Abstract
Density-based clustering is a fundamental and effective tool for recognizing connectivity structure. The density peak, the data object with the maximum density within a predefined sphere, plays a critical role. However, Density Peak Estimation (DPE), the process of identifying the nearest denser relation for each data object, is extremely expensive. The state-of-the-art accelerating solutions that utilize the index are still resource-consuming for large-scale data. In this work, we propose Ultra-DPC, an ultra-scalable and index-free Density Peak Clustering for Euclidean space, to address the challenges above.
We theoretically study the correlation between two seemly different clustering algorithms: p-means and density-based clustering, and provide a novel p-means density estimator. Based on this, first, p-means is used on a set of samples S to find a set of p Local Density Peaks (LDP), where \(p \ll N\), and N is the number of data objects. Second, so as an informative LDP-wise affinity graph is conducted, and then it is enriched by a Random Walk process to incorporate the clues from the non-LDP objects. Third, the importance of LDP is estimated and the most important ones are chosen as the seeds. Finally, the class memberships of the remaining objects are determined according to their relations to the LDP. Ultra-DPC is the fastest DPE method but without reducing the quality of clustering. The evaluation of different medium- and large-scale datasets demonstrates both the efficiency and effectiveness of Ultra-DPC over the state-of-the-art density-based methods.
L. Ma and G. Yang—Equal Contribution.
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References
Barnes, G., Feige, U.: Short random walks on graphs. In: STOC, pp. 728–737. ACM (1993)
Brakensiek, J., Guruswami, V.: Bridging between 0/1 and linear programming via random walks. In: STOC, pp. 568–577. ACM (2019)
Chan, T.H., Guerquin, A., Hu, S., Sozio, M.: Fully dynamic k-center clustering with improved memory efficiency. IEEE Trans. Knowl. Data Eng. 34(7), 3255–3266 (2022)
Chen, X., Cai, D.: Large scale spectral clustering with landmark-based representation. In: AAAI. AAAI Press (2011)
Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995)
Cohen, G., Afshar, S., Tapson, J., van Schaik, A.: EMNIST: extending MNIST to handwritten letters. In: IJCNN, pp. 2921–2926. IEEE (2017)
Du, M., Ding, S., Jia, H.: Study on density peaks clustering based on k-nearest neighbors and principal component analysis. Knowl. Based Syst. 99, 135–145 (2016)
Ester, M., Kriegel, H.P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: KDD, pp. 226–231 (1996)
Fränti, P., Virmajoki, O.: Iterative shrinking method for clustering problems. Pattern Recognit. 39(5), 761–775 (2006)
Hartigan, J.A., Wong, M.A.: Algorithm as 136: a k-means clustering algorithm. J. Roy. Stat. Soc. Ser. C (Appl. Stat.) 28(1), 100–108 (1979)
Hastie, T., Friedman, J.H., Tibshirani, R.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, Cham (2001). https://doi.org/10.1007/978-0-387-84858-7
Huang, D., Wang, C., Peng, H., Lai, J., Kwoh, C.: Enhanced ensemble clustering via fast propagation of cluster-wise similarities. IEEE TSMC. Syst. 51(1), 508–520 (2021)
Huang, D., Wang, C., Wu, J., Lai, J., Kwoh, C.: Ultra-scalable spectral clustering and ensemble clustering. TKDE 32(6), 1212–1226 (2020)
Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)
Hull, J.J.: A database for handwritten text recognition research. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 550–554 (1994)
Jiang, H., Jang, J., Kpotufe, S.: Quickshift++: Provably good initializations for sample-based mean shift. In: ICML, vol. 80, pp. 2299–2308. PMLR (2018)
Kriegel, H., Schubert, E., Zimek, A.: The (black) art of runtime evaluation: Are we comparing algorithms or implementations? Knowl. Inf. Syst. 52(2), 341–378 (2017)
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)
