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MPC: A Novel Internal clustering validity index Based on Midpoint-Involved Distance 1

23rd International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP)

作者： Zuo, Yating Ma, Zhujuan Zhu, Erzhou Anhui Univ Sch Comp Sci & Technol Hefei 230601 Peoples R China Anhui Xinhua Univ Sch Big Data & Artificial Intelligence Hefei 230088 Peoples R China

ISBN: (数字)9789819707980

ISBN: (纸本)9789819707973;9789819707980

As one of the most import machine learning technique, clustering is widely used in many data classification areas. Due to the unsupervised learning feature, the quality of the clustering results needed to be evaluated. In this paper, the MPdist (midpoint-involved distance) based on the midpoint of centers between two clusters is firstly defined to measure the inter-cluster separation. Then, the MPC (MPdist based clustering validity index), a novel internal clustering validity index based on the combination of the new defined inner-cluster compactness and the inter-cluster separation, is proposed to effectively evaluate the validity of the clustering results of many clustering algorithms. Experimental results on testing many types of datasets have demonstrated that the MPC index proposed in this paper is able to quickly handle datasets like spherical datasets, non-spherical datasets and real large-scale datasets.

关键词： clustering validity index clustering algorithm data mining

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IMI2: A fuzzy clustering validity index for multiple imbalanced clusters

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EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartE期238卷

作者： Liu, Fu Wang, Jingyuan Liu, Yun Jilin Univ Coll Commun Engn Changchun Peoples R China Jilin Univ Sch Artificial Intelligence Changchun Peoples R China Jilin Engn Normal Univ Sch Elect & Informat Engn Changchun Peoples R China

The fuzzy c-means (FCM) clustering algorithm requires the pre-definition of the number of clusters. When used for imbalanced datasets, FCM tends to equalize the sizes of clusters and thus produces bad clustering results. Although clustering validity index (CVI) is commonly employed to determine the number of clusters, it is often ineffective for bad clustering results of FCM. To address this issue, we have previously proposed a fuzzy CVI, namely IMI, for imbalanced datasets. However, IMI encounters issues when the number of clusters exceeds three, as it tends to divide the majority clusters into multiple subclusters. In this paper, a novel CVI, IMI2, is proposed to enhance the performance of IMI. IMI2 adopts a two-step clustering algorithm that merges some clusters from the IMI result based on their separation values. This enhancement overcomes the limitations of IMI, rendering IMI2 an excellent CVI capable of accurately determining the number of clusters for datasets with multiple imbalanced clusters. The performance of IMI2 is evaluated using several synthetic and UCI datasets. The results demonstrate that IMI2 outperforms other methods in terms of its superior performance for multiple imbalanced clusters. IMI2 retains the good performance of IMI for datasets with two or three clusters, while significantly improving it for multiple imbalanced clusters.

关键词： clustering clustering validity index FCM Imbalanced datasets Merging

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A new robust fuzzy clustering validity index for imbalanced data sets

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INFORMATION SCIENCES 2021年 547卷 579-591页

作者： Liu, Yun Jiang, Yanfang Hou, Tao Liu, Fu Jilin Univ Coll Commun Engn Changchun Peoples R China First Hosp Jilin Univ Changchun Peoples R China

Determining the number of clusters of a data set, which is usually evaluated by a clustering validity index (CVI), is a significant issue in clustering analysis. While several CVIs have been proposed, the imperfect clustering results of the fuzzy c-means (FCM) clustering algo-rithm on imbalanced data sets may affect their decisions. To address this problem, the impact of imperfect clustering results on the traditional CVI is first analyzed, and it is found that the distance between two imbalanced clusters becomes closer, which will subsequently impact the separation metric. Inspired by this, a new fuzzy CVI called the imbalanced index (IMI) is proposed in this paper. IMI is the ratio of the fuzzy compactness and separation metrics. The main characteristic of IMI is the new definition of the separation metric, in which the imbalance ratio of two clusters is used to enlarge the distance between their centers. IMI is then employed to evaluate the clustering results of FCM on a variety of data sets, and is compared with several well-known CVIs. The experimental results demonstrate that IMI is robust to the imperfect clustering results of FCM caused by imbalanced data distributions and achieves superior performance as compared to other CVIs. (C) 2020 Elsevier Inc. All rights reserved.

关键词： clustering analysis clustering validity index Fuzzy c-means method Imbalanced data sets

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Determination of hyperparameter and similarity norm for electrical tomography algorithm using clustering validity index

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MEASUREMENT 2023年第1期216卷

作者： Dong, Fanpeng Yue, Shihong Liu, Xuezhen Wang, Huaxiang Tianjin Univ Sch Elect Engn & Automat Tianjin 300072 Peoples R China

Electrical tomography (ET) is an advanced visualization technique owing to low cost, fast response, noninvasiveness and non-radiation advantages. ET must depend on an imaging algorithm to visually reconstruct all objects, and almost all algorithms with high spatial resolution contain a vital parameter at least. Moreover, the similarity norm plays an important role in the ET imaging process. If they cannot accurately be determined, the ET reconstruction quality is not guaranteed. In this paper, according the clustering mechanism of the ET process, a clustering validity index (CVI) is used to determine both the hyperparameter and similarity norm in the ET algorithm, while CVI originally is used to find the optimal number of clusters among various candidates. The within-cluster and between-cluster distances in CVI are newly defined by not only the grey level but also the neighboring information of any pixel in an ET image. Two representative ET algorithms act for a general framework to validate the proposed method along various hyperparameters and similarity norms. Experimental results show that the proposed method can improve the spatial resolution of the ET image by finding optimal parameter and the similarity norm.

