1. bookVolume 2021 (2021): Issue 4 (October 2021)
Journal Details
License
Format
Journal
eISSN
2299-0984
First Published
16 Apr 2015
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4 times per year
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English
access type Open Access

SoK: Efficient Privacy-preserving Clustering

Published Online: 23 Jul 2021
Page range: 225 - 248
Received: 28 Feb 2021
Accepted: 16 Jun 2021
Journal Details
License
Format
Journal
eISSN
2299-0984
First Published
16 Apr 2015
Publication timeframe
4 times per year
Languages
English
Abstract

Clustering is a popular unsupervised machine learning technique that groups similar input elements into clusters. It is used in many areas ranging from business analysis to health care. In many of these applications, sensitive information is clustered that should not be leaked. Moreover, nowadays it is often required to combine data from multiple sources to increase the quality of the analysis as well as to outsource complex computation to powerful cloud servers. This calls for efficient privacy-preserving clustering. In this work, we systematically analyze the state-of-the-art in privacy-preserving clustering. We implement and benchmark today’s four most efficient fully private clustering protocols by Cheon et al. (SAC’19), Meng et al. (ArXiv’19), Mohassel et al. (PETS’20), and Bozdemir et al. (ASIACCS’21) with respect to communication, computation, and clustering quality. We compare them, assess their limitations for a practical use in real-world applications, and conclude with open challenges.

Keywords

[1] Z. Qian, Z. M. Mao, Y. Xie, and F. Yu, “On Network-level Clusters for Spam Detection.” in NDSS, 2010. Search in Google Scholar

[2] K. Kourou, T. P. Exarchos, K. P. Exarchos, M. V. Karamouzis, and D. I. Fotiadis, “Machine learning applications in cancer prognosis and prediction,” Computational and Structural Biotechnology Journal, 2015.10.1016/j.csbj.2014.11.005 Search in Google Scholar

[3] M. Ahmed, A. N. Mahmood, and M. R. Islam, “A Survey of Anomaly Detection Techniques in Financial Domain,” in Future Generation Computer Systems, 2016.10.1016/j.future.2015.01.001 Search in Google Scholar

[4] F. Masulli and A. Schenone, “A fuzzy clustering based segmentation system as support to diagnosis in medical imaging,” Artificial Intelligence in Medicine, 1999.10.1016/S0933-3657(98)00069-4 Search in Google Scholar

[5] S. Gauch, M. Speretta, A. Chandramouli, and A. Micarelli, “User profiles for personalized information access,” in The adaptive web, 2007. Search in Google Scholar

[6] A. Chaturvedi, J. D. Carroll, P. E. Green, and J. A. Rotondo, “A feature-based approach to market segmentation via overlapping k-centroids clustering,” Journal of Marketing Research, 1997.10.2307/3151899 Search in Google Scholar

[7] C. Gentry and D. Boneh, A fully homomorphic encryption scheme. Stanford university Stanford, 2009. Search in Google Scholar

[8] W. Wu, J. Liu, H. Wang, J. Hao, and M. Xian, “Secure and efficient outsourced K-means clustering using fully homomorphic encryption with ciphertext packing technique,” in TDKE, 2020.10.1109/TKDE.2020.2969633 Search in Google Scholar

[9] J. H. Cheon, D. Kim, and J. H. Park, “Towards a practical cluster analysis over encrypted data,” in SAC, 2019.10.1007/978-3-030-38471-5_10 Search in Google Scholar

[10] D. Demmler, T. Schneider, and M. Zohner, “ABY - A framework for efficient mixed-protocol secure two-party computation,” in NDSS, 2015.10.14722/ndss.2015.23113 Search in Google Scholar

[11] P. Mohassel, M. Rosulek, and N. Trieu, “Practical privacy-preserving K-means clustering,” in PETS, 2020.10.2478/popets-2020-0080 Search in Google Scholar

[12] P. Bunn and R. Ostrovsky, “Secure two-party K-means clustering,” in CCS, 2007.10.1145/1315245.1315306 Search in Google Scholar

[13] F.-Y. Rao, B. K. Samanthula, E. Bertino, X. Yi, and D. Liu, “Privacy-preserving and outsourced multi-user K-means clustering,” in CIC, 2015.10.1109/CIC.2015.20 Search in Google Scholar

