Spectral Partitioning Method Research Articles

Co-Clustering by Directly Solving Bipartite Spectral Graph Partitioning.

Bipartite spectral graph partitioning (BSGP) method as a co-clustering method, has been widely used in document clustering, which simultaneously clusters documents and words by making full use of the duality between documents and words. It consists of two steps: 1) graph construction and 2) singular value decomposition on the bipartite graph to compute a continuous cluster assignment matrix, followed by post-processing to get the discrete solution. However, the generated graph is unstructured and fixed. It heavily relies on the quality of the graph construction. Moreover, the two-stage process may deviate from directly solving the primal problem. In order to tackle these defects, a novel bipartite graph partitioning method is proposed to learn a bipartite graph with exactly c connected components (c is the number of clusters), which can obtain clustering results directly. Furthermore, it is experimentally and theoretically proved that the solution of the proposed model is the discrete solution of the primal BSGP problem for a special situation. Experimental results on synthetic and real-world datasets exhibit the superiority of the proposed method.

Wave spectral partitioning for the SWIM spectrometer based on the wave age and parameter optimization method

The paper proposes a wave spectral partitioning method for the surface waves investigation and monitoring (SWIM) spectrometer based on the wave age and parameter optimization (WA-PO) method. The wave age criterion is a way to identify waves as wind waves or swells, and parameter optimization methods enable the modeling of wave spectra. The combination of the two can use the spectrum models to fit the SWIM spectra based on clarifying whether the spectrum models belong to wind waves or swells, which achieves spectral partitioning. The WA-PO method consists of four steps: peaks region dividing, spectral peaks searching, objective function constructing, and model parameters optimizing. The results show that compared with the partition products provided by the SWIM, the partition parameters obtained from the WA-PO method are closer to those of the Integrated Ocean Waves for Geophysical and other Applications (IOWAGA) numerical hindcast dataset developed from the WAVEWATCH III (WW3). The WA-PO method can prevent over-partitioning of the wave spectra and detect wind-wave components hidden in the swell partition.

A worldwide coastal analysis of the climate wave systems

Wind generated waves of a sea state are generally the result of the superposition of wind sea and swells, making the frequency-direction wave energy distribution crucial for comprehending this behavior. Wave spectral partitioning methods provide groups of waves with similar characteristics, thus they have been usually applied to identify wind sea and swell. In addition, several swells can coexist in a sea state. This study develops a method to estimate the wave systems and analyze their characteristics over the coast worldwide using 32year (1989-2020) historical information and more than 10.000 locations. A wave system is considered as the long-term climate conditions prevailing over a frequency-direction wave energy area collecting similar environmental and physical characteristics. The method is applied for the hourly time series of the directional wave spectra. First, the watershed clustering algorithm is used and the partitions found are classified as wind sea or swells based on a wave age criterion. The information obtained from the swell spectral partitions is then used to estimate the probability of their occurrence within specific frequency-direction bins and the clustering algorithm is applied anew to this population in order to identify the number of significant long-term climate wave systems locally and their characteristics. Outcomes reveal that on average swells coexist with wind sea in approximately 70% of the global coast, whereas about 25% is predominantly dominated by pure swells and the wind sea dominates only in the 5%. Only the 2% of the global coast line presents one swell wave system. About 50% of the global coastal locations exhibit three and four, whereas the 15% presents two swell wave systems. The analysis shows that about 30% of the coastal locations present at least five swell wave systems, mostly on Pacific islands and enclosed seas.

A parallel computing framework for large-scale microscopic traffic simulation based on spectral partitioning

This paper introduces a parallel computing framework based on the Spectral Partitioning (SP) method designed to enhance the computational efficiency of large-scale microscopic traffic simulation (LSMTS). The framework employs the SP method to partition road networks, taking into account vehicle information and road information as constitutive components for node weight determination. Micro-simulation relies on vehicle information from both preceding and following vehicles to accurately infer the operational states of a vehicle. However, network partitioning can disrupt the flow of vehicle information, resulting in its loss. To address this, the proposed framework incorporates a boundary transmission method to ensure simulation accuracy and precision. This study presents an improved SP (iSP) method tailored for LSMTS, further enhancing the partitioning results achieved through the SP method. Lastly, the framework's validity is confirmed through road network experiments of varying scales and densities, with comparisons made to existing parallel simulation methods. The results demonstrate that the framework significantly reduces the execution time of simulation tasks while maintaining a high level of load balance and minimizing communication overhead.

