Abstract
Sequences of event intervals occur in several application domains, while their inherent complexity hinders scalable solutions to tasks such as clustering and classification. In this paper, we propose a novel spectral embedding representation of event interval sequences that relies on bipartite graphs. More concretely, each event interval sequence is represented by a bipartite graph by following three main steps: (1) creating a hash table that can quickly convert a collection of event interval sequences into a bipartite graph representation, (2) creating and regularizing a bi-adjacency matrix corresponding to the bipartite graph, (3) defining a spectral embedding mapping on the bi-adjacency matrix. In addition, we show that substantial improvements can be achieved with regard to classification performance through pruning parameters that capture the nature of the relations formed by the event intervals. We demonstrate through extensive experimental evaluation on five real-world datasets that our approach can obtain runtime speedups of up to two orders of magnitude compared to other state-of-the-art methods and similar or better clustering and classification performance.
This work was partly supported by the VR-2016-03372 Swedish Research Council Starting Grant, as well as the EXTREME project funded by the Digital Futures framework.
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Notes
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This is even an underestimate as for the cases where competitors that did not finish within the one-hour execution time limit, our approach is at least 300 times faster.
References
Allen, J.F.: Maintaining knowledge about temporal intervals. CACM 26(11), 832–843 (1983)
Bornemann, L., Lecerf, J., Papapetrou, P.: STIFE: a framework for feature-based classification of sequences of temporal intervals. In: Calders, T., Ceci, M., Malerba, D. (eds.) DS 2016. LNCS (LNAI), vol. 9956, pp. 85–100. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46307-0_6
Chaudhuri, K., Chung, F., Tsiatas, A.: Spectral clustering of graphs with general degrees in the extended planted partition model. In: COLT, p. 35-1 (2012)
De Lara, N., Bonald, T.: Spectral embedding of regularized block models. In: ICLR (2020)
Joseph, A., Yu, B., et al.: Impact of regularization on spectral clustering. Ann. Stat. 44(4), 1765–1791 (2016)
Kostakis, O., Gionis, A.: On mining temporal patterns in dynamic graphs, and other unrelated problems. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds.) COMPLEX NETWORKS 2017 2017. SCI, vol. 689, pp. 516–527. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72150-7_42
Kostakis, O., Papapetrou, P.: On searching and indexing sequences of temporal intervals. Data Min. Knowl. Disc. 31(3), 809–850 (2017). https://doi.org/10.1007/s10618-016-0489-3
Kotsifakos, A., Papapetrou, P., Athitsos, V.: IBSM: interval-based sequence matching. In: SDM, pp. 596–604. SIAM (2013)
Kunegis, J.: Exploiting the structure of bipartite graphs for algebraic and spectral graph theory applications. Internet Math. 11(3), 201–321 (2015)
Lam, H.T., Mörchen, F., Fradkin, D., Calders, T.: Mining compressing sequential patterns. SADM 7(1), 34–52 (2014)
Liu, L., Wang, S., Hu, B., Qiong, Q., Wen, J., Rosenblum, D.S.: Learning structures of interval-based Bayesian networks in probabilistic generative model for human complex activity recognition. PR 81, 545–561 (2018)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, pp. 849–856 (2002)
Perera, D., Kay, J., Koprinska, I., Yacef, K., Zaïane, O.R.: Clustering and sequential pattern mining of online collaborative learning data. TKDE 21(6), 759–772 (2008)
Pissinou, N., Radev, I., Makki, K.: Spatio-temporal modeling in video and multimedia geographic information systems. GeoInformatica 5(4), 375–409 (2001)
Qin, T., Rohe, K.: Regularized spectral clustering under the degree-corrected stochastic blockmodel. In: NIPS, pp. 3120–3128 (2013)
Ramasamy, D., Madhow, U.: Compressive spectral embedding: sidestepping the SVD. In: NIPS, pp. 550–558 (2015)
Schmidt, M., Palm, G., Schwenker, F.: Spectral graph features for the classification of graphs and graph sequences. CompStat 29(1–2), 65–80 (2014)
Sheetrit, E., Nissim, N., Klimov, D., Shahar, Y.: Temporal probabilistic profiles for sepsis prediction in the ICU. In: KDD, pp. 2961–2969 (2019)
Shi, J., Malik, J.: Normalized cuts and image segmentation. TPAMI 22(8), 888–905 (2000)
Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
Von Luxburg, U., Belkin, M., Bousquet, O.: Consistency of spectral clustering. ANN STAT 36, 555–586 (2008)
Wang, J., Han, J.: Bide: efficient mining of frequent closed sequences. In: ICDE, p. 79. IEEE (2004)
Zhang, Y., Rohe, K.: Understanding regularized spectral clustering via graph conductance. In: NIPS, pp. 10631–10640 (2018)
Zhou, Z., Amini, A.A.: Analysis of spectral clustering algorithms for community detection: the general bipartite setting. JMLR 20(47), 1–47 (2019)
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Lee, Z., Girdzijauskas, Š., Papapetrou, P. (2021). Z-Embedding: A Spectral Representation of Event Intervals for Efficient Clustering and Classification. In: Hutter, F., Kersting, K., Lijffijt, J., Valera, I. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2020. Lecture Notes in Computer Science(), vol 12457. Springer, Cham. https://doi.org/10.1007/978-3-030-67658-2_41
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