[14] A. Jäschke and F. Armknecht, “Unsupervised Machine Learning on Encrypted Data,” in SAC, 2018. Search in Google Scholar

[15] H. Kim and J. Chang, “A privacy-preserving k-means clustering algorithm using secure comparison protocol and density-based center point selection,” in International Conference on Cloud Computing, 2018.10.1109/CLOUD.2018.00138 Search in Google Scholar

[16] H. Keller, H. Möllering, T. Schneider, and H. Yalame, “Balancing quality and efficiency in private clustering with affinity propagation,” in SECRYPT, 2021.10.5220/0010547801730184 Search in Google Scholar

[17] S. Zahur and D. Evans, “Circuit structures for improving efficiency of security and privacy tools,” in IEEE S&P, 2013.10.1109/SP.2013.40 Search in Google Scholar

[18] B. Bozdemir, S. Canard, O. Ermis, H. Möllering, M. Önen, and T. Schneider, “Privacy-preserving density-based clustering,” in ASIACCS, 2021.10.1145/3433210.3453104 Search in Google Scholar

[19] X. Meng, D. Papadopoulos, A. Oprea, and N. Triandopoulos, “Private two-party cluster analysis made formal & scalable,” arXiv:1904.04475v2, 2019. Search in Google Scholar

[20] O. Goldreich, S. Micali, and A. Wigderson, “How to play any mental game,” in STOC, 1987.10.1145/28395.28420 Search in Google Scholar

[21] A. C.-C. Yao, “How to generate and exchange secrets,” in FOCS, 1986. Search in Google Scholar

[22] J. Liu, L. Xiong, J. Luo, and J. Z. Huang, “Privacy preserving distributed DBSCAN clustering,” in Transactions on Data Privacy, 2013.10.1145/2320765.2320819 Search in Google Scholar

[23] N. Kumar, M. Rathee, N. Chandran, D. Gupta, A. Rastogi, and R. Sharma, “CrypTFlow: Secure TensorFlow inference,” in IEEE S&P, 2020.10.1109/SP40000.2020.00092 Search in Google Scholar

[24] D. Rathee, M. Rathee, N. Kumar, N. Chandran, D. Gupta, A. Rastogi, and R. Sharma, “CrypTFlow2: Practical 2-party secure inference,” in CCS, 2020.10.1145/3372297.3417274 Search in Google Scholar

[25] P. Mishra, R. Lehmkuhl, A. Srinivasan, W. Zheng, and R. A. Popa, “Delphi: A cryptographic inference service for neural networks,” in USENIX Security, 2020.10.1145/3411501.3419418 Search in Google Scholar

[26] A. Patra, T. Schneider, A. Suresh, and H. Yalame, “ABY2. 0: Improved mixed-protocol secure two-party computation,” in USENIX Security, 2021. Search in Google Scholar

[27] V. Haralampieva, D. Rueckert, and J. Passerat-Palmbach, “A systematic comparison of encrypted machine learning solutions for image classification,” in PPMLP, 2020.10.1145/3411501.3419432 Search in Google Scholar

[28] F. Boemer, R. Cammarota, D. Demmler, T. Schneider, and H. Yalame, “MP2ML: A mixed-protocol machine learning framework for private inference,” in ARES, 2020.10.1145/3411501.3419425 Search in Google Scholar

[29] L. Song, H. Wu, W. Ruan, and W. Han, “SoK: Training machine learning models over multiple sources with privacy preservation,” in arXiv:2012.03386, 2020. Search in Google Scholar

[30] H. C. Tanuwidjaja, R. Choi, S. Baek, and K. Kim, “Privacy-preserving deep learning on machine learning as a service—a comprehensive survey,” in IEEE Access, 2020.10.1109/ACCESS.2020.3023084 Search in Google Scholar

[31] Á. Kiss, M. Naderpour, J. Liu, N. Asokan, and T. Schneider, “SoK: modular and efficient private decision tree evaluation,” in PETS, 2019.10.2478/popets-2019-0026 Search in Google Scholar

