Journal Home > Volume 2 , issue 3

Approximations based on random Fourier features have recently emerged as an efficient and elegant method for designing large-scale machine learning tasks. Unlike approaches using the Nyström method, which randomly samples the training examples, we make use of random Fourier features, whose basis functions (i.e., cosine and sine ) are sampled from a distribution independent from the training sample set, to cluster preference data which appears extensively in recommender systems. Firstly, we propose a two-stage preference clustering framework. In this framework, we make use of random Fourier features to map the preference matrix into the feature matrix, soon afterwards, utilize the traditional k-means approach to cluster preference data in the transformed feature space. Compared with traditional preference clustering, our method solves the problem of insufficient memory and greatly improves the efficiency of the operation. Experiments on movie data sets containing 100 000 ratings, show that the proposed method is more effective in clustering accuracy than the Nyström and k-means, while also achieving better performance than these clustering approaches.


menu
Abstract
Full text
Outline
About this article

Efficient Preference Clustering via Random Fourier Features

Show Author's information Jingshu LiuLi Wang( )Jinglei Liu
College of Data Science, Taiyuan University of Technology, Jinzhong 030600, China.
School of Computer and Control Engineering, Yantai University, Yantai 264005, China.

Abstract

Approximations based on random Fourier features have recently emerged as an efficient and elegant method for designing large-scale machine learning tasks. Unlike approaches using the Nyström method, which randomly samples the training examples, we make use of random Fourier features, whose basis functions (i.e., cosine and sine ) are sampled from a distribution independent from the training sample set, to cluster preference data which appears extensively in recommender systems. Firstly, we propose a two-stage preference clustering framework. In this framework, we make use of random Fourier features to map the preference matrix into the feature matrix, soon afterwards, utilize the traditional k-means approach to cluster preference data in the transformed feature space. Compared with traditional preference clustering, our method solves the problem of insufficient memory and greatly improves the efficiency of the operation. Experiments on movie data sets containing 100 000 ratings, show that the proposed method is more effective in clustering accuracy than the Nyström and k-means, while also achieving better performance than these clustering approaches.

Keywords:

