  Compared with traditional news media, social media nowadays provides a richer
and more timely source of news. We are interested in multi-spatial level event
detection from geo-tagged tweet streams. Specifically, in this paper we (1)
examine the statistical characteristic for the time series of the number of
geo-tagged tweets posted from specific regions during a short time interval,
e.g., ten seconds or one minute; (2) verify from over thirty datasets that
while almost all such time series exhibit self-similarity, those that
correspond to events, especially short-term and unplanned outbursts, follow a
power-law distribution; (3) demonstrate that these findings can be applied to
facilitate event detection from tweet streams. We propose two
algorithms---Power-law basic and Power-law advanced, where Power-law basic only
checks the existence of power-law distributions in the time series from tweet
streams at multi-spatial scales, without looking into the content of each
tweet, and Power-law advanced integrates power-law verification with semantic
analysis via word embedding. Our experiments on multiple datasets show that by
considering spatio-temporal statistical distributions of tweets alone, the
seemingly naive algorithm of Power-law basic achieves comparable results with
more advanced event detection methods, while the semantic analysis enhanced
version, Power-law advanced, can significantly increase both the precision and
the recall.
