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1.1.4 Distribution changes in data streams
In traditional DBMSs, it is reasonable to assume that the data set is static,
i.e., the data elements are samples from a static distribution. However,
this does not hold for many real-world data stream applications. Typically,
fast data streams are created by continuous activity over long periods of
time. It is natural that the underlying phenomena can change over time
and, thus, the distribution of the values of the data in the stream may
show significant changes over time. This is referred to as data evolution,
dynamic stream, time-changing data, or concept-drifting data [3, 69, 78,
157].
The distribution change in the stream can be either a slow and gradual
long term process (we refer to this as distribution drift in the rest of the
thesis), or a significant sudden change (we refer to this as distribution
shift). Both types of changes can be commonly observed in many streambased
applications.
Example 1 (distribution drift). Scientists have been using temperature
and precipitation detecting sensors to monitor annual hydrologic processes
[33]. A study of the climate trends in California shows that, due to the
increasing concentrations of atmospheric carbon dioxide, the mean value
of the annual runoff shows a 37% decrease over a 100 year period [10].
Example 2 (distribution shift). To gain a greater share of consumer
expenditures, a special “loyalty program” is proposed by a retail brand.
By monitoring the daily transactions of multiple outlets, a 14% increase
in gross sales is observed immediately after the introduction of the loyalty
program, indicating a positive impact of this proposed program [128].
Distribution changes over data streams have significant impact on most
of the DSMSs. A stream processing model built previously may not be
efficient or accurate after the data evolve, since some characteristics observed
earlier in the data will no longer hold. Hence, if a distribution
change occurs in the stream, it is important for the user to be notified of
this change. The DSMS needs to be adjusted to reflect this change and
new results should be generated for the data under the new distribution.
There is a considerable amount of work that focus on distribution
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