scholarly journals A Parameter-Free Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

2020 ◽  
Author(s):  
Margaux Filippi ◽  
Irina Rypina ◽  
Alireza Hadjighasem ◽  
Thomas Peacock
Keyword(s):  
Spectral Clustering ◽  
Duffing Oscillator ◽  
A Priori ◽  
Clustering Algorithms ◽  
Lagrangian Dynamics ◽  
User Input ◽  
Structure Detection ◽  
Clustering Approach ◽  
Coastal Flow ◽  
Spectral Clustering Method

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al (2016), a new parameter-free spectral clustering approach is developed that automatically identifies parameters and does not require any user-input choices. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The parameter-free spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically-generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different.

scholarly journals An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 39
Author(s):  
Margaux Filippi ◽  
Irina I. Rypina ◽  
Alireza Hadjighasem ◽  
Thomas Peacock
Keyword(s):  
Spectral Clustering ◽  
Duffing Oscillator ◽  
A Priori ◽  
Clustering Algorithms ◽  
Optimal Parameters ◽  
Lagrangian Dynamics ◽  
User Input ◽  
Structure Detection ◽  
Clustering Approach ◽  
Coastal Flow

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different.

scholarly journals Social Network Community Detection Using Agglomerative Spectral Clustering

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ulzii-Utas Narantsatsralt ◽  
Sanggil Kang
Keyword(s):  
Social Network ◽  
Complex Networks ◽  
Community Detection ◽  
Spectral Clustering ◽  
Clustering Algorithms ◽  
Real Life ◽  
Clustering Method ◽  
Network Community ◽  
Improved Performance ◽  
Spectral Clustering Method

Community detection has become an increasingly popular tool for analyzing and researching complex networks. Many methods have been proposed for accurate community detection, and one of them is spectral clustering. Most spectral clustering algorithms have been implemented on artificial networks, and accuracy of the community detection is still unsatisfactory. Therefore, this paper proposes an agglomerative spectral clustering method with conductance and edge weights. In this method, the most similar nodes are agglomerated based on eigenvector space and edge weights. In addition, the conductance is used to identify densely connected clusters while agglomerating. The proposed method shows improved performance in related works and proves to be efficient for real life complex networks from experiments.

scholarly journals Segmentation of cDNA Microarray Images using Parallel Spectral Clustering

2013 ◽  
Vol 2 (1) ◽  
pp. 1-8
Author(s):  
Sandrine Mouysset ◽  
Ronan Guivarch ◽  
Joseph Noailles ◽  
Daniel Ruiz
Keyword(s):  
Spectral Clustering ◽  
A Priori ◽  
Quantitative Information ◽  
Microarray Technology ◽  
A Priori Information ◽  
Number Of Clusters ◽  
Microarray Image ◽  
Priori Information ◽  
Parallel Strategy ◽  
Spectral Clustering Method

Microarray technology generates large amounts of expression level of genes to be analyzed simultaneously. This analysis implies microarray image segmentation to extract the quantitative information from spots. Spectral clustering is one of the most relevant unsupervised methods able to gather data without a priori information on shapes or locality. We propose and test on microarray images a parallel strategy for the Spectral Clustering method based on domain decomposition with a criterion to determine the number of clusters.

Bezdek-Type Fuzzified Co-Clustering Algorithm

2015 ◽  
Vol 19 (6) ◽  
pp. 852-860 ◽  
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Suitable Parameter ◽  
Fuzzy Clustering Methods ◽  
Clustering Approach ◽  
Parameter Values ◽  
Vectorial Data

In this study, two co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are proposed for categorical multivariate data. The two proposed algorithms are motivated by the fact that there are only two fuzzy co-clustering methods currently available – entropy regularization and quadratic regularization – whereas there are three fuzzy clustering methods for vectorial data: entropy regularization, quadratic regularization, and Bezdek-type fuzzification. The first proposed algorithm forms the basis of the second algorithm. The first algorithm is a variant of a spherical clustering method, with the kernelization of a maximizing model of Bezdek-type fuzzy clustering with multi-medoids. By interpreting the first algorithm in this way, the second algorithm, a spectral clustering approach, is obtained. Numerical examples demonstrate that the proposed algorithms can produce satisfactory results when suitable parameter values are selected.

scholarly journals Identifying cell types from single-cell data based on similarities and dissimilarities between cells

2021 ◽  
Vol 22 (S3) ◽  
Author(s):  
Yuanyuan Li ◽  
Ping Luo ◽  
Yi Lu ◽  
Fang-Xiang Wu
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Spectral Clustering ◽  
Incidence Matrix ◽  
Expression Patterns ◽  
Cell Types ◽  
Clustering Method ◽  
Different Types ◽  
Cell Data ◽  
Spectral Clustering Method

