Abstract
We propose an extension of the canonical polyadic (CP) tensor model where one of the latent factors is allowed to vary through data slices in a constrained way. The components of the latent factors, which we want to retrieve from data, can vary from one slice to another up to a diffeomorphism. We suppose that the diffeomorphisms are also unknown, thus merging curve registration and tensor decomposition in one model, which we call registered CP. We present an algorithm to retrieve both the latent factors and the diffeomorphism, which is assumed to be in a parametrized form. At the end of the paper, we show simulation results comparing registered CP with other models from the literature.
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References
Becker, H., Albera, L., Comon, P., Gribonval, R., Wendling, F., Merlet, I.: Brain source imaging: from sparse to tensor models. IEEE Signal Process. Mag. 32(6), 100–112 (2015)
Bro, R., Andersson, C.A., Kiers, H.A.L.: PARAFAC2-Part II. Modeling chromatographic data with retention time shifts. J. Chemom. 13(3–4), 295–309 (1999)
Cabral Farias, R., Cohen, J.E., Comon, P.: Exploring multimodal data fusion through joint decompositions with flexible couplings. IEEE Trans. Signal Process. 64(18), 4830–4844 (2016)
Comon, P., Luciani, X., De Almeida, A.L.F.: Tensor decompositions, alternating least squares and other tales. J. Chemom. 23(7–8), 393–405 (2009)
Gillis, N., Glineur, F.: Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization. Neural Comput. 24(4), 1085–1105 (2012)
Harshman, R.A., Hong, S., Lundy, M.E.: Shifted factor analysis–Part I: models and properties. J. Chemom. 17(7), 363–378 (2003)
Harshman, R.A.: PARAFAC2: mathematical and technical notes. UCLA working papers in phonetics, vol. 22, no. 3044, p. 122215 (1972)
Hong, S.: Warped factor analysis. J. Chemom. 23(7–8), 371–384 (2009)
James, G.M.: Curve alignment by moments. Ann. Appl. Stat 1, 480–501 (2007)
Kneip, A., Gasser, T.: Statistical tools to analyze data representing a sample of curves. Ann. Stat. 20(3), 1266–1305 (1992)
Marini, F., Bro, R.: Scream: a novel method for multi-way regression problems with shifts and shape changes in one mode. Chemom. Intell. Lab. 129, 64–75 (2013)
Marron, J.S., Ramsay, J.O., Sangalli, L.M., Srivastava, A.: Functional data analysis of amplitude and phase variation. Stat. Sci. 30(4), 468–484 (2015)
Mørup, M., Hansen, L.K., Arnfred, S.M., Lim, L.-H., Madsen, K.H.: Shift-invariant multilinear decomposition of neuroimaging data. NeuroImage 42(4), 1439–1450 (2008)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge (2007)
Ramsay, J.O., Li, X.: Curve registration. J. R. Stat. Soc. Ser. B Stat. Methodol. 60(2), 351–363 (1998)
Rivet, B., Cohen, J.E.: Modeling time warping in tensor decomposition. In: IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2016), pp. 1–5. IEEE (2016)
Rivet, B., Duda, M., Guérin-Dugué, A., Jutten, C., Comon, P.: Multimodal approach to estimate the ocular movements during EEG recordings: a coupled tensor factorization method. In: Conference of the IEEE Engineering in Medicine and Biology Society, pp. 6983–6986. IEEE (2015)
Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech Signal Process. 26(1), 43–49 (1978)
Seichepine, N., Essid, S., Févotte, C., Cappé, O.: Soft nonnegative matrix co-factorization. IEEE Trans. Signal Process. 62(22), 5940–5949 (2014)
Sidiropoulos, N.D., Giannakis, G.B., Bro, R.: Blind PARAFAC receivers for DS-CDMA systems. IEEE Trans. Signal Process. 48(3), 810–823 (2000)
Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis: Applications in the Chemical Sciences. Wiley, Chichester (2005)
Srivastava, A., Wu, W., Kurtek, S., Klassen, E., Marron, J.S.: Registration of functional data using Fisher-Rao metric. arXiv preprint arXiv:1103.3817 (2011)
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Cohen, J.E., Cabral Farias, R., Rivet, B. (2018). Curve Registered Coupled Low Rank Factorization. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_4
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