what-when-how
In Depth Tutorials and Information
Metagroup statistics can be calculated quickly and efficiently using standard
dynamic programming algorithms. hree example algorithms, total number of
meta-groups, average meta-group length, and maximal meta-group length, are as
follows [3].
=
⎧
1
if g is minimal and l
0
⎪
◾
( , )
=
>
P g l
0
if g is minimal and l
0
⎨
⎪
⎪
∑
−
h g E
P h l
( ,
1
)
otherwise
⎩
(
,
)
∈
◾
Total number of meta-groups:
N MG
(
)
= ∑
g P g l
( , )
maximal
1
α
∑
∗
g P g l
( , )
maximal
◾
=
Average meta-group length:
AL MG
(
)
1
α
N MG
(
)
◾
Maximal meta-group length:
MaxL MG
(
) max
=
{ }
l
maximal g
P g l
1
≥
α
,
(
, )
>
0
Most of the algorithms would involve simple loops and minimal computations.
Other meta-group characteristics that can be calculated are the most persistent
meta-group, the most stable meta-group, and the largest meta-group. To find the
most persistent meta-group, one must simply find a meta-group that maximizes the
number of groups associated with it. his is equivalent to inding the longest path
of DAG. To find the most stable (least turnover) meta-group, one must find the
meta-group with maximum sum of edge weights divided by the length of the path.
Once again, this is equivalent to a path found using dynamic programming on a
DAG. Finally, to find the largest meta-group, one must find the meta-group that
maximizes the number of members of the meta-group.
Combining aspects from dynamic modeling and probabilistic models, a more
accurate model can be described. he main factors of this model are individual
interest, group behavior, and time lapse. Using these factors, a dynamic probability
model can be used to predict the user's behavior. It is important to realize the major
distinctions involving dynamic modeling theories that allow the model to predict
the future accurately.
he main idea is the concept of using time as a factor in the model. A static model
will represent a single point in time, which obviously leads to smaller equations and
less complexity in general. However, dynamic models provide a new aspect to look
at internally. Using discrete time steps, new features can be added to the equations,
allowing us to observe patterns in change. his observation of patterns is important
in the creation of a probabilistic model. Probability itself can be implemented stati-
cally, but to use probability in this particular case, time must be used as a factor.
he concept of dynamic network modeling can also be seen in large-scale net-
works. In Reference 4, using a simulation-based approach to understand large-scale
social networks is discussed. Important to this simulation approach are the formal