关键词： Electrical tomography Hyperparameter Similarity norm clustering validity index

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Unsupervised video summarization via clustering validity index

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MULTIMEDIA TOOLS AND APPLICATIONS 2020年第45-46期79卷 33417-33430页

作者： Zhao, Ye Guo, Yanrong Sun, Rui Liu, Zhengqiong Guo, Dan Hefei Univ Technol Hefei 230601 Anhui Peoples R China

Although lots of the prior works have been proposed to solve the representative selection problem of video summarization, the main difficulty is still left for determining the optimal representatives' number of the raw videos that are not annotated. In this paper, we propose an unsupervised video summarization method by motion-based frame selection and a novel clustering validity indexes to determine the optimal representatives of the original video. The proposed framework segments shots and selects candidate frames by evaluating their forward and backward motion and can automatically select representatives to highlight all the significant visual properties. Shots are segmented uniformly and the frame with the largest motion is extracted in each segmentation to form the video candidate frame subset. Then Affinity Propagation combined with the validity index is used to automatically select the optimal representatives from the candidate frame subset. Our experimental result on several benchmark datasets demonstrates the robustness and effectiveness of our proposed method.

关键词： Video summarization Frame selection Representative selection clustering validity index

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Fast and stable clustering analysis based on Grid-mapping K-means algorithm and new clustering validity index

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NEUROCOMPUTING 2019年 363卷 149-170页

作者： Zhu, Erzhou Zhang, Yuanxiang Wen, Peng Liu, Feng Anhui Univ Sch Comp Sci & Technol Hefei 230601 Anhui Peoples R China

As a classical data analysis technique, clustering plays the important role in identifying natural structures of target datasets. However, many of the existing clustering methods, including clustering algorithms and clustering validity indexes (CVIs), are still suffering from problems of low efficiency, poor clustering accuracy, poor stability and more sensitivity to noise points. In this paper, by mapping datasets to grids, the Grid-K-means algorithm is firstly proposed to overcome drawbacks of the traditional K-means algorithm. Then, by utilizing grid points as the weighted representative points to process datasets, a new clustering validity index (BCVI) is designed to better evaluate the quality of clustering results generated by the Grid-K-means algorithm. Based on the monotonous feature of BCVI and the linear combination of intra-cluster compactness and inter-cluster separation of clusters, BCVI consumes much lower time cost in finding the optimal clustering number (K-opt) than the commonly used method that utilizes the empirical rule K-max <=root n to calculate the K-opt. Experimental results on testing many types of datasets have demonstrated that the Grid-K-means algorithm is faster and more accurate than the traditional ones. Meanwhile, the experimental results on testing BCVI and seven existing CVIs have shown that the new BCVI is superior to the traditional ones in terms of clustering stability and data processing speed. (C) 2019 Elsevier B.V. All rights reserved.

关键词： clustering analysis Grid clustering algorithm Partitional clustering algorithm clustering validity index

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Effective Hierarchical Cluster Analysis Based on New clustering validity index

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电脑学刊 2020年第1期31卷 119-133页

作者： Er-Zhou Zhu Yin-Yin Ju Da-Wei Liu Yang Li Dong Liu Zhu-Juan Ma

clustering analysis plays an important role in finding natural structures of datasets. It is widely used in many areas, such as data mining, pattern recognition and image processing. By generating a set of nested partitions of datasets, hierarchical clustering algorithms provide more information than partitional clustering algorithms. However, due to the generated clustering hierarchies are too complex to analyze, many existing hierarchical clustering algorithms cannot properly process many non-spherical and overlapping datasets. clustering validity index is the key technique for forming the optimal clustering partitions and evaluating the clustering results generated by clustering algorithms. However, many existing clustering validity indexes suffer from instability and narrow range of applications. Aiming at these problems, the traditional Average-Linkage hierarchical clustering algorithm is firstly improved for better processing the above irregular datasets. Then, a new clustering validity index (MSTI) is defined to stably and effectively evaluate the clustering results of the improved algorithm. Finally, the new algorithm for determining the optimal clustering number is designed by leveraging the improved Average- Linkage hierarchical clustering algorithm and the new MSTI. Experimental results have shown that our new clustering method is stable, accurate and efficient in processing many kinds of datasets.

