Abstract
Data stream values are often associated with multiple aspects. For example each value observed at a given time-stamp from environmental sensors may have an associated type (e.g., temperature, humidity, etc.) as well as location. Time-stamp, type and location are the three aspects, which can be modeled using a tensor (high-order array). However, the time aspect is special, with a natural ordering, and with successive time-ticks having usually correlated values. Standard multiway analysis ignores this structure. To capture it, we propose 2 Heads Tensor Analysis (2-heads), which provides a qualitatively different treatment on time. Unlike most existing approaches that use a PCA-like summarization scheme for all aspects, 2-heads treats the time aspect carefully. 2-heads combines the power of classic multilinear analysis with wavelets, leading to a powerful mining tool. Furthermore, 2-heads has several other advantages as well: (a) it can be computed incrementally in a streaming fashion, (b) it has a provable error guarantee and, (c) it achieves significant compression ratio against competitors. Finally, we show experiments on real datasets, and we illustrate how 2-heads reveals interesting trends in the data. This is an extended abstract of an article published in the Data Mining and Knowledge Discovery journal.
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References
Acar E, Çamtepe SA, Krishnamoorthy MS, Yener B (2005) Modeling and multiway analysis of chatroom tensors. In: ISI, pp 256–268
Bader BW, Kolda TG (2006) Algorithm 862: MATLAB tensor classes for fast algorithm prototyping. ACM Trans Math Softw 32(4): 635–653. doi:10.1145/1186785.1186794
Chew PA, Bader BW, Kolda TG, Abdelali A (2007) Cross-language information retrieval using parafac2. In: KDD, ACM Press, New York, NY, USA, pp 143–152
Daubechies I (1992) Ten lectures on wavelets. Capital City Press, Montpelier, Vermont. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
De Lathauwer L, Moor BD, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4): 1253–1278
Gilbert AC, Kotidis Y, Muthukrishnan S, Strauss MJ (2003) One-pass wavelet decompositions of data streams. IEEE Trans Knowl Data Eng 15(3): 541–554
Kolda TG, Bader BW, Kenny JP (2005) Higher-order web link analysis using multilinear algebra. In: ICDM
Papadimitriou S, Brockwell A, Faloutsos C (2003) Adaptive, hands-off stream mining. In: VLDB
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd edn. Cambridge University Press
Sun J-T, Zeng H-J, Liu H, Lu Y, Chen Z (2005) Cubesvd: a novel approach to personalized web search. In: WWW, pp 382–390
Sun J, Papadimitriou S, Yu P (2006a) Window-based tensor analysis on high-dimensional and multi-aspect streams. In: Proceedings of the international conference on data mining (ICDM)
Sun J, Tao D, Faloutsos C (2006b) Beyond streams and graphs: dynamic tensor analysis. In: KDD
Tucker LR (1966) Some mathematical notes on three-mode factor analysis. Psychometrika 31(3):279–311
Vasilescu MAO, Terzopoulos D (2002) Multilinear analysis of image ensembles: tensorfaces. In: ECCV
Xu D, Yan S, Zhang L, Zhang H-J, Liu Z, Shum H-Y (2005) Concurrent subspaces analysis. In: CVPR
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Responsible editors: Walter Daelemans, Bart Goethals, and Katharina Morik.
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Sun, J., Tsourakakis, C.E., Hoke, E. et al. Two heads better than one: pattern discovery in time-evolving multi-aspect data. Data Min Knowl Disc 17, 111–128 (2008). https://doi.org/10.1007/s10618-008-0112-3
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DOI: https://doi.org/10.1007/s10618-008-0112-3