Spatiotemporal distributions of air-sea CO2 flux modulated by windseas in the Southern Indian Ocean

The Southern Indian Ocean is a major reservoir for rapid carbon exchange with the atmosphere, plays a key role in the world’s carbon cycle. To understand the importance of anthropogenic CO2 uptake in the Southern Indian Ocean, a variety of methods have been used to quantify the magnitude of the CO2 flux between air and sea. The basic approach is based on the bulk formula—the air-sea CO2 flux is commonly calculated by the difference in the CO2 partial pressure between the ocean and the atmosphere, the gas transfer velocity, the surface wind speed, and the CO2 solubility in seawater. However, relying solely on wind speed to measure the gas transfer velocity at the sea surface increases the uncertainty of CO2 flux estimation. Recent studies have shown that the generation and breaking of ocean waves also significantly affect the gas transfer process at the air-sea interface. In this study, we highlight the impact of windseas on the process of air-sea CO2 exchange and address its important role in CO2 uptake in the Southern Indian Ocean. We run the WAVEWATCH III model to simulate surface waves in this region over the period from January 1st 2002 to December 31st 2021. Then, we use the spectral partitioning method to isolate windseas and swells from total wave fields. Finally, we calculate the CO2 flux based on the new semiempirical equation for gas transfer velocity considering only windseas. We found that after considering windseas’ impact, the seasonal mean zonal flux (mmol/m2·d) increased approximately 10%-20% compared with that calculated solely on wind speed in all seasons. Evolution of air-sea net carbon flux (PgC) increased around 5.87%-32.12% in the latest 5 years with the most significant seasonal improvement appeared in summer. Long-term trend analysis also indicated that the CO2 absorption capacity of the whole Southern Indian Ocean gradually increased during the past 20 years. These findings extend the understanding of the roles of the Southern Indian Ocean in the global carbon cycle and are useful for making management policies associated with marine environmental protection and global climatic change mitigation.

A quick solution to optimal coordinated voltage-control, based on dimension-reduction of power system via Modified Ward-PV

Voltage control and Voltage stability are the most important issues in the power system. The purpose of this paper is to investigate the emergency voltage control in power systems. One of the most important proposed methods to solve this issue is optimal coordinated voltage control (OCVC), which is based on the model predictive control (MPC). Time limitations for preventing voltage collapse is the most critical constraint to solve an OCVC problem. In this paper, the Modified WARD-PV will be proposed to reduce the dimension of the power system and consequently, the speed of solving problem is increased. In this method, immediately after occurrence a fault, the power system is partitioned to into three subsystems by spectral graph partitioning method. Partitioning is based on reactive power flow through the lines. The subsystems, which are far from fault, will be replaced by the reduced model. This method will drastically reduce the number of system equations and will boost the speed of solving problem. The simulations results obtained on New England IEEE 39-Bus System reveals that the proposed method acts more precise than dimension reduction of power system based on linearization of external subsystems, but the speed of solving problem decrease.

Intelligent Vulnerability Analysis for Connectivity and Critical-Area Integrity in IoV

The large-scale connectivity of Internet of Vehicles (IoV) is an important challenge for the Intelligent Transportation Systems (ITS). Intelligence vulnerability analysis is an excellent solution. However, existing methods for analyzing connectivity vulnerability have ignored the existence of critical areas in the system. Due to the heterogeneities of the IoV environments and services, the failure of some specific areas may seriously damage connectivity and system performance. To this end, in this paper we focus on both the dynamic connectivity and the critical-area integrity, and propose an intelligent vulnerability analysis method to effectively identify the critical area of extreme vulnerability. Specifically, we consider an intelligent analysis scenario in which roadside servers continuously learn IoV heterogeneous environment and dynamic topology, and then translate the learning results into a flexible disruption cost problem. Based on this, we utilize the spectral partitioning method to identify the minimum-cost set of topological elements whose failure not only severely damages system connectivity but also disrupts its critical areas. Furthermore, we confirm that the identified set can be used to optimize disruption cost problem, thus intelligently improving vulnerability. Simulation results show that our proposed method can effectively identify vulnerable elements and prevent significant loss in the IoV system connectivity and performance.

