Spectral Clustering Based on Sparse Representation

2014 ◽  
Vol 556-562 ◽  
pp. 3822-3826
Author(s):  
Chen Xiao Hu ◽  
Xian Chun Zou
Keyword(s):  
Sparse Representation ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Similarity Metrics ◽  
Distance Metrics ◽  
Information Propagation ◽  
Discriminative Ability ◽  
Two Samples ◽  
Better Than

Spectral clustering is an efficient clustering algorithm based the information propagation between neighborhood nodes. Its performance is largely dependent on the distance metrics, thus it is possible to boost its performance by adapting more reliable distance metric. Given the advantages of sparse representation in discriminative ability, robust to noisy and more faithfully to measure the similarity between two samples, we propose an sparse representation algorithm based on sparse representation. The experimental study on several datasets shows that, the proposed algorithm performs better than the sparse clustering algorithms based on other similarity metrics.

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.

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.

scholarly journals An Improved Spectral Clustering Community Detection Algorithm Based on Probability Matrix

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Shuxia Ren ◽  
Shubo Zhang ◽  
Tao Wu
Keyword(s):  
Community Detection ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Transition Probability ◽  
Clustering Algorithms ◽  
Detection Algorithm ◽  
Community Information ◽  
The Mean ◽  
Community Detection Algorithm ◽  
Spectral Clustering Algorithm

The similarity graphs of most spectral clustering algorithms carry lots of wrong community information. In this paper, we propose a probability matrix and a novel improved spectral clustering algorithm based on the probability matrix for community detection. First, the Markov chain is used to calculate the transition probability between nodes, and the probability matrix is constructed by the transition probability. Then, the similarity graph is constructed with the mean probability matrix. Finally, community detection is achieved by optimizing the NCut objective function. The proposed algorithm is compared with SC, WT, FG, FluidC, and SCRW on artificial networks and real networks. Experimental results show that the proposed algorithm can detect communities more accurately and has better clustering performance.

Texture Image Segmentation Using Affinity Propagation and Spectral Clustering

2015 ◽  
Vol 29 (05) ◽  
pp. 1555009 ◽  
Author(s):  
Hui Du ◽  
Yuping Wang ◽  
Xiaopan Dong
Keyword(s):  
Image Segmentation ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Computational Cost ◽  
Affinity Propagation ◽  
Texture Image ◽  
Texture Image Segmentation ◽  
Two Phases ◽  
Representative Points

Clustering is a popular and effective method for image segmentation. However, existing cluster methods often suffer the following problems: (1) Need a huge space and a lot of computation when the input data are large. (2) Need to assign some parameters (e.g. number of clusters) in advance which will affect the clustering results greatly. To save the space and computation, reduce the sensitivity of the parameters, and improve the effectiveness and efficiency of the clustering algorithms, we construct a new clustering algorithm for image segmentation. The new algorithm consists of two phases: coarsening clustering and exact clustering. First, we use Affinity Propagation (AP) algorithm for coarsening. Specifically, in order to save the space and computational cost, we only compute the similarity between each point and its t nearest neighbors, and get a condensed similarity matrix (with only t columns, where t << N and N is the number of data points). Second, to further improve the efficiency and effectiveness of the proposed algorithm, the Self-tuning Spectral Clustering (SSC) is used to the resulted points (the representative points gotten in the first phase) to do the exact clustering. As a result, the proposed algorithm can quickly and precisely realize the clustering for texture image segmentation. The experimental results show that the proposed algorithm is more efficient than the compared algorithms FCM, K-means and SOM.

scholarly journals A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2021 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Public Dataset ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, a traditional machine learning method, plays a significant role in data analysis. Most clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although the Elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on the manual identification of the elbow points on the visualization curve. Thus, experienced analysts cannot clearly identify the elbow point from the plotted curve when the plotted curve is fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to yield a statistical metric that estimates an optimal cluster number when clustering on a dataset. First, the average degree of distortion obtained by the Elbow method is normalized to the range of 0 to 10. Second, the normalized results are used to calculate the cosine of intersection angles between elbow points. Third, this calculated cosine of intersection angles and the arccosine theorem are used to compute the intersection angles between elbow points. Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a well-known public dataset (Iris Dataset) demonstrated that the estimated optimal cluster number obtained by our newly proposed method is better than the widely used Silhouette method.

scholarly journals A Spectral Clustering Algorithm Improved by P Systems

2018 ◽  
Vol 13 (5) ◽  
pp. 759-771 ◽  
Author(s):  
Guangchun Chen ◽  
Juan Hu ◽  
Hong Peng ◽  
Jun Wang ◽  
Xiangnian Huang
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Membrane Computing ◽  
Clustering Algorithms ◽  
P System ◽  
Comparison Results ◽  
Clustering Effect ◽  
Computing Framework ◽  
Spectral Clustering Algorithm ◽  
Selection Of

Using spectral clustering algorithm is diffcult to find the clusters in the cases that dataset has a large difference in density and its clustering effect depends on the selection of initial centers. To overcome the shortcomings, we propose a novel spectral clustering algorithm based on membrane computing framework, called MSC algorithm, whose idea is to use membrane clustering algorithm to realize the clustering component in spectral clustering. A tissue-like P system is used as its computing framework, where each object in cells denotes a set of cluster centers and velocity-location model is used as the evolution rules. Under the control of evolutioncommunication mechanism, the tissue-like P system can obtain a good clustering partition for each dataset. The proposed spectral clustering algorithm is evaluated on three artiffcial datasets and ten UCI datasets, and it is further compared with classical spectral clustering algorithms. The comparison results demonstrate the advantage of the proposed spectral clustering algorithm.

