Geography Reference
In-Depth Information
To address this problem, a sliding window is considered around the time when each request
is made, as done in [28]. With the use of this sliding window, recency values are computed as
shown in Equation 3.
max
(
T
i
)
SWL
,
if object i was requested before
Δ
recency
=
(3)
SWL
otherwise
where
T
i
is the time since that tile was last requested.
Recency values calculated that way can already be normalized as stated before in Equation 2.
Δ
Frequency values are computed as follows. For a given request, if a previous request of the
same tile was received inside the window, its frequency value is incremented by 1. Otherwise,
frequency value is divided by the number of windows it is away from. This is reflected in
Equation 4.
⎨
⎩
+
T
i
≤
f requency
1
if
SWL
Δ
max
f requency
Δ
,1
otherwise
f requency
=
(4)
T
i
SWL
Size input is directly extracted from server logs. As opposite to conventional Web proxies
where requested object sizes can be very heterogeneous, in a web map all objects are image
tiles with the same dimensions (typically 256x256 pixels). Those images are usually rendered
in efficient formats such as PNG, GIF or JPEG that rarely reach 100 kilobytes in size. As
discussed in [8], due to greater variation in colors and patterns, the popular areas, stored
as compressed image files, use a larger proportion of disk space than the relatively empty
non-cached tiles. Because of the dependency between the file size and the “popularity” of tiles,
Parameter
Value
Architecture
Feed-forward Multilayer Perceptron
Hidden layers
2
Neurons per hidden layer
3
Inputs
3 (recency, frequency, size)
Output
1 (probability of a future request)
Activation functions
Log-sigmoid in hidden layers, Hyperbolic tangent
sigmoid in output layer
Error function
Minimum Square Error (mse)
Training algorithm
Backpropagation with momentum
Learning method
Supervised learning
Weights update mode
Batch mode
Learning rate
0.05
Momentum constant
0.2
Table 4.
Neural network parameters