[32] U. Stemmer, “Locally private K-means clustering,” in ACM-SIAM Symposium on Discrete Algorithms, 2020.10.1137/1.9781611975994.33 Search in Google Scholar

[33] L. Ni, C. Li, X. Wang, H. Jiang, and J. Yu, “DPMCDBSCAN: Differential privacy preserving multi-core DBSCAN clustering for network user data,” in IEEE Access, 2018.10.1109/ACCESS.2018.2824798 Search in Google Scholar

[34] M.-F. Balcan, T. Dick, Y. Liang, W. Mou, and H. Zhang, “Differentially private clustering in high-dimensional Euclidean spaces,” in ICML, 2017. Search in Google Scholar

[35] D. Su, J. Cao, N. Li, E. Bertino, M. Lyu, and H. Jin, “Differentially private K-means clustering and a hybrid approach to private optimization,” in TOPS, 2017.10.1145/2857705.2857708 Search in Google Scholar

[36] D. Su, J. Cao, N. Li, E. Bertino, and H. Jin, “Differentially private K-means clustering,” in Data and Application Security and Privacy, 2016.10.1145/2857705.2857708 Search in Google Scholar

[37] W. Wu and H. Huang, “A DP-DBSCAN clustering algorithm based on differential privacy preserving,” in Computer Engineering and Science, 2015. Search in Google Scholar

[38] M. Abadi, A. Chu, I. Goodfellow, H. B. McMahan, I. Mironov, K. Talwar, and L. Zhang, “Deep learning with differential privacy,” in CCS, 2016.10.1145/2976749.2978318 Search in Google Scholar

[39] R. Shokri and V. Shmatikov, “Privacy-preserving deep learning,” in CCS, 2015.10.1145/2810103.2813687 Search in Google Scholar

[40] D. Xu and Y. Tian, “A comprehensive survey of clustering algorithms,” in Annals of Data Science, 2015.10.1007/s40745-015-0040-1 Search in Google Scholar

[41] R. Xu and D. Wunsch, “Survey of clustering algorithms,” in TNN, 2005.10.1109/TNN.2005.845141 Search in Google Scholar

[42] A. K. Jain, M. N. Murty, and P. J. Flynn, “Data clustering: A review,” in ACM Computing Surveys, 1999.10.1145/331499.331504 Search in Google Scholar

[43] Q. Zhang, L. T. Yang, Z. Chen, and P. Li, “PPHOPCM: privacy-preserving high-order possibilistic c-means algorithm for big data clustering with cloud computing,” IEEE Transactions on Big Data, 2017. Search in Google Scholar

[44] M. Hamidi, M. Sheikhalishahi, and F. Martinelli, “Privacy preserving Expectation Maximization (EM) clustering construction,” in DCAI, 2019.10.1007/978-3-319-94649-8_31 Search in Google Scholar

[45] X. Lin, C. Clifton, and M. Zhu, “Privacy-preserving clustering with distributed EM mixture modeling,” in Knowledge and Information Systems, 2005.10.1007/s10115-004-0148-7 Search in Google Scholar

[46] I. V. Anikin and R. M. Gazimov, “Privacy preserving DB-SCAN clustering algorithm for vertically partitioned data in distributed systems,” in International Siberian Conference on Control and Communications, 2017.10.1109/SIBCON.2017.7998473 Search in Google Scholar

[47] M. S. Rahman, A. Basu, and S. Kiyomoto, “Towards outsourced privacy-preserving multiparty DBSCAN,” in PRDC, 2017.10.1109/PRDC.2017.42 Search in Google Scholar

[48] I. De and A. Tripathy, “A secure two party hierarchical clustering approach for vertically partitioned data set with accuracy measure,” in Recent Advances in Intelligent Informatics, 2014.10.1007/978-3-319-01778-5_16 Search in Google Scholar

[49] G. Jagannathan, K. Pillaipakkamnatt, R. Wright, and D. Umano, “Communication-efficient privacy-preserving clustering,” in Transactions on Data Privacy, 2010. Search in Google Scholar

[50] A. İnan, S. V. Kaya, Y. Saygın, E. Savaş, A. A. Hintoğlu, and A. Levi, “Privacy preserving clustering on horizontally partitioned data,” in TDKE, 2007.10.1016/j.datak.2007.03.015 Search in Google Scholar

