Database Reference
In-Depth Information
Furthermore, as noted earlier, in this chapter we do not consider the
cases where either inter-arrival times within a single stream vary wildly,
or where arrival times across two different streams are not (approxi-
mately) synchronized. These settings have been studies somewhat less
extensively, and are beyond our scope. Finally, it is possible to orga-
nize collections of streams into more than one “dimensions” (or modes),
leading to tensor stream models [63]; this is also beyond the scope of
this chapter.
The rest of the chapter is organized as follows: Section 2 presents
work on data streams and stream mining, for both single and multiple
time series streams. Section 3 and 4 overview some of the background
of common models to characterize correlations across many series, as
well as across time, respectively. Section 5 describes a method for e-
cient incremental update of multivariate forecasts, which can be used to
spot unexpected values. Section 6 describes in detail a core method for
anomaly detection based on these principles and Section 7 shows how its
output can be interpreted and immediately utilized, both by humans,
and for further data analysis. Section 8 illustrates the interplay be-
tween filtering and dimensionality reduction, showing how ideas related
to Section 6 can be used for ecient and effective streaming pattern
discovery across time, rather than across series. Finally, the conclusions
are presented in Section 9.
2. Broader Overview
The area of dimensionality reduction and filtering is too extensive
to be fully covered in a single chapter. Therefore, in this section, we
will provide a broader overview of the related techniques, before going
into some of the important techniques in greater detail. As mentioned
before, in this chapter we focus specifically on work in the context of
data mining and knowledge discovery, although correlation analysis has
been both studied and used in numerous disciplines. Broadly speaking,
the correlations can either be across streams (leading to dimensionality
reduction) or across different time units in the same stream (leading
to compression and filtering). Although this division is not perfect, as
techniques are often related, we will next discuss these aspects of cor-
relation analysis separately. Furthermore, for techniques that combine
correlation analysis across streams and across time, interested readers
may consult, e.g., [63].