Liu, B., Bai, B., Xie, W., Guo, Y., Chen, H.: Task-optimized user clustering based on mobile app usage for cold-start recommendations. In: KDD, pp. 3347–3356. ACM (2022)
Liu, R., Wang, H., Yu, X.: Shared-nearest-neighbor-based clustering by fast search and find of density peaks. Inf. Sci. 450, 200–226 (2018)
Loosli, G., Canu, S., Bottou, L.: Training invariant support vector machines using selective sampling. In: Large Scale Kernel Machines, vol. 2 (2007)
MacQueen, J.: Classification and analysis of multivariate observations. In: 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
McInnes, L., Healy, J.: UMAP: uniform manifold approximation and projection for dimension reduction. CoRR abs/1802.03426 (2018)
Mohan, M., Monteleoni, C.: Beyond the nyström approximation: speeding up spectral clustering using uniform sampling and weighted kernel k-means. In: IJCAI (2017)
Najafi, M., He, L., Yu, P.S.: Outlier-robust multi-view subspace clustering with prior constraints. In: ICDM, pp. 439–448. IEEE (2021)
Nguyen, X.V., Epps, J., Bailey, J.: Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. J. Mach. Learn. Res. 11, 2837–2854 (2010)
Paudel, B., Bernstein, A.: Random walks with erasure: diversifying personalized recommendations on social and information networks. In: WWW, pp. 2046–2057. ACM (2021)
Rasool, Z., Zhou, R., Chen, L., Liu, C., Xu, J.: Index-based solutions for efficient density peak clustering. IEEE Trans. Knowl. Data Eng. 34(5), 2212–2226 (2022)
Rice, J.A.: Mathematical statistics and data analysis. Cengage Learning (2006)
Rodriguez, A., Laio, A.: Clustering by fast search and find of density peaks. Science 344(6191), 1492–1496 (2014)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)
Vedaldi, A., Soatto, S.: Quick shift and kernel methods for mode seeking. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5305, pp. 705–718. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88693-8_52
Yang, G., et al.: Litewsec: a lightweight framework for web-scale spectral ensemble clustering. In: TKDE, pp. 1–12 (2023)
Yang, G., Deng, S., Yang, Y., Gong, Z., Chen, X., Hao, Z.: LiteWSC: a lightweight framework for web-scale spectral clustering. In: Bhattacharya, A., et al. (eds.) DASFAA. LNCS, vol. 13246, pp. 556–573. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-00126-0_40
Yang, G., et al.: RESKM: a general framework to accelerate large-scale spectral clustering. Pattern Recogn. 137, 109275 (2022)
Yang, G., Lv, H., Yang, Y., Gong, Z., Chen, X., Hao, Z.: FastDEC: clustering by fast dominance estimation. In: Amini, M.R., Canu, S., Fischer, A., Guns, T., Kralj Novak, P., Tsoumakas, G. (eds.) ECML-PKDD. LNCS, vol. 13713. Springer, Cham (2022)
Yang, Y., et al.: Graphlshc: towards large scale spectral hypergraph clustering. Inf. Sci. 544, 117–134 (2021)
Zheng, X., Ren, C., Yang, Y., Gong, Z., Chen, X., Hao, Z.: QuickDSC: clustering by quick density subgraph estimation. Inf. Sci. 581, 403–427 (2021)
Acknowledgments
This work was supported by National Key D&R Program of China (2019YFB1600704, 2021ZD0111501), NSFC (61603101, 61876043, 61976052, 71702065), NSF of Guangdong Province (2021A1515011941), State’s Key Project of Research and Development Plan (2019YFE0196400), NSF for Excellent Young Scholars (62122022), Guangzhou STIC (EF005/FST-GZG/2019/GSTIC), NSFC & Guangdong Joint Fund (U1501254), the Science and Technology Development Fund, Macau SAR (0068/2020/AGJ, SKL-IOTSC(UM)-2021–2023, GDST (2020B1212030003), MYRG2022-00192-FST, Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong, Shenzhen (B10120210117-OF09).
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Ma, L., Yang, G., Chen, X., Yang, Y., Gong, Z., Hao, Z. (2024). Ultra-DPC: Ultra-scalable and Index-Free Density Peak Clustering. In: Song, X., Feng, R., Chen, Y., Li, J., Min, G. (eds) Web and Big Data. APWeb-WAIM 2023. Lecture Notes in Computer Science, vol 14334. Springer, Singapore. https://doi.org/10.1007/978-981-97-2421-5_10
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