Fuzzy Similarity Measure Based Spectral Clustering Framework for Noisy Image Segmentation

2017 ◽  
Vol 25 (04) ◽  
pp. 649-673 ◽  
Author(s):  
Subhanshu Goyal ◽  
Sushil Kumar ◽  
M. A. Zaveri ◽  
A. K. Shukla
Keyword(s):  
Similarity Measure ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Spatial Information ◽  
Clustering Algorithms ◽  
Gaussian Kernel ◽  
Similarity Matrix ◽  
Fuzzy Similarity ◽  
Level Information ◽  
Fuzzy C Means Clustering

In recent times, graph based spectral clustering algorithms have received immense attention in many areas like, data mining, object recognition, image analysis and processing. The commonly used similarity measure in the clustering algorithms is the Gaussian kernel function which uses sensitive scaling parameter and when applied to the segmentation of noise contaminated images leads to unsatisfactory performance because of neglecting the spatial pixel information. The present work introduces a novel framework for spectral clustering which embodied local spatial information and fuzzy based similarity measure to tackle the above mentioned issues. In our approach, firstly we filter the noise components from original image by using the spatial and gray–level information. The similarity matrix is then constructed by employing a similarity measure which takes into account the fuzzy c-partition matrix and vectors of the cluster centers obtained by fuzzy c-means clustering algorithm. In the last step, spectral clustering technique is realized on derived similarity matrix to obtain the desired segmentation result. Experimental results on segmentation of synthetic and Berkeley benchmark images with noise demonstrates the effectiveness and robustness of the proposed method, giving it an edge over the clustering based segmentation method reported in the literature.

An Improved Spectral Clustering Algorithm Using Minimum Maximum Principle

2012 ◽  
Vol 182-183 ◽  
pp. 1881-1884
Author(s):  
Xiu Fang Xu ◽  
Sen Xu ◽  
Tian Zhou
Keyword(s):  
Maximum Principle ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Document Clustering ◽  
Experimental Results ◽  
Eigenvalue Decomposition ◽  
Spectral Algorithm ◽  
Low Dimensional ◽  
Spectral Clustering Algorithm ◽  
Better Than

In this paper a novel document clustering spectral algorithm is proposed, which uses a minimum maximum principle. Firstly the low dimensional embedding of documents is attained by eigenvalue decomposition, and then a minimum maximum principle is used to get the initial seeds for k-means algorithm. Finally, K-means algorithm is performed to get the clustering results. Experimental results show that the clustering results found by this method is better than traditional clustering algorithm.

scholarly journals Response-Only Damage Detection Approach of CFRP Gas Tanks Using Clustering and Vibrational Measurements

2021 ◽  
Vol 2 (4) ◽  
pp. 1057-1072
Author(s):  
Ilias Zacharakis ◽  
Dimitrios Giagopoulos
Keyword(s):  
Damage Detection ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Aerospace Industry ◽  
Power Spectral ◽  
Detection Approach ◽  
Type V ◽  
Experimental Structure ◽  
Selection Of

The advancements in the automotive, aviation, and aerospace industry have led to an increased usage of CFRP high-pressure gas tanks. In order to avoid any fatal accidents, the inspection procedures require accuracy, but also practicality, to be used in the industry. The presented work focuses on response-only metrics from vibrational experimental measurements of the CFRP tank. The power spectral density and transmittance function curves are both compared for the accuracy and ability to be used as metrics for damage detection. Along with the selection of the proper metric, an appropriate clustering algorithm that can accurately group similar states of the structure is of high importance. Two clustering algorithms, agglomerative hierarchical and spectral clustering, are employed and compared for their performance. A small Type V CFRP tank is used as an experimental structure on this benchmark problem. In order to create realistic material damage, the tank is placed on an impact system multiple times where different damage magnitudes are created. After each new state and damage magnitude on the tank, vibrational experimental data are collected. Using the collected data, all the combinations of the mentioned metrics and algorithms are executed and properly compared to evaluate their accuracy.

scholarly journals Service Partition Method Based on Particle Swarm Fuzzy Clustering

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hong Xia ◽  
Qingyi Dong ◽  
Hui Gao ◽  
Yanping Chen ◽  
ZhongMin Wang
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Particle Swarm ◽  
Cluster Center ◽  
Fuzzy Clustering Algorithm ◽  
Partition Method ◽  
Service Data ◽  
Optimal Cluster ◽  
Better Than

It is difficult to accurately classify a service into specific service clusters for the multirelationships between services. To solve this problem, this paper proposes a service partition method based on particle swarm fuzzy clustering, which can effectively consider multirelationships between services by using a fuzzy clustering algorithm. Firstly, the algorithm for automatically determining the number of clusters is to determine the number of service clusters based on the density of the service core point. Secondly, the fuzzy c -means combined with particle swarm optimization algorithm to find the optimal cluster center of the service. Finally, the fuzzy clustering algorithm uses the improved Gram-cosine similarity to obtain the final results. Extensive experiments on real web service data show that our method is better than mainstream clustering algorithms in accuracy.

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