Two heads better than one: pattern discovery in time-evolving multi-aspect data
- 306 Downloads
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.
KeywordsTensor Multilinear analysis Stream mining Wavelet
Unable to display preview. Download preview PDF.
- Acar E, Çamtepe SA, Krishnamoorthy MS, Yener B (2005) Modeling and multiway analysis of chatroom tensors. In: ISI, pp 256–268Google Scholar
- Chew PA, Bader BW, Kolda TG, Abdelali A (2007) Cross-language information retrieval using parafac2. In: KDD, ACM Press, New York, NY, USA, pp 143–152Google Scholar
- Daubechies I (1992) Ten lectures on wavelets. Capital City Press, Montpelier, Vermont. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PAGoogle Scholar
- Kolda TG, Bader BW, Kenny JP (2005) Higher-order web link analysis using multilinear algebra. In: ICDMGoogle Scholar
- Papadimitriou S, Brockwell A, Faloutsos C (2003) Adaptive, hands-off stream mining. In: VLDBGoogle Scholar
- Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd edn. Cambridge University PressGoogle Scholar
- Sun J-T, Zeng H-J, Liu H, Lu Y, Chen Z (2005) Cubesvd: a novel approach to personalized web search. In: WWW, pp 382–390Google Scholar
- 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)Google Scholar
- Sun J, Tao D, Faloutsos C (2006b) Beyond streams and graphs: dynamic tensor analysis. In: KDDGoogle Scholar
- Vasilescu MAO, Terzopoulos D (2002) Multilinear analysis of image ensembles: tensorfaces. In: ECCVGoogle Scholar
- Xu D, Yan S, Zhang L, Zhang H-J, Liu Z, Shum H-Y (2005) Concurrent subspaces analysis. In: CVPRGoogle Scholar