Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Window-based Tensor Analysis on High-dimensional and Multi-aspect Streams
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Two heads better than one: pattern discovery in time-evolving multi-aspect data
Data Mining and Knowledge Discovery
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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 (PARAFAC [1], Tucker [5], DTA/STA [3], WTA [2]) 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 [4].