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A distributed and incremental SVD algorithm for agglomerative data analysis on large networks. (English) Zbl 1349.15041

15A23 Factorization of matrices
65F20 Numerical solutions to overdetermined systems, pseudoinverses
Full Text: DOI arXiv
[1] E. Agullo, J. Demmel, J. Dongarra, B. Hadri, J. Kurzak, J. Langou, H. Ltaief, P. Luszczek, and S. Tomov, Numerical linear algebra on emerging architectures: The plasma and magma projects, J. Phys. Conf. Ser., 180 (2009), 012037, .
[2] W. K. Allard, G. Chen, and M. Maggioni, Multi-scale geometric methods for data sets II: Geometric multi-resolution analysis, Appl. Comput. Harmon. Anal., 32 (2012), pp. 435–462, . · Zbl 1242.42038
[3] C. G. Baker, K. A. Gallivan, and P. Van Dooren, Low-rank incremental methods for computing dominant singular subspaces, Linear Algebra Appl., 436 (2012), pp. 2866–2888, . · Zbl 1241.65036
[4] L. Balzano and S. J. Wright, On GROUSE and incremental SVD, in proceedings of the IEEE 5th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013, pp. 1–4, .
[5] M. Brand, Fast low-rank modifications of the thin singular value decomposition, Linear Algebra Appl., 415 (2006), pp. 20–30, . · Zbl 1088.65037
[6] S. Browne, J. Dongarra, N. Garner, G. Ho, and P. Mucci, A portable programming interface for performance evaluation on modern processors, Int. J. High Performance Comput. Appl., 14 (2000), pp. 189–204, .
[7] J. R. Bunch and C. P. Nielsen, Updating the singular value decomposition, Numer. Math., 31 (1978), pp. 111–129, . · Zbl 0421.65028
[8] J. R. Bunch, C. P. Nielsen, and D. C. Sorensen, Rank-one modification of the symmetric eigenproblem, Numer. Math., 31 (1978), pp. 31–48, . · Zbl 0369.65007
[9] E. Chan, M. Heimlich, A. Purkayastha, and R. van de Geijn, Collective communication: theory, practice, and experience, Concurrency Comput. Practice Experience, 19 (2007), pp. 1749–1783, .
[10] L. De Lathauwer, B. De Moor, and J. Vandewalle, A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1253–1278, . · Zbl 0962.15005
[11] R. D. Degroat, Noniterative subspace tracking, IEEE Trans. Signal Process., 40 (1992), pp. 571–577, .
[12] J. Demmel, L. Grigori, M. Hoemmen, and J. Langou, Communication-optimal parallel and sequential QR and LU factorizations, SIAM J. Sci. Comput., 34 (2012), pp. A206–A239, . · Zbl 1241.65028
[13] G. Golub and W. Kahan, Calculating the singular values and pseudo-inverse of a matrix, J. SIAM Ser. B Numer. Anal., 2 (1965), pp. 205–224, . · Zbl 0194.18201
[14] G. H. Golub, Some modified matrix eigenvalue problems, SIAM Rev., 15 (1973), pp. 318–334. · Zbl 0254.65027
[15] M. Gu and S. C. Eisenstat, Downdating the singular value decomposition, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 793–810, . · Zbl 0828.65039
[16] M. Gu, Stanley, S. C. Eisenstat, and I. O, A Stable and Fast Algorithm for Updating the Singular Value Decomposition, Tech. report, Yale, University, 1994. · Zbl 0807.65029
[17] A. Haidar, J. Kurzak, and P. Luszczek, An improved parallel singular value algorithm and its implementation for multicore hardware, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, New York, ACM, 2013, pp. 90:1–90:12, .
[18] N. Halko, P. G. Martinsson, and J. A. Tropp, Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, SIAM Rev., 53 (2011), pp. 217–288, . · Zbl 1269.65043
[19] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1994. · Zbl 0801.15001
[20] E. R. Jessup and D. C. Sorensen, A parallel algorithm for computing the singular value decomposition of a matrix, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 530–548, . · Zbl 0797.65037
[21] I. T. Jolliffe, Principal Component Analysis, 2nd ed., Springer Ser. Statist., Springer-Verlag, New York, 2002. · Zbl 1011.62064
[22] T. G. Kolda, G. Ballard, and W. N. Austin, Parallel Tensor Compression for Large-Scale Scientific Data., Sandia National Laboratories, 2015, .
