Database Reference
In-Depth Information
Algorithm 2
SPIRIT
Initialize
k
←
1
Initialize total energy estimates of
x
t
and
x
t
per time tick to
E ←
0
and
E
1
←
0. Then,
for
each new point that arrives
do
Update
w
i
,for1
≤ i ≤ k
(TrackW).
Update the estimates (for 1
≤ i ≤ k
)
1)
E
i
+
y
t,i
t
2
(
t
−
(
t
−
1)
E
+
x
t
E
i
←
E
←
and
.
t
Let the estimate of retained energy be
E
(
k
)
:=
i
=1
E
i
.
E
(
k
)
<f
E
E
then
Start estimating
w
k
+1
(initialising as in TrackW)
Initialise
E
k
+1
←
if
0
Increase
k
←
k
+1.
end if
if
E
(
k
)
>F
E
E
then
Discard
w
k
and
E
k
Decrease
k
←
k
−
1
end if
end for
6.3 Exponential Forgetting
We can adapt to more recent behavior by using an exponential forget-
ting factor, 0
<λ<
1. This allows us to follow trend drifts over time.
We use the same
λ
for the estimation of both
w
i
and of the AR models
(see Section 7.1). However, we also have to properly keep track of the
energy, discounting it with the same rate, i.e., the update at each step
is:
1)
E
i
+
y
t,i
t
2
λ
(
t
−
λ
(
t
−
1)
E
+
x
t
E
i
←
E
←
and
.
t
Typical choices are 0
.
96
≤ λ ≤
0
.
98 [27]. As long as the values of
x
t
do not vary wildly, the exact value of
λ
is not crucial. We use
λ
=
0
.
96 throughout. A value of
λ
= 1 makes sense when we know that
the sequence is stationary (rarely true in practice, as most sequences
gradually drift). Note that the value of
λ
does not affect the computation
cost of our method. In this sense, an exponential forgetting factor is
