Biomedical Engineering Reference
In-Depth Information
Table 2.3
Method B: gene
occurrence for all predictors
(First iteration)
f
1
f
2
f
3
f
4
f
5
f
6
f
7
x
1
0.59
0.68
0.57
0.69
0.60
1.00
x
2
0.24
0.41
0.29
0.33
0.49
0.51
x
3
0.65
0.48
0.76
0.58
0.56
0.17
x
4
0.39
0.40
0.78
0.54
0.44
0.29
x
5
0.56
0.30
0.27
0.44
0.39
0.36
x
6
0.42
0.54
0.52
0.41
0.44
0.67
x
7
0.64
0.63
0.24
0.48
0.32
0.45
score. This final predictor is formed by listing the 3 input genes that correspond to the
3 entries that were used to compute the highest resolution score. Similar to method
A, we reiterate the process by regenerating the table after discarding all predictor sets
that do not contain predictors that were selected in previous steps. Method B has the
advantage of being more robust when no
single
predictor has a significantly higher
occurrence frequency than others. However, there is no guarantee that the predictor
selected by method B is a valid predictor. If this happens, we select the column with
the next highest resolution score.
2.5.3
Method AB
In our experiments, we also use a hybrid
method AB
which works in the following
manner. Both methods A and B are used to select their best predictor. If both methods
produce the same predictor
f
i
, we select this predictor as a final predictor. If not,
we list the best predictors for each gene, for both methods. If multiple predictors
match for both methods, we choose the final predictor as the one with the highest
weighted sum of the resolution ratio and resolution score. The resolution ratio is
weighted by 0.3 and the resolution score is weighted by 0.7. The weighting factor
for the resolution ratio is lower since the resolution ratio values of any gene are often
close to 1. In such a situation, we would like to favor method B. If no predictor is
produced by the previous step, we look at the top five predictors of method A for each
gene and calculate the weighted sum of their resolution ratio and resolution score.
The predictor with the highest weighted sum is selected as the final predictor. The
process is reiterated, regenerating the histogram and table at each step, discarding
any predictor sets that do not contain any of the previously selected final predictors.
With this combined approach, we are able to select predictors with a higher degree
of confidence and robustness.
We process our All-SAT data from melanoma attractor data of [
3
] using methods A,
B, and AB. Results are shown in Table
2.4
and shows what predictor was selected for
each gene and the accompanying resolution ratio, resolution score, or weighted sum.
From the results, we can draw several conclusions:
The iterative steps in regenerating the histogram (or table) Gene histogram retain
only cubes (predictor sets) that contain previously selected final predictors. Hence
the final predictor set from
each
method is a valid satisfying cube of the SAT
formula
S
.