[23] J. T. Kwok and H. Zhao, Incremental eigen decomposition, in Proceedings of ICANN, 2003, pp. 270–273.
[24] Y. Li, On incremental and robust subspace learning, Pattern Recognition, 37 (2004), pp. 1509–1518, . · Zbl 1070.68591
[25] F. Liu and F. Seinstra, Adaptive parallel householder bidiagonalization, in Euro-Par 2009 Parallel Processing, H. Sips, D. Epema, and H.-X. Lin, eds., Lecture Notes in Comput. Sci. 5704, Springer, Berlin, 2009, pp. 821–833, .
[26] F. Liu and F. J. Seinstra, GPU-based parallel householder bidiagonalization, in Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing, New York, ACM, 2010, pp. 288–291, .
[27] H. Ltaief, P. Luszczek, and J. Dongarra, High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures, ACM Trans. Math. Software, 39 (2013), pp. 16:1–16:22, . · Zbl 1295.65145
[28] P. Ma, M. W. Mahoney, and B. Yu, A statistical perspective on algorithmic leveraging, J. Mach. Learn. Res., 16 (2015), pp. 861–911. · Zbl 1337.62164
[29] X. Meng, J. K. Bradley, B. Yavuz, E. R. Sparks, S. Venkataraman, D. Liu, J. Freeman, D. B. Tsai, M. Amde, S. Owen, D. Xin, R. Xin, M. J. Franklin, R. Zadeh, M. Zaharia, and A. Talwalkar, MLlib: Machine Learning in Apache Spark, CoRR, abs/1505.06807, 2015. · Zbl 1360.68697
[30] M. Moonen, P. V. Dooren, and J. Vandewalle, A singular value decomposition updating algorithm for subspace tracking, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1015–1038, . · Zbl 0759.65017
[31] I. V. Oseledets, Tensor-train decomposition, SIAM J. Sci. Comput., 33 (2011), pp. 2295–2317, . · Zbl 1232.15018
[32] D. Skoc̆aj and A. Leonardis, Incremental and robust learning of subspacerepresentations, Image Vision Comput., 26 (2008), pp. 27–38, .
[33] G. W. Stewart, An updating algorithm for subspace tracking, IEEE Trans. Signal Process., 40 (1992), pp. 1535–1541, .
[34] W. Řeh\ruřek, Scalability of Semantic Analysis in Natural Language Processing, Ph.D. thesis, Masaryk University, 2011.
[35] T. White, Hadoop: The Definitive Guide, O’Reilly Media, Sebastopol, CA, 2009.
[36] M. Zaharia, M. Chowdhury, T. Das, A. Dave, J. Ma, M. McCauley, M. J. Franklin, S. Shenker, and I. Stoica, Resilient distributed datasets: A fault-tolerant abstraction for in-memory cluster computing, in Proceedings of the 9th USENIX Conference on Networked Systems Design and Implementation, Berkeley, CA, USENIX Association, 2012, pp. 2–2, .
[37] M. Zaharia, M. Chowdhury, M. J. Franklin, S. Shenker, and I. Stoica, Spark: Cluster computing with working sets, in Proceedings of the 2d USENIX Conference on Hot Topics in Cloud Computing, Berkeley, CA, USENIX Association, 2010, pp. 10–10, .
[38] H. Zha and H. D. Simon, On updating problems in latent semantic indexing, SIAM J. Sci. Comput., 21 (1999), pp. 782–791, . · Zbl 0952.65034
[39] H. Zhao, P. C. Yuen, and J. T. Kwok, A novel incremental principal component analysis and its application for face recognition, IEEE Trans. Systems Man Cybernet. B, 36 (2006), pp. 873–886, .
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