[51] H. Steinhaus, “Sur la division des corp materiels en parties,” in Bulletin L’Académie Polonaise des Science, 1956. Search in Google Scholar

[52] B. S. Everitt, S. Landau, M. Leese, and D. Stahl, “Cluster analysis,” in Wiley, 2011.10.1002/9780470977811 Search in Google Scholar

[53] K. Fukunaga and L. Hostetler, “The estimation of the gradient of a density function, with applications in pattern recognition,” in TIT, 1975.10.1109/TIT.1975.1055330 Search in Google Scholar

[54] X. Xu, M. Ester, H.-P. Kriegel, and J. Sander, “A distribution-based clustering algorithm for mining in large spatial databases,” in ICDE, 1998. Search in Google Scholar

[55] J. M. Pena, J. A. Lozano, and P. Larranaga, “An empirical comparison of four initialization methods for the K-means algorithm,” in Pattern Recognition Letters, 1999.10.1016/S0167-8655(99)00069-0 Search in Google Scholar

[56] Zhexue Huang and M. K. Ng, “A fuzzy k-modes algorithm for clustering categorical data,” in TFS, 1999.10.1109/91.784206 Search in Google Scholar

[57] J. Zhan, “Privacy preserving K-medoids clustering,” in SMC, 2007.10.1109/ICSMC.2007.4414177 Search in Google Scholar

[58] K.-P. Lin, “Privacy-preserving kernel K-means clustering outsourcing with random transformation,” Knowledge and Information Systems, 2016.10.1007/s10115-016-0923-2 Search in Google Scholar

[59] A. K. Jain and R. C. Dubes, Algorithms for clustering data. Prentice-Hall, 1988. Search in Google Scholar

[60] M. Ester, H.-P. Kriegel, J. Sander, X. Xu et al., “A density-based algorithm for discovering clusters in Large spatial databases with noise.” in SIGKDD, 1996. Search in Google Scholar

[61] Y. Ren, C. Domeniconi, G. Zhang, and G. Yu, “A weighted adaptive mean shift clustering algorithm.” Search in Google Scholar

[62] M. Ester, “Density-based clustering,” in Encyclopedia of Database Systems. Springer, 2009.10.1007/978-0-387-39940-9_605 Search in Google Scholar

[63] M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” in ACM SIGMOD, 1999.10.1145/304182.304187 Search in Google Scholar

[64] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” in Journal of the Royal Statistical Society, 1977.10.1111/j.2517-6161.1977.tb01600.x Search in Google Scholar

[65] P. Paillier, “Public-key cryptosystems based on composite degree residuosity classes,” in EUROCRYPT, 1999. Search in Google Scholar

[66] J. H. Cheon, A. Kim, M. Kim, and Y. Song, “Homomorphic encryption for arithmetic of approximate numbers,” in ASIACRYPT, 2017.10.1007/978-3-319-70694-8_15 Search in Google Scholar

[67] A. Shamir, “How to share a secret,” in Communication of the ACM, 1979.10.1145/359168.359176 Search in Google Scholar

[68] O. Goldreich, Foundations of cryptography: volume 2, basic applications. Cambridge university press, 2009. Search in Google Scholar

[69] P. Mohassel and Y. Zhang, “SecureML: A system for scalable privacy-preserving machine learning,” in IEEE S&P, 2017.10.1109/SP.2017.12 Search in Google Scholar

[70] S. Kamara and M. Raykova, “Secure outsourced computation in a multi-tenant cloud,” in IBM Workshop on Cryptography and Security in Clouds, 2011. Search in Google Scholar

[71] S. K. Dash, D. P. Mishra, R. Mishra, and S. Dash, “Privacy preserving K-medoids clustering: An approach towards securing data in mobile cloud architecture,” in Conference on Computational Science, Engineering and Information Technology, 2012.10.1145/2393216.2393290 Search in Google Scholar

[72] A. Amirbekyan and V. Estivill-Castro, “Privacy preserving DBSCAN for vertically partitioned data,” in Intelligence and Security Informatics, 2006.10.1007/11760146_13 Search in Google Scholar