Abstract Background With the development of the technology of single-cell sequence, revealing homogeneity and heterogeneity between cells has become a new area of computational systems biology research. However, the clustering of cell types becomes more complex with the mutual penetration between different types of cells and the instability of gene expression. One way of overcoming this problem is to group similar, related single cells together by the means of various clustering analysis methods. Although some methods such as spectral clustering can do well in the identification of cell types, they only consider the similarities between cells and ignore the influence of dissimilarities on clustering results. This methodology may limit the performance of most of the conventional clustering algorithms for the identification of clusters, it needs to develop special methods for high-dimensional sparse categorical data. Results Inspired by the phenomenon that same type cells have similar gene expression patterns, but different types of cells evoke dissimilar gene expression patterns, we improve the existing spectral clustering method for clustering single-cell data that is based on both similarities and dissimilarities between cells. The method first measures the similarity/dissimilarity among cells, then constructs the incidence matrix by fusing similarity matrix with dissimilarity matrix, and, finally, uses the eigenvalues of the incidence matrix to perform dimensionality reduction and employs the K-means algorithm in the low dimensional space to achieve clustering. The proposed improved spectral clustering method is compared with the conventional spectral clustering method in recognizing cell types on several real single-cell RNA-seq datasets. Conclusions In summary, we show that adding intercellular dissimilarity can effectively improve accuracy and achieve robustness and that improved spectral clustering method outperforms the traditional spectral clustering method in grouping cells.

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.

scholarly journals Automatic Updates of Transition Potential Matrices in Dempster-Shafer Networks Based on Evidence Inputs

Sensors ◽  
2020 ◽  
Vol 20 (13) ◽  
pp. 3727
Author(s):  
Joel Dunham ◽  
Eric Johnson ◽  
Eric Feron ◽  
Brian German
Keyword(s):  
Sensor Fusion ◽  
A Priori ◽  
Evidential Reasoning ◽  
Unmanned Aerial Systems ◽  
Sufficient Information ◽  
User Input ◽  
Transition Potential ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Aerial Systems

Sensor fusion is a topic central to aerospace engineering and is particularly applicable to unmanned aerial systems (UAS). Evidential Reasoning, also known as Dempster-Shafer theory, is used heavily in sensor fusion for detection classification. High computing requirements typically limit use on small UAS platforms. Valuation networks, the general name given to evidential reasoning networks by Shenoy, provides a means to reduce computing requirements through knowledge structure. However, these networks use conditional probabilities or transition potential matrices to describe the relationships between nodes, which typically require expert information to define and update. This paper proposes and tests a novel method to learn these transition potential matrices based on evidence injected at nodes. Novel refinements to the method are also introduced, demonstrating improvements in capturing the relationships between the node belief distributions. Finally, novel rules are introduced and tested for evidence weighting at nodes during simultaneous evidence injections, correctly balancing the injected evidenced used to learn the transition potential matrices. Together, these methods enable updating a Dempster-Shafer network with significantly less user input, thereby making these networks more useful for scenarios in which sufficient information concerning relationships between nodes is not known a priori.

A Hard C-Means Clustering Algorithm Incorporating Membership KL Divergence and Local Data Information for Noisy Image Segmentation

2017 ◽  
Vol 32 (04) ◽  
pp. 1850012 ◽  
Author(s):  
R. R. Gharieb ◽  
G. Gendy ◽  
H. Selim
Keyword(s):  
Image Segmentation ◽  
Membership Function ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cluster Center ◽  
Local Data ◽  
Cluster Membership ◽  
Kl Divergence ◽  
Clustering Approach ◽  
Center Distance

In this paper, the standard hard C-means (HCM) clustering approach to image segmentation is modified by incorporating weighted membership Kullback–Leibler (KL) divergence and local data information into the HCM objective function. The membership KL divergence, used for fuzzification, measures the proximity between each cluster membership function of a pixel and the locally-smoothed value of the membership in the pixel vicinity. The fuzzification weight is a function of the pixel to cluster-centers distances. The used pixel to a cluster-center distance is composed of the original pixel data distance plus a fraction of the distance generated from the locally-smoothed pixel data. It is shown that the obtained membership function of a pixel is proportional to the locally-smoothed membership function of this pixel multiplied by an exponentially distributed function of the minus pixel distance relative to the minimum distance provided by the nearest cluster-center to the pixel. Therefore, since incorporating the locally-smoothed membership and data information in addition to the relative distance, which is more tolerant to additive noise than the absolute distance, the proposed algorithm has a threefold noise-handling process. The presented algorithm, named local data and membership KL divergence based fuzzy C-means (LDMKLFCM), is tested by synthetic and real-world noisy images and its results are compared with those of several FCM-based clustering algorithms.

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.

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