关键词： clustering validity index hierarchical clustering optimal clustering number

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An effective partitional clustering algorithm based on new clustering validity index

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APPLIED SOFT COMPUTING 2018年 71卷 608-621页

作者： Zhu, Erzhou Ma, Ruhui Anhui Univ Sch Comp Sci & Technol Hefei 230601 Anhui Peoples R China Shanghai Jiao Tong Univ Dept Comp Sci & Engn Shanghai 200240 Peoples R China

As an unsupervised pattern classification method, clustering partitions the input datasets into groups or clusters. It plays an important role in identifying the natural structure of the target datasets. Now, it has been widely used in data mining, pattern recognition, image processing and so on. However, due to different settings of the parameters and random selection of initial centers, traditional clustering algorithms may produce different clustering partitions for a single dataset. clustering validity index (CVI) is an important method for evaluating the effect of clustering results generated by clustering algorithms. However, many of the existing CVIs suffer from complex computation, low time efficiency and narrow range of applications. In order to make clustering algorithms more stable, traditional K -means is firstly improved by the density parameters based initial center selection method other than randomly selecting initial centers. Then, in order to enlarge the application range of clustering and better evaluate the clustering partition results, a new variance based clustering validity index (VCVI) from the point of view of spatial distribution of datasets is designed. Finally, a new partitional clustering algorithm integrated with the improved K -means algorithm and the newly introduced VCVI is designed to optimize and determine the optimal clustering number (Kopf) for a wide range of datasets. Furthermore, the commonly used empirical rule Kmax 5.,/T -t is reasonably explained by the newly designed VCVI. The new algorithm integrated with VCVI is compared with traditional algorithms integrated with five commonly used CVIs. The experimental results show that our new clustering method is more accurate and stable while consuming relatively lower running time. (C) 2018 Elsevier B.V. All rights reserved.

关键词： K-means Partitional clustering clustering validity index

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Effective and Optimal clustering Based on New clustering validity index 22

Effective and Optimal Clustering Based on New Clustering Val...

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22nd IEEE International Conference on Computer Supported Cooperative Work in Design (CSCWD)

作者： Zhu, Erzhou Li, Peng Ma, Zhujuan Li, Xuejun Liu, Feng Anhui Univ Sch Comp Sci & Technol Hefei Anhui Peoples R China Anhui Agr Univ Sch Econ & Technol Hefei Anhui Peoples R China

ISBN: (纸本)9781538614822

As an important tool, clustering validity index (CVI) is usually used to evaluate the validity of the clustering results and determine the optimal clustering number (K-opt). However, the existing CVIs have some shortcomings, such as too complex calculation, low computational efficiency and narrow range of applications. Aiming at these problems, an improved K-means algorithm that uses density parameters for initial centers selection is firstly proposed to make the results of traditional clustering algorithms more stable. Then, a new variance based clustering validity index (VCVI) from the perspective of spatial distribution of data sets is introduced to extend the application of the partitional clustering algorithms and better evaluate the effect of clustering results. Finally, a new algorithm integrated with the improved K-means algorithm and the new proposed VCVI is designed to effectively determine the K(opt )and the optimal clustering partition. The experimental results have shown that the new proposed algorithm with VCVI is effective in forming the K(opt )and the optimal clustering partition for the tested data sets.

关键词： optimal clustering number partitional clustering algorithm clustering validity index K-value optimization

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MSTI: A New clustering validity index for Hierarchical clustering 4

MSTI: A New Clustering Validity Index for Hierarchical Clust...

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4th Annual International Conference on Network and Information Systems for Computers (ICNISC)

作者： Li, Peng Liu, Feng Zhua, Er-Zhou Anhui Univ Sch Comp Sci & Technol Natl Nat Sci Fdn China Hefei Peoples R China

ISBN: (纸本)9781538669563

The clustering validity index (CVI) is an important tool to measure the clustering effect and determine the optimal clustering number (K-opt). However, most of the existing CVIs cannot properly deal with some non-spherical distributions data sets and data sets with great differences in sample size and density among clusters. This paper proposes a revised hierarchical clustering algorithm based on the new clustering validity index (MSTI). Firstly, the new index uses spanning tree related knowledge to construct minimum spanning tree in inter clusters and maximum spanning tree in intra clusters. Then, the new MSTI is defined as the ratio of the cost of the minimum spanning tree among clusters to the cost of maximum spanning tree in each cluster. Under this circumstance, the K-opt is acquired when the above ratio reaches the biggest value. Finally, the new algorithm for optimizing and determining the K-opt is designed by leveraging the Average-Linkage hierarchical clustering algorithm and the new proposed MSTI. We compared the new algorithm integrated with MSTI with the traditional algorithms integrated with 4 commonly used CVIs by utilizing 3 simulated datasets and 3 UCI datasets. The experimental results have shown that the new proposed algorithm integrated with MSTI is effective and accurate in determining the K-opt and the optimal clustering partition for all the tested data sets.

关键词： optimal clustering number clustering validity index hierarchical clustering cost spanning tree

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