random Fourier features, matrix decomposition, similarity matrix
Received: 13 November 2018 Accepted: 13 February 2019 Published: 04 April 2019 Issue date: September 2019
References(30)
[1]
E. Arias-Castro, G. Lerman, and T. Zhang, Spectral clusteringbased on local PCA, Journal of Machine Learning Research, vol. 18, no. 1, pp. 253-309, 2017.
[2]
Y. Yang, F. Shen, Z. Huang, H. T. Shen, and X. Li, Discrete nonnegative spectral clustering, IEEE Transactions on Knowledge and Data Engineering, vol. 29, no. 9, pp. 1834-1845, 2017.
[3]
L. Wang, J. C. Bezdek, C. Leckie, and R. Kotagiri, Selective sampling for approximate clustering of very large data sets, International Journal of Intelligent Systems, vol. 23, no. 3, pp. 313-331, 2008.
[4]
R. Xu and D. C. W. Ii, Survey of clustering algorithms, IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 645-678, 2005.
[5]
S. Sun, J. Zhao, and J. Zhu, A review of nystrom methods for large-scale machine learning, Information Fusion, vol. 26, no. 1, pp. 36-48, 2015.
[6]
R. Langone, R. Mall, C. Alzate, and J. A. K. Suykens, Kernel spectral clustering and applications, in Unsupervised Learning Algorithms. 2016, pp. 135-161.
[7]
X. Zhang, L. Zong, Q. You, and X. Yong, Sampling for nystrom extension-based spectral clustering: Incremental perspective and novel analysis, ACM Transactions on Knowledge Discovery from Data, vol. 11, no. 1, pp. 7: 1-7: 25, 2016.
[8]
B. C. Fowlkes, S. Belongie, F. Chung, and J. Malik, Spectral grouping using the nystroquotom method, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 214-225, 2010.
[9]
Y. Sun, J. Gao, X. Hong, B. Mishra, and B. Yin, Heterogeneous tensor decomposition for clustering via manifold optimization, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 38, no. 3, pp. 476-489, 2016.
[10]
S. Wang and Z. Zhang, Efficient algorithms and error analysis for the modified nystrom method, in Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, Reykjavik, Iceland, 2014, pp. 996-1004.
[11]
W. Wang and Z. Zhang, Improving CUR matrix decomposition and the Nystrom approximation via adaptive sampling, Journal of Machine Learning Research, vol. 14, no. 1, pp. 2729-2769, 2013.
[12]
X. Chen and D. Cai, Large scale spectral clustering with landmark-based representation. in Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, 2011, pp. 313-318.
[13]
L. Wang and M. Dong, Exemplar-based low-rank matrix decomposition for data clustering, Data Mining and Knowledge Discovery, vol. 29, no. 2, pp. 324-357, 2015.
[14]
S. Wang, L. Luo, and Z. Zhang, SPSD matrix approximation via column selection: Theories, algorithms, and extensions, Journal of Machine Learning Research, vol. 17, no. 1, pp. 1697-1745, 2016.
[15]
S. Wang, Z. Zhang, and T. Zhang, Towards more efficient SPSD matrix approximation and CUR matrix decomposition, Journal of Machine Learning Research, vol. 17, no. 1, pp. 7329-7377, 2016.
[16]
P. S. Bradley and U. M. Fayyad, Refining initial points for kmeans clustering, in Fifteenth International Conference on Machine Learning, 1998, pp. 91-99.
[17]
H. Zha, X. He, C. Ding, H. Simon, and M. Gu, Spectral relaxation for k-means clustering, in Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, Vancouver, Canada, 2001, pp. 1057-1064.
[18]
L. Wang, M. Rege, M. Dong, and Y. Ding, Low-rank kernel matrix factorization for large-scale evolutionary clustering, IEEE Transactions on Knowledge and Data Engineering, vol. 24, no. 6, pp. 1036-1050, 2012.
[19]
F. R. Bach and M. I. Jordan, Learning spectral clustering, Advances in Neural Information Processing Systems, vol. 16, no. 2, pp. 305-312, 2004.
[20]
A. Dempster, Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society, vol. 39, no. 1, pp. 1-38, 1977.
[21]
D. A. Spielman, Spectral graph theory and its applications, in Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, Washington, DC, USA, 2007, pp. 29-38.
[22]
W. Y. Chen, Y. Song, H. Bai, C. J. Lin, and E. Y. Chang, Parallel spectral clustering in distributed systems, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 3, pp. 568-586, 2010.
[23]
C. Alzate and J. A. K. Suykens, Multiway spectral clustering with out-of-sample extensions through weighted kernel PCA, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 2, pp. 335-347, 2010.
[24]
F. Lauer and C. Schnorr, Spectral clustering of linear subspaces for motion segmentation, in Proceedings of the IEEE 12th International Conference on Computer Vision, Kyoto, Japan, 2009, pp. 678-685.
[25]
J. Malik and J. Shi, Normalized cuts and image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888-905, 2000.
[26]
J. A. Hartigan and M. A. Wong, A k-means clustering algorithm, Applied Statistics, vol. 28, no. 1, pp. 100-108, 1979.
[27]
A. E. Alaoui and M. W. Mahoney, Fast randomized kernel ridge regression with statistical guarantees, in Proceedings of the 28th International Conference on Neural Information Processing Systems, Montreal, Canada, 2015, pp. 775-783.
[28]
A. Vedaldi and A. Zisserman, Efficient additive kernels via explicit feature maps, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 3, pp. 480-492, 2012.
[29]
A. Rahimi and B. Recht, Random features for large-scale kernel machines, in Proceedings of the 20th International Conference on Neural Information Processing Systems, Vancouver, Canada, 2007, pp. 1177-1184.
[30]
L. He, N. Ray, Y. Guan, and H. Zhang, Fast large-scale spectral clustering via explicit feature mapping, IEEE Transactions on Cybernetics, vol. 49, no. 3, pp. 1058-1071, 2019.
Publication history
Copyright
Acknowledgements
Rights and permissions

Publication history

Received: 13 November 2018
Accepted: 13 February 2019
Published: 04 April 2019
Issue date: September 2019

Copyright

© The author(s) 2019

Acknowledgements

We gratefully acknowledge the detailed and helpful comments of the anonymous reviewers, who have enabled us to considerably improve this paper. This work was supported by the National Natural Science Foundation of China (Nos. 61872260 and 61592419), the Natural Science Foundation of Shanxi Province (No. 201703D421013).

Rights and permissions

Reprints and Permission requests may be sought directly from editorial office.

Return