[73] K. A. Kumar and C. P. Rangan, “Privacy preserving DB-SCAN algorithm for clustering,” in Advanced Data Mining and Applications, 2007.10.1007/978-3-540-73871-8_7 Search in Google Scholar

[74] W.-j. Xu, L.-s. Huang, Y.-l. Luo, Y.-f. Yao, and W. Jing, “Protocols for privacy-preserving DBSCAN clustering,” in International Journal of Security and Its Applications, 2007. Search in Google Scholar

[75] D. Jiang, A. Xue, S. Ju, W. Chen, and H. Ma, “Privacy-preserving DBSCAN on horizontally partitioned data,” in International Symposium on IT in Medicine and Education, 2008.10.1109/ITME.2008.4744034 Search in Google Scholar

[76] N. Almutairi, F. Coenen, and K. Dures, “Secure third party data clustering using ϕ data: Multi-user order preserving encryption and super secure chain distance matrices,” in International Conference on Innovative Techniques and Applications of Artificial Intelligence, 2018.10.5220/0006890800410050 Search in Google Scholar

[77] G. Jagannathan, K. Pillaipakkamnatt, and R. N. Wright, “A new privacy-preserving distributed K-clustering algorithm,” in SDM, 2006.10.1137/1.9781611972764.47 Search in Google Scholar

[78] M. Sheikhalishahi and F. Martinelli, “Privacy preserving clustering over horizontal and vertical partitioned data,” in Symposium on Computers and Communications, 2017.10.1109/ISCC.2017.8024694 Search in Google Scholar

[79] P. K. Prasad and C. P. Rangan, “Privacy preserving birch algorithm for clustering over vertically partitioned databases,” in Workshop on Secure Data Management, 2006.10.1007/11844662_7 Search in Google Scholar

[80] K. Prasad and P. Rangan, “Privacy preserving birch algorithm for clustering over arbitrarily partitioned databases,” ADMA, 2007.10.1007/11844662_7 Search in Google Scholar

[81] X. Zhu, M. Liu, and M. Xie, “Privacy-preserving affinity propagation clustering over vertically partitioned data,” in International Conference on Intelligent Networking and Collaborative Systems, 2012.10.1109/iNCoS.2012.71 Search in Google Scholar

[82] J. Vaidya and C. Clifton, “Privacy-preserving K-means clustering over vertically partitioned data,” in SIGKDD, 2003.10.1145/956750.956776 Search in Google Scholar

[83] G. Jagannathan and R. N. Wright, “Privacy-preserving distributed K-means clustering over arbitrarily partitioned data,” in SIGKDD, 2005.10.1145/1081870.1081942 Search in Google Scholar

[84] S. Jha, L. Kruger, and P. McDaniel, “Privacy preserving clustering,” in ESORICS, 2005.10.1007/11555827_23 Search in Google Scholar

[85] S. Samet, A. Miri, and L. Orozco-Barbosa, “Privacy preserving K-means clustering in multi-party environment,” in SECRYPT, 2007. Search in Google Scholar

[86] C. Su, F. Bao, J. Zhou, T. Takagi, and K. Sakurai, “Privacy-preserving two-party K-means clustering via secure approximation,” in AINA, 2007.10.1109/AINAW.2007.295 Search in Google Scholar

[87] M. C. Doganay, T. B. Pedersen, Y. Saygin, E. Savaş, and A. Levi, “Distributed privacy preserving K-means clustering with additive secret sharing,” in International Workshop on Privacy and Anonymity in Information Society, 2008.10.1145/1379287.1379291 Search in Google Scholar

[88] Z. Erkin, T. Veugen, T. Toft, and R. L. Lagendijk, “Privacy-preserving user clustering in a social network,” in Information Forensics and Security, 2009.10.1109/WIFS.2009.5386476 Search in Google Scholar

[89] J. Sakuma and S. Kobayashi, “Large-scale k-means clustering with user-centric privacy-preservation,” in Knowledge and Information Systems, 2010.10.1007/s10115-009-0243-x Search in Google Scholar

