Biology Reference
In-Depth Information
2.
One of the following three conditions is satisfied (“disconnect further” criteria):
a.
The average edge weight of the component is greater than half the average
edge weight of the complete graph.
b.
The distance between its smallest and largest vertices is greater than or equal
to half this distance in the complete graph. For the complete graph, the dis-
tance is the graph's highest weight.
c.
Finally, if the above two conditions fail, a third one is applied: disconnect
the component if it leads to a substantial increase in the information content
carried by the discretized vector.
The result of applying only the first two criteria is analogous to SLC clustering with
the important property that the algorithm chooses the appropriate level to terminate.
Applying the third condition, the information measure criterion may, however, result
in a clustering which is inconsistent with any iteration of the SLC.
Exercise 3.18.
Consider the following vector
v
1
=
(
1
.
3
,
2
.
1
,
7
.
2
,
9
.
05
,
10
.
5
,
11
. Plot the vector entries on the real number line and propose an appropriate
discretization based on your intuition. How did you decide on the number of discrete
states? Would your decision change if the entry 4.6 is added?
.
00
)
Exercise 3.19.
Discretize vector
v
1
from Problem
3.18
using the specified
method.
1.
Interval.
2.
Quantile.
3.
The hybrid method presented in this section.
Exercise 3.20.
If you know that the experimental data is very noisy, would you be
willing to use a smaller or a larger number of discrete states?
Exercise 3.21.
,is
to be discretized and it is known that
v
1
and
v
2
are strongly correlated (assume
Spearman rank correlation). Howwould you discretize
v
2
based on your discretization
of
v
1
?
Suppose a second vector,
v
2
=
(
0
.
8
,
1
.
8
,
3
.
1
,
8
.
0
,
9
.
5
,
10
.
7
)
Project 3.7.
Use the principle of relationship discretization that
is behind
Hartemink's
information-preserving discretization method to discretize
v
1
and
v
2
.
References
[1] Jacob F, Monod J. Genetic regulatory mechanisms in the synthesis of proteins.
J Mol Biol 1961;3(3):318-56.
[2] Setty Y, Mayo A, Surette M, Alon U. Detailed map of a cis-regulatory input
function. PANS 2003;100(13):7702-7.
[3] Mayo A, Setty Y, Shavit S, Zaslaver A, Alon U. Plasticity of the cis-regulatory
input function of a gene. PLoS Biology 2006;4(4):0555-61.
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