Database Reference
In-Depth Information
TimeíSeries
Amnesic Function
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Figure 7.2.
Depiction of an amnesic approximation, using the piecewise linear ap-
proximation technique (the most recent values of the data series are on the left; the
oldest values are on the right) [70].
be more forgiving of error in older data. We call this kind of time series
approximation
amnesic
, since the fidelity of approximation decreases
with time, and it therefore requires less memory for the events further
inthepast(see
Figure7.2
).
For example, the Environmental Observation and Forecasting Sys-
tem
5
[90] operates in a way that allows for some sensors only intermittent
connections to the sink (through a repeater station that is not always
available). Since the station does not know how long it will be oine,
and has a finite buffer, amnesic approximation is an effective way to
record the data.
We need a way to specify for each point in time the amount of error
allowed for the approximation of the time series. In order to achieve
this goal, we use the
amnesic function
A
(
x
), which returns the accept-
able approximation error for every point of the data series. We define
two forms of amnesic functions, namely, the
relative
and the
absolute
amnesic functions. A relative amnesic function determines the relative
approximation error we can tolerate for every point in the time series
(e.g., we can specify that when we approximate a point that is twice as
old, we will accept twice as much error). When we use relative amnesic
functions, we fix the amount of memory that we are allowed to use for
the approximation of the data. On the other hand, an absolute am-
5
This is a large-scale distributed system designed to monitor, model, and forecast wide-
area physical processes, such as river systems.
