Spectral K-way ratio-cut partitioning and clustering

Chan, P.K.; Schlag, Martine D. F.; Zien, Jason Y.

doi:10.1109/43.310898

Cited by 347 publications

(116 citation statements)

References 20 publications

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“…[34] for details). In the clustering analysis community, two-way clustering is also found to be inefficient due to the fact that separate eigenvalue problems need to be solved repeatedly [48,70,71].…”

Section: B Hierarchical Partitioning Of the Transfer-operatormentioning

confidence: 99%

Spectral-clustering approach to Lagrangian vortex detection

et al. 2016

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One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

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Section: B Hierarchical Partitioning Of the Transfer-operatormentioning

confidence: 99%

Spectral-clustering approach to Lagrangian vortex detection

et al. 2016

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“…There are many examples, the best known of which is modularity, initially proposed as a stopping rule for the divisive heuristic mentioned above and later considered as an independent criterion. Other well-known criteria are the k-way cut [8,9], the normalized cut [10,11], the ratio cut [9], the modularity density and its variants [12,13], and strength maximization subject to strong or weak constraints on the communities (see Sec. II) [14,15].…”

Section: Introductionmentioning

confidence: 99%

Finding communities in networks in the strong and almost-strong sense

et al. 2012

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Finding communities, or clusters or modules, in networks can be done by optimizing an objective function defined globally and/or by specifying conditions which must be satisfied by all communities. Radicchi et al. [Proc. Natl. Acad. Sci. USA 101, 2658 (2004)] define a susbset of vertices of a network to be a community in the strong sense if each vertex of that subset has a larger inner degree than its outer degree. A partition in the strong sense has only strong communities. In this paper we first define an enumerative algorithm to list all partitions in the strong sense of a network of moderate size. The results of this algorithm are given for the Zachary karate club data set, which is solved by hand, as well as for several well-known real-world problems of the literature. Moreover, this algorithm is slightly modified in order to apply it to larger networks, keeping only partitions with the largest number of communities. It is shown that some of the partitions obtained are informative, although they often have only a few communities, while they fail to give any information in other cases having only one community. It appears that degree 2 vertices play a big role in forcing large inhomogeneous communities. Therefore, a weakening of the strong condition is proposed and explored: we define a partition in the almost-strong sense by substituting a nonstrict inequality to a strict one in the definition of strong community for all vertices of degree 2. Results, for the same set of problems as before, then give partitions with a larger number of communities and are more informative.

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“…Therefore, the building partitioning problem can be directly related to graph partitioning schemes which partition an initial graph into subgraphs by removing a number of its edges. It is worth mentioning that many fast heuristic algorithms for large graphs can be found in the literature (see for example [18], [19], [20], [21]). However, they do not offer the same level of performance as exact algorithms that provide optimal solutions.…”

Section: B Exact Graph Partitioningmentioning

confidence: 99%

“…Create a singleton block forl 12: Set Imp← T rue 13: return M, Imp 14: end function In more detail, at the beginning of the dividing phase, each row of the matrix is inserted into a block of its own Dividing Phase 1: Set the maximum block size M 2: for all rows i do 3: Generate singleton block M i = {i} 4: repeat 5: Set Imp← F alse 6: for all rows i do 7: for all rows j do 8: if f (i) = f (j) then 9: Compute S i→f (j) and S i→f (j) 10: if (S i→f (j) > 0 OR S i→f (j) > 0) then 11: if (S i→f (j) > S j→f (i) ) then 12: [M, Imp] = CHANGEBLK(i, f (j), M,Imp) 13: else if (S i→f (j) < S j→f (i) ) then 14: [M, Imp] = CHANGEBLK(j, f (i), M,Imp) 15: else if (S i→f (j) = S j→f (i) ) then 16: if (|M f (i) | ≥ |M f (j) |) then 17: [M, Imp] = CHANGEBLK(i, f (j), M,Imp) 18:…”

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confidence: 99%

Partitioning of Intelligent Buildings for Distributed Contaminant Detection and Isolation

Kyriacou

Timotheou

Michaelides

et al. 2017

IEEE Trans. Emerg. Top. Comput. Intell.

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Intelligent buildings are responsible for ensuring indoor air quality for their occupants under normal operation as well as under possibly harmful contaminant events. An emerging environmental application involves the monitoring of intelligent buildings against harmful events by incorporating various sensing technologies and using sophisticated algorithms to detect and isolate such events. In this context, both centralized and distributed approaches have been proposed, with the latter having significant benefits in terms of complexity, scalability, reliability and performance. This paper considers the automatic partitioning of the building into subsystems, which enables the distributed simulation, modeling, analysis and management of the intelligent building while ensuring the effective detection and isolation of contaminants in the building interior. Specifically, we develop both a high-quality heuristic algorithm and an optimal Mixed Integer Linear Programming (MILP) formulation for the building partitioning problem. The MILP formulation is based on graph partitioning techniques, while the heuristic is based on matrix clustering techniques. Both approaches partition the building into subsystems while ensuring (i) maximum decoupling between the various subsystems, (ii) strong connectivity between the zones of each subsystem and (iii) control of the size of the subsystems with respect to the number of allocated zones. A combination of the two approaches is also proposed for reconfiguring an initial partitioning composition in real time in order to accommodate partitioning needs that arise from dynamic system changes. . His research focuses on the modeling and system-wide solution of problems in complex and uncertain environments that require real-time and close to optimal decisions by developing optimisation, machine learning and computational intelligence techniques. Application areas of his work include intelligent transportation systems, communication systems, and smart buildings.Michalis P. Michaelides (S'04-M'9) is a tenuretrack Lecturer with the

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Spectral K-way ratio-cut partitioning and clustering

Cited by 347 publications

References 20 publications

Spectral-clustering approach to Lagrangian vortex detection

Spectral-clustering approach to Lagrangian vortex detection

Finding communities in networks in the strong and almost-strong sense

Partitioning of Intelligent Buildings for Distributed Contaminant Detection and Isolation

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