[90] M. Upmanyu, A. M. Namboodiri, K. Srinathan, and C. V. Jawahar, “Efficient privacy preserving K-means clustering,” in Pacific-Asia Workshop on Intelligence and Security Informatics, 2010.10.1007/978-3-642-13601-6_17 Search in Google Scholar

[91] T.-K. Yu, D. Lee, S.-M. Chang, and J. Zhan, “Multi-party K-means clustering with privacy consideration,” in ISPA, 2010. Search in Google Scholar

[92] M. Beye, Z. Erkin, and R. L. Lagendijk, “Efficient privacy preserving K-means clustering in a three-party setting,” in Information Forensics and Security, 2011.10.1109/WIFS.2011.6123148 Search in Google Scholar

[93] Z. Lin and J. W. Jaromczyk, “Privacy preserving two-party K-means clustering over vertically partitioned dataset,” in ISI, 2011.10.1109/ISI.2011.5983998 Search in Google Scholar

[94] S. Patel, S. Garasia, and D. Jinwala, “An efficient approach for privacy preserving distributed K-means clustering based on shamir’s secret sharing scheme,” in Trust Management VI, 2012.10.1007/978-3-642-29852-3_9 Search in Google Scholar

[95] Z. Erkin, T. Veugen, T. Toft, and R. L. Lagendijk, “Privacy-preserving distributed clustering,” in EURASIP Journal on Information Security, 2013.10.1186/1687-417X-2013-4 Search in Google Scholar

[96] S. Patel, V. Patel, and D. Jinwala, “Privacy preserving distributed K-means clustering in malicious model using zero knowledge proof,” in Distributed Computing and Internet Technology, 2013.10.1007/978-3-642-36071-8_33 Search in Google Scholar

[97] D. Liu, E. Bertino, and X. Yi, “Privacy of outsourced K-means clustering,” in ASIACCS, 2014.10.1145/2590296.2590332 Search in Google Scholar

[98] X. Liu, Z. L. Jiang, S. M. Yiu, X. Wang, C. Tan, Y. Li, Z. Liu, Y. Jin, and J. Fang, “Outsourcing two-party privacy preserving K-means clustering protocol in wireless sensor networks,” in MSN, 2015.10.1109/MSN.2015.42 Search in Google Scholar

[99] S. J. Patel, D. Punjani, and D. C. Jinwala, “An efficient approach for privacy preserving distributed clustering in semi-honest model using elliptic curve cryptography,” International Journal of Network Security, 2015. Search in Google Scholar

[100] V. Baby and N. S. Chandra, “Distributed threshold K-means clustering for privacy preserving data mining,” in ICACCI, 2016.10.1109/ICACCI.2016.7732393 Search in Google Scholar

[101] Z. Gheid and Y. Challal, “Efficient and privacy-preserving K-means clustering for big data mining,” in IEEE Trust-Com/BigDataSE/ISPA, 2016.10.1109/TrustCom.2016.0140 Search in Google Scholar

[102] H. Rong, H. Wang, J. Liu, J. Hao, and M. Xian, “Outsourced k-means clustering over encrypted data under multiple keys in spark framework,” in Security and Privacy in Communication Networks, 2017.10.1007/978-3-319-78813-5_4 Search in Google Scholar

[103] K. Xing, C. Hu, J. Yu, X. Cheng, and F. Zhang, “Mutual privacy preserving K-means clustering in social participa-tory sensing,” in TII, 2017.10.1109/TII.2017.2695487 Search in Google Scholar

[104] J. Yuan and Y. Tian, “Practical privacy-preserving MapReduce based K-means clustering over large-ccale dataset,” in TCM, 2019.10.1109/TCC.2017.2656895 Search in Google Scholar

[105] Z. L. Jiang, N. Guo, Y. Jin, J. Lv, Y. Wu, Z. Liu, J. Fang, S. Yiu, and X. Wang, “Efficient two-party privacy-preserving collaborative k-means clustering protocol supporting both storage and computation outsourcing,” Information Sciences, 2020.10.1016/j.ins.2019.12.051 Search in Google Scholar

[106] Y. Zou, Z. Zhao, S. Shi, L. Wang, Y. Peng, Y. Ping, and B. Wang, “Highly secure privacy-preserving outsourced k-means clustering under multiple keys in cloud computing,” in Security and Communication Networks, 2020.10.1155/2020/1238505 Search in Google Scholar

