scholarly journals Multiway p-spectral graph cuts on Grassmann manifolds

2021 ◽  
Author(s):  
Dimosthenis Pasadakis ◽  
Christie Louis Alappat ◽  
Olaf Schenk ◽  
Gerhard Wellein
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Unconstrained Minimization ◽  
Graph Cuts ◽  
Graph Laplacian ◽  
Clustering Methods ◽  
Real World Datasets ◽  
Comparative Results ◽  
Spectral Clustering Algorithm

AbstractNonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for $$p\in (1,2]$$ p ∈ ( 1 , 2 ] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.

scholarly journals An Enhanced Spectral Clustering Algorithm with S-Distance

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 596
Author(s):  
Krishna Kumar Sharma ◽  
Ayan Seal ◽  
Enrique Herrera-Viedma ◽  
Ondrej Krejcar
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Spatial Clustering ◽  
Clustering Algorithms ◽  
Rank Test ◽  
Customer Churn ◽  
Signed Rank ◽  
Signed Rank Test ◽  
Spectral Clustering Algorithm ◽  
Industrial Databases

Calculating and monitoring customer churn metrics is important for companies to retain customers and earn more profit in business. In this study, a churn prediction framework is developed by modified spectral clustering (SC). However, the similarity measure plays an imperative role in clustering for predicting churn with better accuracy by analyzing industrial data. The linear Euclidean distance in the traditional SC is replaced by the non-linear S-distance (Sd). The Sd is deduced from the concept of S-divergence (SD). Several characteristics of Sd are discussed in this work. Assays are conducted to endorse the proposed clustering algorithm on four synthetics, eight UCI, two industrial databases and one telecommunications database related to customer churn. Three existing clustering algorithms—k-means, density-based spatial clustering of applications with noise and conventional SC—are also implemented on the above-mentioned 15 databases. The empirical outcomes show that the proposed clustering algorithm beats three existing clustering algorithms in terms of its Jaccard index, f-score, recall, precision and accuracy. Finally, we also test the significance of the clustering results by the Wilcoxon’s signed-rank test, Wilcoxon’s rank-sum test, and sign tests. The relative study shows that the outcomes of the proposed algorithm are interesting, especially in the case of clusters of arbitrary shape.

The Spectrum Segmentation Algorithm of Multimode Vibration Signal Based on Spectral Clustering

2011 ◽  
Vol 121-126 ◽  
pp. 2372-2376
Author(s):  
Dan Dan Wang ◽  
Yu Zhou ◽  
Qing Wei Ye ◽  
Xiao Dong Wang
Keyword(s):  
Wave Packet ◽  
Frequency Domain ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Wave Packets ◽  
Vibration Signal ◽  
Segmentation Algorithm ◽  
Frequency Curve ◽  
Macroscopic Observation ◽  
Spectral Clustering Algorithm

The mode peaks in frequency domain of vibration signal are strongly interfered by strong noise, causing the inaccuracy mode parameters. According to this situation, this paper comes up with the thought of mode-peak segmentation based on the spectral clustering algorithm. First, according to the concept of wave packet, the amplitude-frequency of vibration signal is divided into wave packets. Taking each wave packet as a sample of clustering algorithm, the spectral clustering algorithm is used to classify these wave packets. The amplitude-frequency curve of a mode peak becomes a big wave packet in macroscopic. The experiment to simulation signals indicates that this spectral clustering algorithm could accord with the macroscopic observation of mode segmentation effectively, and has outstanding performance especially in strong noise.

Research on Spectral Clustering

2014 ◽  
Vol 687-691 ◽  
pp. 1350-1353
Author(s):  
Li Li Fu ◽  
Yong Li Liu ◽  
Li Jing Hao
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Theoretical Foundation ◽  
Clustering Algorithms ◽  
Spectral Graph Theory ◽  
Graph Partition ◽  
Mining Areas ◽  
Spectral Graph ◽  
Definition Of ◽  
Spectral Clustering Algorithm

Spectral clustering algorithm is a kind of clustering algorithm based on spectral graph theory. As spectral clustering has deep theoretical foundation as well as the advantage in dealing with non-convex distribution, it has received much attention in machine learning and data mining areas. The algorithm is easy to implement, and outperforms traditional clustering algorithms such as K-means algorithm. This paper aims to give some intuitions on spectral clustering. We describe different graph partition criteria, the definition of spectral clustering, and clustering steps, etc. Finally, in order to solve the disadvantage of spectral clustering, some improvements are introduced briefly.

Sectorisation of airspace based on balanced workloads

2019 ◽  
Vol 92 (2) ◽  
pp. 213-221 ◽  
Author(s):  
S.W. Soh ◽  
Z.W. Zhong
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Sector Boundary ◽  
Content Type ◽  
Advantages And Disadvantages ◽  
Standard Linear ◽  
Increasing Demand ◽  
Travel Industry ◽  
Straight Lines ◽  
Spectral Clustering Algorithm

Purpose Given the ever-growing air travel industry, there is an increasing strain on the systems that provide safe flights. Different methods have to be adopted to help to cope with the increasing demand, especially in Southeast Asia. The purpose of this study is to sectorise one existing airspace to better manage sector workloads. Design/methodology/approach Cambodia’s airspace was chosen for this study because it had only one sector and it was quickly approaching its limit. In this paper, after characterising the airspace, it was first bi-partitioned using the spectral clustering algorithm. The weights of the resulting subgraphs were then balanced through a weight-balancing algorithm. Also, a post-processing algorithm established the sector boundary to be drawn. The method was first carried out on one test airspace. Following the successful sectorisation of the test airspace, the actual Cambodian airspace was sectorised. The resulting two new sectors were then calculated to be able to last for approximately five years before they would reach their capacity. Hence, a further sectorisation was carried out. This resulted in four sectors, which were projected to last more than 10 years. Findings The method produced satisfactory results. The methodology presented is proven to be effective in achieving the sectorisation. The workloads of the new sectors obtained are balanced, and the sector boundaries are at least 15 km away from the air routes and nodes. The methodology is also general and can be applied to different scenarios. This means that applications to other airspace in the region are possible, which can further help to increase the safety, efficiency and capacity of the air traffic movement in this region. Originality/value This paper presents one of the approaches for airspace sector designs. The problems are clearly presented with references. The authors discuss the advantages and disadvantages of subdividing airspace and the need to sectorise Cambodia’s airspace, and present a method to solve the sectorisation problem. It is very precious to apply methodologies and algorithms to real cases. The presented method offers significant advantages such as the ease of implementation and efficiency. The problems can easily be solved using standard linear algebra algorithms. Instead of looking at the airspace as a whole, and generating new sector boundaries, our algorithm uses current sector boundaries and bisects them. Moreover, only sectors that require sectorisation would be affected. This algorithm has the advantage of maintaining the current sector boundaries to prevent radical changes to daily operations. The Voronoi diagram used in this work does not generate polygonal cells. It instead calculates the area based on pixels. The advantage of doing this is that it offers higher flexibility. Also, the sector boundary is generated based on straight lines calculated by joining the midpoints of links. This is simple and ensures that sections of the sector boundary are made up of straight, distinct lines. The authors also discuss the problems of the method and presented solutions to them.

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