including commands available to manage jobs and provided application programming interfaces to communicate and synchronize ...
Massively, concurrent searches of keys in B-trees, which are used in many applications, including bioinformatics, were used. ...
ACKNOWLEDGEMENTS We are grateful to Tilera <http://www.tilera.com> for providing hardware and software tools. ...
doi:10.1093/comjnl/bxx114
fatcat:tgpe7rvx45bzxjqmycvabbixpe
Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes
[article]
2020
arXiv
pre-print
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Exploiting the tree-Wasserstein barycenter and its variants, we scale up multi-level clustering and scalable Bayes, especially for large-scale applications where the number of supports in probability measures ...
Drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree-Wasserstein barycenter and its variants. ...
For TW, the number of trees is set to 200 and 500, and tree metrics are constructed by using the farthest-point clustering as in [19] where we set 4 for the number of clusters in the farthest-point clustering ...
arXiv:1910.04483v3
fatcat:duqytl5nbjfm5hzrthkiamiyl4
Advanced Fuzzy Clustering and Decision Tree Plug-Ins for DataEngineTM
[chapter]
2000
Lecture Notes in Computer Science
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It describes the data flow for the induction, pruning, and testing of a decision tree. ...
tree on the training and the test data. 3 (That it is the pruned decision tree that is executed cannot be read directly from this card, though, because it is passed via a file. ...
In contrast, each component generated by a possibilistic clustering algorithm corresponds to a dense region in the data set, i.e. if the actual number of clusters is smaller than c, some clusters might ...
doi:10.1007/10720181_8
fatcat:g77ju35gjvam5h7j27sysmzx5u
Species, Clusters and the 'Tree of Life': A graph-theoretic perspective
[article]
2009
arXiv
pre-print
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We also explore the relationship between these and related clustering constructions. ...
We describe several mathematically precise ways by which one can naturally define collections of subsets of present day individuals so that these subsets are nested (and so form a tree) based purely on ...
Thus, rather than being an isolated set of component graphs -one for each 'species' -the graph G is more like a very large, diffuse 'tree of populations' (see Fig. 1 ), where the populations occasionally ...
arXiv:0908.2885v1
fatcat:mcylrgnmifha7j3ud4dk3mmlni
Sparse tree-based clustering of microbiome data to characterize microbiome heterogeneity in pancreatic cancer
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:2007.15812v2 fatcat:h6xhiigdyrdhdiyazdg4an6vduOther Versions
respects: we incorporate feature selection, learn the appropriate number of clusters from the data, and integrate information on the tree structure relating the observed features. ...
We propose a novel unsupervised clustering approach in the Bayesian framework that innovates over existing model-based clustering approaches, such as the Dirichlet multinomial mixture model, in three key ...
Beyond the limited scalability of DMM, the machine-learning and model-based clustering methods listed above share a common limitation: the number of clusters needs to be either taken as known, or chosen ...
arXiv:2007.15812v3
fatcat:w2ta7hbhbjdtbbja33r7k7feeu
Self-Organizing Topological Tree for Online Vector Quantization and Data Clustering
2005
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)
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Index Terms-Data clustering, online learning, self-organizing map (SOM), tree structure, vector quantization (VQ). ...
Besides the enhanced clustering performance, due to the online learning capability, the memory requirement of the proposed SOTT hybrid clustering algorithm is independent of the size of the data set, making ...
There is little or no advantage in increasing the path search factor beyond . ...
doi:10.1109/tsmcb.2005.846651
pmid:15971919
fatcat:7h5eyboj2bc4ppzgdglvvigbjq
Enhancement of Hierarchy Cluster-Tree Routing for Wireless Sensor Network
2009
Computer and Information Science
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Each round is composed of three phases: cluster formation, cluster-tree construction, data transmission. ...
CHs are selected in cluster formation phase and aggregate the data collected from its CMs in data transmission phase. If the cluster-tree is constructed, CHs forward the aggregated data to BS. ...
CMs send collected data to the closest one among the MCH and two SCHs.
Cluster-tree Construction A cluster-tree is built to link MCHs with BS in this phase. ...
doi:10.5539/cis.v2n4p89
fatcat:nhc7jiwirrhstorva4xsgky4pa
Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem
2012
Journal of Problem Solving
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We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention ...
The results indicate that for both the TSP and MST-P the participants tended to produce better quality solutions when the stimuli were highly clustered compared to random, and similarly, better quality ...
Under this approach (derived independently by Clark & Evans, 1954, and Hertz, 1909) , clustering, randomness and regularity are conceptualized as laying along a continuum, as demonstrated in Figure 2 ...
doi:10.7771/1932-6246.1117
fatcat:u52afxdwzzhyxckvan5w4rfsfm
Tree-based modelling for the classification of mammographic benign and malignant micro-calcification clusters
2017
Multimedia tools and applications
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in the clusters and their distribution and is based on the topology of the trees and the connectivity of the micro-calcifications. ...
The idea of using tree structure based on the distance of individual calcifications for the classification of benign and malignant micro-calcification clusters is novel and closely related to clinical ...
They analysed the topological structure by using multiscale morphology and investigated the number of independent subgraphs and the average degree of nodes as feature vectors. ...
doi:10.1007/s11042-017-4522-3
fatcat:vx7i3cjyibbktfkmcczv6dxif4
Species, clusters and the 'Tree of life': A graph-theoretic perspective
2010
Journal of Theoretical Biology
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We also explore the relationship between these and related clustering constructions. ...
We describe several mathematically precise ways by which one can naturally define collections of subsets of present day individuals so that these subsets are nested (and so form a tree) based purely on ...
A.D. and T.W. thank the CAS, the BMBF, and the MPG for financial support. V.M. and T.W. thank the Engineering and Physical Sciences Research Council (EPSRC) for its support [Grant EP/D068800/1]. ...
doi:10.1016/j.jtbi.2010.05.031
pmid:20561974
fatcat:aopqocqwevcklchty4fmxhpoea
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