[107] Y. Wang, “Notes on two fully homomorphic encryption schemes without bootstrapping.” Cryptology ePrint Archive, Report 2015/519.10.1007/978-3-319-16745-9_13 Search in Google Scholar

[108] Y. Cai and C. Tang, “Privacy of outsourced two-party k-means clustering,” Concurrency and Computation: Practice and Experience, 2019. Search in Google Scholar

[109] S. M. Sarmento and N. Horta, “Enhancing a pairs trading strategy with the application of machine learning,” in Expert Systems with Applications, 2020.10.1016/j.eswa.2020.113490 Search in Google Scholar

[110] R. Adusumilli, “DBSCAN Clustering for Trading,” 2020, https://towardsdatascience.com/dbscan-clustering-for-trading-4c48e5ebffc8. Search in Google Scholar

[111] S. Panigrahi, A. Kundu, S. Sural, and A. K. Majumdar, “Credit card fraud detection: A fusion approach using dempster–shafer theory and bayesian learning,” in Information Fusion, 2009.10.1016/j.inffus.2008.04.001 Search in Google Scholar

[112] A. Sangers, M. van Heesch, T. Attema, T. Veugen, M. Wiggerman, J. Veldsink, O. Bloemen, and D. Worm, “Secure Multiparty PageRank Algorithm for Collaborative Fraud Detection,” in FC, 2019.10.1007/978-3-030-32101-7_35 Search in Google Scholar

[113] A. Chaturvedi, J. Carroll, P. Green, and J. A. Rotondo, “A feature-based approach to market segmentation via overlapping k-centroids clustering,” Journal of Marketing Research, 1997.10.2307/3151899 Search in Google Scholar

[114] Y. S. Cho, S. C. Moon, S. C. Noh, and K. H. Ryu, “Implementation of personalized recommendation system using k-means clustering of item category based on rfm,” in ICMIT, 2012.10.1109/ICMIT.2012.6225835 Search in Google Scholar

[115] Q. Guo, X. Lu, Y. Gao, J. Zhang, B. Yan, D. Su, A. Song, X. Zhao, and G. Wang, “Cluster Analysis: A New Approach for Identification of Underlying Risk Factors for Coronary Artery Disease in Essential Hypertensive Patients,” in Scientific Reports, 2017.10.1038/srep43965 Search in Google Scholar

[116] F. Masulli and A. Schenone, “A fuzzy clustering based segmentation system as support to diagnosis in medical imaging,” Artificial Intelligence in Medicine, 1999.10.1016/S0933-3657(98)00069-4 Search in Google Scholar

[117] L. Braun, D. Demmler, T. Schneider, and O. Tkachenko, “MOTION - A framework for mixed-protocol multi-party computation,” Cryptology ePrint Archive, Report 2020/1137. Search in Google Scholar

[118] M. Keller, “MP-SPDZ: a versatile framework for multi-party computation,” in CCS, 2020.10.1145/3372297.3417872 Search in Google Scholar

[119] A. Dalskov, D. Escudero, and M. Keller, “Secure evaluation of quantized neural networks,” PETS, 2020.10.2478/popets-2020-0077 Search in Google Scholar

[120] “HEAAN,” https://github.com/snucrypto/HEAAN, 2020. Search in Google Scholar

[121] “Paillier library,” http://acsc.cs.utexas.edu/libpaillier, 2010. Search in Google Scholar

[122] A. Ultsch, “Clustering with SOM,” in Workshop on Self-Organizing Maps, 2005. Search in Google Scholar

[123] D. Graves and W. Pedrycz, “Kernel-based fuzzy clustering and fuzzy clustering: A comparative experimental study,” in Fuzzy Sets and Systems, 2010.10.1016/j.fss.2009.10.021 Search in Google Scholar

[124] M. Gagolewski, “Benchmark suite for clustering algorithms version 1,” 2020, https://github.com/gagolews/clustering_benchmarks_v1. Search in Google Scholar