Network Partitioning Algorithms for Solving the Traffic Assignment Problem using a Decomposition Approach

Recent methods in the literature to parallelize the traffic assignment problem consider partitioning a network into subnetworks to reduce the computation time. In this article, a partitioning method is sought that generates subnetworks minimizing the computation time of a decomposition approach for solving the traffic assignment (DSTAP). The aim is to minimize the number of boundary nodes, the interflow between subnetworks, and the computation time when the traffic assignment problem is solved in parallel on the subnetworks. Two different methods for partitioning are tested. The first is an agglomerative clustering heuristic that reduces the subnetwork boundary nodes. The second is a flow weighted spectral partitioning algorithm that uses the normalized graph Laplacian to partition the network. The performance of both algorithms is assessed on different test networks. The results indicate that the agglomerative heuristic generates subnetworks with a lower number of boundary nodes, which reduces the per iteration computation time of DSTAP. However, the partitions generated may be heavily imbalanced leading to a higher computation time when the subnetworks are solved in parallel separately at a particular DSTAP iteration. For the Austin network partitioned into four subnetworks, the agglomerative heuristic requires 3.5 times more computation time to solve the subnetworks in parallel. The results also show that the spectral partitioning method is superior for minimizing the interflow between subnetworks. This leads to a faster convergence rate of the DSTAP algorithm.

Deep sparse representation-based mid-level visual elements discovery in fine-grained classification

In this paper, we propose a new mid-level visual elements discovery method and apply it to the fine-grained classification. We present the duality between image patches and features extracted by the convolutional winner-take-all autoencoder (CONV-WTA-AE). The sparsity constraints used by CONV-WTA-AE make a group of objects sharing the same feature components. Hence, the image patches could be clustered by their sharing feature components and the feature components can be clustered by their co-occurrence in the image patches. We propose formulating the mid-level visual elements mining as a bipartite graph partitioning problem. The spectral partitioning algorithm is employed to co-cluster image patches and feature components. The CONV-WTA-AE is an unsupervised feature learning method. Hence, it avoids using expensive annotations. Our experiments demonstrate that the spectral partitioning method is very efficient but only the confident instances in a cluster are well discriminated. The similarity metric used by this algorithm is not accurate enough. Hence, we propose training a group of linear support vector machine (SVM) to refine the clustering results. These SVMs will be trained on the initial confident instances and provide a better discriminative similarity. Then we can re-assign instances to each clusters. To avoid overfitting, this process is iterated on many data subsets. We conduct a series of experiments on the MNIST dataset to verify our algorithm. The experimental results show that our method can discover meaningful image patch clusters. In the fine-grained classification task, visual elements are input into an ensemble of convolutional neural networks. The experiments on the CompCars dataset illustrate that our method can achieve the state-of-the-art performance.

Efficient Partitioning of Water Distribution Networks Using a Graph-Theoretical Approach

We present an efficient graph-theoretical method for partitioning water distribution networks (WDNs) into district metered areas (DMAs). The proposed algorithm consists of two main parts, namely WDN partitioning and DMA connection, and is tested on a real-life WDN, for which different weight cases are compared. The efficiency of the proposed DMA connection algorithm, in regard to the traditional combinatorics approach, is shown for various numbers of established DMAs. The final solution is selected according to the multi-criteria evaluation model, which was developed in order to reduce the subjective influence in the selection process and considers hydraulic, cost, and topological criteria. The results show that the newly proposed spectral partitioning method, namely generalized normalized cut, is appropriate for WDN partitioning and that we can further improve the quality of the obtained solutions by considering appropriate topological and cost-based WDN information in the partitioning process.

Spectral partitioning and fuzzy C-means based clustering algorithm for big data wireless sensor networks

In wireless sensor networks, sensor nodes are usually powered by battery and thus have very limited energy. Saving energy is an important goal in designing a WSN. It is known that clustering is an effective method to prolong network lifetime. Due to the development of big data, there are more sensor nodes and data needed to process. So how to cluster sensor nodes cooperatively and achieve an optimal number of clusters in a big data WSN is an open issue. In this paper, we first propose an analytical model to give the optimal number of clusters in a wireless sensor network. We then propose a centralized cluster algorithm based on spectral partitioning method. After that, we present a distributed implementation of the clustering algorithm based on fuzzy C-means method. Finally, we conduct extensive simulations, and the results show that the proposed algorithms outperform the hybrid energy-efficient distributed (HEED) clustering algorithm in terms of energy cost and network lifetime.

