Quanxue Gao;Fangfang Li;Qianqian Wang;Xinbo Gao;Dacheng Tao
{"title":"基于流形的多视图k均值","authors":"Quanxue Gao;Fangfang Li;Qianqian Wang;Xinbo Gao;Dacheng Tao","doi":"10.1109/TPAMI.2024.3521022","DOIUrl":null,"url":null,"abstract":"Although numerous clustering algorithms have been developed, many existing methods still rely on the <italic>K</i>-means technique to identify clusters of data points. However, the performance of <italic>K</i>-means is highly dependent on the accurate estimation of cluster centers, which is challenging to achieve optimally. Furthermore, it struggles to handle linearly non-separable data. To address these limitations, from the perspective of manifold learning, we reformulate multi-view <italic>K</i>-means into a manifold-based multi-view clustering formulation that eliminates the need for computing centroid matrix. This reformulation ensures consistency between the manifold structure and the data labels. Building on this, we propose a novel multi-view <italic>K</i>-means model incorporating the tensor rank constraint. Our model employs the indicator matrices from different views to construct a third-order tensor, whose rank is minimized via the tensor Schatten <italic>p</i>-norm. This approach effectively leverages the complementary information across views. By utilizing different distance functions, our proposed model can effectively handle linearly non-separable data. Extensive experimental results on multiple databases demonstrate the superiority of our proposed model.","PeriodicalId":94034,"journal":{"name":"IEEE transactions on pattern analysis and machine intelligence","volume":"47 4","pages":"3175-3182"},"PeriodicalIF":0.0000,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Manifold Based Multi-View K-Means\",\"authors\":\"Quanxue Gao;Fangfang Li;Qianqian Wang;Xinbo Gao;Dacheng Tao\",\"doi\":\"10.1109/TPAMI.2024.3521022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Although numerous clustering algorithms have been developed, many existing methods still rely on the <italic>K</i>-means technique to identify clusters of data points. However, the performance of <italic>K</i>-means is highly dependent on the accurate estimation of cluster centers, which is challenging to achieve optimally. Furthermore, it struggles to handle linearly non-separable data. To address these limitations, from the perspective of manifold learning, we reformulate multi-view <italic>K</i>-means into a manifold-based multi-view clustering formulation that eliminates the need for computing centroid matrix. This reformulation ensures consistency between the manifold structure and the data labels. Building on this, we propose a novel multi-view <italic>K</i>-means model incorporating the tensor rank constraint. Our model employs the indicator matrices from different views to construct a third-order tensor, whose rank is minimized via the tensor Schatten <italic>p</i>-norm. This approach effectively leverages the complementary information across views. By utilizing different distance functions, our proposed model can effectively handle linearly non-separable data. Extensive experimental results on multiple databases demonstrate the superiority of our proposed model.\",\"PeriodicalId\":94034,\"journal\":{\"name\":\"IEEE transactions on pattern analysis and machine intelligence\",\"volume\":\"47 4\",\"pages\":\"3175-3182\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE transactions on pattern analysis and machine intelligence\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10812771/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE transactions on pattern analysis and machine intelligence","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10812771/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Although numerous clustering algorithms have been developed, many existing methods still rely on the K-means technique to identify clusters of data points. However, the performance of K-means is highly dependent on the accurate estimation of cluster centers, which is challenging to achieve optimally. Furthermore, it struggles to handle linearly non-separable data. To address these limitations, from the perspective of manifold learning, we reformulate multi-view K-means into a manifold-based multi-view clustering formulation that eliminates the need for computing centroid matrix. This reformulation ensures consistency between the manifold structure and the data labels. Building on this, we propose a novel multi-view K-means model incorporating the tensor rank constraint. Our model employs the indicator matrices from different views to construct a third-order tensor, whose rank is minimized via the tensor Schatten p-norm. This approach effectively leverages the complementary information across views. By utilizing different distance functions, our proposed model can effectively handle linearly non-separable data. Extensive experimental results on multiple databases demonstrate the superiority of our proposed model.