Tabular data abound in many data stores: traditional relational databases store tables, and new applications also generate massive tabular datasets. For example, consider the geographic distribution of cell phone traffic at different base stations across the country (which can be represented by a table indexed by latitude and longitude), or the evolution of traffic at Internet routers over time (which can be represented by a table indexed by time, source and destination IP addresses). Detecting similarity patterns in such data sets (e.g., which geographic regions have similar cell phone usage distribution, which IP subnet traffic distributions over time intervals are similar, etc) is of great importance. Identification of such patterns poses many conceptual challenges (what is a suitable similarity distance function for two “regions”) as well as technical challenges (how to perform similarity computations efficiently as massive tables get accumulated over time) that we address.
We present methods for determining similar regions in massive tabular data. Our methods are for computing the “distance” between any two subregions of a tabular data: they are approximate, but highly accurate as we prove mathematically, and they are fast, running in time nearly linear in the table size. Our methods are general since these distance computations can be applied to any mining or similarity algorithms that use Lp norms. A novelty of our distance computation procedures is that they work for any Lp norms - not only the traditional p=2 or p=1, but for all p<=2; the choice of p, say fractional p, provides an interesting alternative similarity behavior! We use our algorithms in a detailed experimental study of the clustering patterns in real tabular data obtained from one of AT&T's data stores and show that our methods are substantially faster than straightforward methods while remaining highly accurate, and able to detect interesting patterns by varying the value of p.
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