Multi-level spectral graph partitioning method

In this article, a new method for multi-level and balanced division of non-directional graphs (MSGP) is introduced. Using the eigenvectors of the Laplacian matrix of graphs, the method has a spectral approach which has superiority over local methods (Kernighan–Lin and Fiduccia-Mattheyses) with a global division ability. Bisection, which is a spectral method, can divide the graph by using the Fiedler vector, while the recursive version of this method can divide into multiple levels. However, the spectral methods have two disadvantages: (1) high processing costs; (2) dividing the sub-graphs independently. With a better understanding of the eigenvectors of the whole graph, and by discovering the confidential information owned, MSGP can divide the graphs into balanced and multi-leveled without recursive processing. Inspired by Haar wavelets, it uses the eigenvectors with a binary heap tree. The comparison results in seven existing methods (some are community detection algorithms) on regular and irregular graphs which clearly demonstrate that MSGP works about 14,4 times faster than the others to produce a proper partitioning result.

Low-complexity Spectral Partitioning based MUSIC Algorithm for Automotive Radar

This paper proposes a low-complexity spectral partitioning (SP) based MUSIC algorithm for automotive radar. For short-range radar (SRR), the range accuracy and resolution of 24 GHz ISM band radar should be improved because the requirements of automotive sensing become more demanding over time. To improve the performance of range estimation, high resolution based algorithms such as the estimation of signal parameters via rotational invariance techniques (ESPRIT) and multiple signal classification (MUSIC) have been proposed. However, in a low signal-to-noise ratio (SNR), the high resolution algorithm shows degraded performance to estimate the parameters. To solve this problem, SP based high resolution algorithms have been studied recently. However, for real-time operation, the conventional SP method cannot be applied to automotive radar due to its high complexity. Therefore, a low complexity SP based MUSIC is designed to maintain the performance of the range accuracy and resolution in a low SNR environment. While the complexity of the proposed algorithm is less than the SP-MUSIC, Monte-Carlo simulation results and experimental results show that the estimation performance of the proposed method is similar to that of SP-MUSIC in terms of various parameters.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18719

Geometric multiscale community detection: Markov stability and vector partitioning

Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov Stability in terms of a time-dependent spectral embedding, where the Markov time acts as an inhomogeneous geometric resolution factor that zooms the components of the node vectors at different rates. Our geometric formulation encompasses both modularity and the multi-resolution Potts model, which are shown to correspond to vector partitioning in a pseudo-Euclidean space, and is also linked to spectral partitioning methods, where the number of eigenvectors used corresponds to the dimensionality of the underlying embedding vector space. Inspired by the Louvain optimisation for community detection, we then propose an algorithm based on a graph-theoretical heuristic for the vector partitioning problem. We apply the algorithm to the spectral optimisation of modularity and Markov Stability community detection. The spectral embedding based on the transition matrix eigenvectors leads to improved partitions with higher information content and higher modularity than the eigen-decomposition of the modularity matrix. We illustrate the results with random network benchmarks.

Wind waves climatology of the Southeast Pacific Ocean

ABSTRACTThe climatology of wind waves over the Southeast Pacific is analysed using a 32‐year hindcast from the WaveWatch III model, complemented by satellite‐derived significant wave height (SWH) and buoy measurements for validation. Using partitioned spectral data, a regional climatology of wind sea and swell parameters was constructed. In general, the simulated SWH shows a good agreement with satellite and in situ SWH measurements, although the model appears to have a spatially uniform bias of approximately 0.3 m. The spatial pattern of SWH is clearly influenced by the meridional variation of mean surface wind speed, where the stronger winds over the Southern Ocean play a significant role generating higher waves at higher latitudes. Nevertheless, regional features are observed in the annual variability of SWH, which are associated with the existence of atmospheric coastal low‐level jets off the coast of Peru and central Chile. In particular, the seasonal variation of these synoptic scale jets shows a direct relationship with the annual variability of SWH and with the probability of occurrence of wind sea conditions. Off the coast of Peru at approximately 15°S the coastal low‐level jet is strongest during austral winter, increasing the wind sea SWH. In contrast, off central Chile, there is an important increase of wind sea SWH during summer. The seasonal variation of the wind sea component leads to a contrasting seasonal variation of the total SWH at these locations: off Peru the coastal jet amplifies the annual variability of SWH, while off Central Chile the annual variability of SWH is suppressed by the presence of the coastal jet. Although the general conclusions of this research are considered to be robust, we discuss the limitations of the spectral partitioning method used to distinguish wind sea and swell‐sea states.