[125] O. Arbelaitz, I. Gurrutxaga, J. Muguerza, J. M. Pérez, and I. Perona, “An extensive comparative study of cluster validity indices,” Pattern Recognition, 2013.10.1016/j.patcog.2012.07.021 Search in Google Scholar

[126] L. Hubert and P. Arabie, “Comparing partitions,” Journal of Classification, 1985.10.1007/BF01908075 Search in Google Scholar

[127] N. X. Vinh, J. Epps, and J. Bailey, “Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance,” Journal of Machine Learning Research, 2010.10.1145/1553374.1553511 Search in Google Scholar

[128] P. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,” Journal of Computational and Applied Mathematics, 1987.10.1016/0377-0427(87)90125-7 Search in Google Scholar

[129] T. Cali«ski and J. Harabasz, “A dendrite method for cluster analysis,” in Communications in Statistics-theory and Methods, 1974.10.1080/03610927408827101 Search in Google Scholar

[130] D. Arthur and S. Vassilvitskii, “K-means++: The advantages of careful seeding,” ACM-SIAM Symposium on Discrete Algorithms, 2007. Search in Google Scholar

[131] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg et al., “Scikit-learn: Machine learning in Python,” JMLR, 2011. Search in Google Scholar

[132] Y. Lindell, “How to simulate it–a tutorial on the simulation proof technique,” Tutorials on the Foundations of Cryptography, 2017.10.1007/978-3-319-57048-8_6 Search in Google Scholar

[133] B. Li and D. Micciancio, “On the security of homomorphic encryption on approximate numbers,” Cryptology ePrint Archive, Report 2020/1533.10.1007/978-3-030-77870-5_23 Search in Google Scholar

[134] J. H. Cheon, S. Hong, and D. Kim, “Remark on the security of CKKS scheme in practice,” Cryptology ePrint Archive, Report 2020/1581. Search in Google Scholar

[135] B. J. Frey and D. Dueck, “Clustering by passing messages between data points,” Science, 2007.10.1126/science.1136800 Search in Google Scholar

[136] X. Liu, M. Yin, J. Luo, and W. Chen, “An improved affinity propagation clustering algorithm for large-scale data sets,” in International Conference on Natural Computation, 2013.10.1109/ICNC.2013.6818103 Search in Google Scholar

[137] F. Shang, L. Jiao, J. Shi, F. Wang, and M. Gong, “Fast affinity propagation clustering: A multilevel approach,” Pattern Recognition, 2012.10.1016/j.patcog.2011.04.032 Search in Google Scholar

[138] D. Dueck, Affinity propagation: clustering data by passing messages, 2009. Search in Google Scholar

[139] A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science, 2014.10.1126/science.1242072 Search in Google Scholar

[140] T. Zhang, R. Ramakrishnan, and M. Livny, “Birch: An efficient data clustering method for very large databases,” ACM SIGMOD, 1996.10.1145/233269.233324 Search in Google Scholar

[141] C. E. Rasmussen et al., “The infinite Gaussian mixture model,” in NIPS, 1999. Search in Google Scholar

[142] X. He, D. Cai, Y. Shao, H. Bao, and J. Han, “Laplacian regularized gaussian mixture model for data clustering,” IEEE Transactions on Knowledge and Data Engineering, 2010.10.1109/TKDE.2010.259 Search in Google Scholar

[143] J. P. Patist, W. Kowalczyk, and E. Marchiori, “Maintaining gaussian mixture models of data streams under block evolution,” in International Conference on Computational Science, 2006.10.1007/11758501_175 Search in Google Scholar

[144] R. C. Pinto and P. M. Engel, “A fast incremental gaussian mixture model,” PloS one, 2015.10.1371/journal.pone.0141942 Search in Google Scholar

[145] J. H. Cheon, K. Han, A. Kim, M. Kim, and Y. Song, “Bootstrapping for approximate homomorphic encryption,” in EUROCRYPT, 2018.10.1007/978-3-319-78381-9_14 Search in Google Scholar

[146] J. H. Cheon, D. Kim, D. Kim, H. H. Lee, and K. Lee, “Numerical method for comparison on homomorphically encrypted numbers,” in ASIACRYPT, 2019.10.1007/978-3-030-34621-8_15 Search in Google Scholar

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