Database Reference
In-Depth Information
Table 6.1.
An Example of Wavelet Coecient Computation
Granularity (Order
k
)
Averages
DWT Coe
cients
Φvalues
ψ
values
k
=4
(8,6,2,3,4,6,6,5)
-
k
=3
(7,2.5,5,5.5)
(1, -0.5,-1, 0.5)
k
=2
(4.75, 5.25)
(2.25, -0.25)
k
=1
(5)
(-0.25)
1
(8, 6, 2, 3, 4, 6, 6, 5)
-0.5
-1
0.5
(7, 2.5, 5, 5.5)
2.25
-0.25
(4.75, 5.25)
-0.25
(5)
5
Figure 6.1.
Illustration of the Wavelet Decomposition
or the second-order moments. The count-min sketch is typically more
effective for problems such as frequency-estimation of individual items
than the projection-based AMS sketch. However, the AMS sketch is
more effective for problems such as second-moment estimation.
Wavelet Decomposition:
Another widely known synopsis represen-
tation in data stream computation is that of the wavelet representation.
One of the most widely used representations is the
Haar Wavelet
.We
will discuss this technique in detail in this section.
This technique is particularly simple to implement, and is widely used
in the literature for hierarchical decomposition and summarization. The
basic idea in the wavelet technique is to create a decomposition of the
data characteristics into a set of wavelet functions and basis functions.
The property of the wavelet method is that the higher order coecients