A quick method to solve the optimal coordinated voltage control problem based on reduction of system dimensions

This paper presents a new method to speed up the solving process of the optimal coordinated voltage control (OCVC) problem. To this end, after occurrence of a fault, the power system is initially partitioned into interior, boundary and exterior zones by spectral graph partitioning method. Partitioning is based on the fact that voltage instability just after the fault, is a local phenomenon, therefore the variation of boundary and exterior variables is smaller than that of interior ones. Then, the equations of boundary and exterior zones are linearized, the algebraic variables and equations of exterior zone are removed and a considerable decrease in the number of power system equations is obtained which is equal to a reduction in the system dimensions. As a result the determination process of the optimal control actions is fastened. Also, based on the monotonic behavior of long-term voltages, a new method of predicting voltage trajectory is proposed, in which two points are used: the first point referring to the system state just after applying the control actions, which is called jumping point and the final one referring to the steady state of the system. In a case study on the New England 39-bus power system, it was verified that using this method a remarkable increase in calculation speed can be obtained while retaining the system precision.

Grouping interdependent tasks: Using spectral graph partitioning to study complex systems

Research summary: This article uses spectral graph partitioning to advance strategic management research, and focuses on the study of complex systems that contain strongly connected components with component interactions that are weighted and directed. The spectral graph partitioning method complements existing methods, especially, when external architectural artifacts do not exist or are less than certain. We illustrate this methodology using a U.S. airline's production system. We highlight some useful metrics and show how researchers can apply this method to generate additional architectural insights.Managerial summary: We describe a method for analyzing the architecture of complex systems that contain directed and weighted component interactions, and in which each component is interdependent (directly or indirectly) on every other component. Using the spectra of a complex system, the method is not only tractable but also provides good and predictable groupings. We illustrate this method using the firm-level production task system of a firm found in the U.S. passenger airline sector. The method is useful if the system architecture is hidden, in flux, or both. The method may also permit a holistic comparison of different systems and their architectures. We discuss metrics and illustrate how they can provide additional architectural insights. Copyright © 2015 John Wiley & Sons, Ltd.

Identification of ‘energetic’ swell waves in a tidal strait

Energetic swell waves present a significant coastal hazard. Overtopping is particularly sensitive to these longer period waves, potentially resulting in coastal flooding. In narrow tidal seas which are linked to large oceans, such as the English Channel, the importance of swell for design considerations is not immediately obvious. However, historical experience shows occasional severe impacts from long period waves, such as on 6th February 1904, 13th February 1979 and most recently two events in February 2014. When wave buoy measurements are analyzed using spectral partitioning methods, it is possible to identify swell wave systems with significant energy within the overall spectrum. This often coincides with the occurrence of storm waves, which might mask the presence of the swell component without such analysis. Two case studies where flooding occurred during storm events are examined in this paper. It has been possible to associate individual spectral components with the occurrence of overtopping of coastal defences at a particular location. Further investigation of the characteristics and frequency of energetic swell waves are recommended to enhance prediction and the design of coastal defences, and hence reduce their consequences.

Spectral clustering with epidemic diffusion

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a spectral partitioning method that exploits the properties of epidemic diffusion. An epidemic is a dynamic process that, unlike the random walk, simultaneously transitions to all the neighbors of a given node. We show that the replicator, an operator describing epidemic diffusion, is equivalent to the symmetric normalized Laplacian of a reweighted graph with edges reweighted by the eigenvector centralities of their incident nodes. Thus, more weight is given to edges connecting more central nodes. We describe a method that partitions the nodes based on the componentwise ratio of the replicator's second eigenvector to the first and compare its performance to traditional spectral clustering techniques on synthetic graphs with known community structure. We demonstrate that the replicator gives preference to dense, clique-like structures, enabling it to more effectively discover communities that may be obscured by dense intercommunity linking.

Community detection and graph partitioning

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, which allows us to apply any of the many well-understood partitioning algorithms to the solution of community detection problems. We illustrate the approach by adapting the Laplacian spectral partitioning method to perform community inference, testing the resulting algorithm on a range of examples, including computer-generated and real-world networks. Both the quality of the results and the running time rival the best previous methods.