plot.mcfs: Plots various MCFS result components
In rmcfs: The MCFS-ID Algorithm for Feature Selection and Interdependency Discovery
Description
Usage
Arguments
Examples
Description
Plots various aspects of the MCFS-ID result.
Usage
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## S3 method for class 'mcfs'
plot(x, type = c("features", "ri", "id", "distances", "cv", "cmatrix", "heatmap"),
size = NA,
ri_permutations = c("max", "all", "sorted", "none"),
diff_bars = TRUE,
features_margin = 10,
cv_measure = c("wacc", "acc", "pearson", "MAE", "RMSE", "SMAPE"),
heatmap_norm = c('none', 'norm', 'scale'),
heatmap_fun = c('median', 'mean'),
color = c('darkred'),
gg = TRUE,
cex = 1, ...)
Arguments
x
'mcfs' S3 object - result of the MCFS-ID experiment returned by mcfs function.
type
features plots top features set along with their RI. It is a horizontal barplot that shows important features in red color and unimportant in grey.
ri plots top features set with their RIs as well as max RI obtained from permutation experiments. Red color denotes important features.
id plots top ID values obtained from the MCFS-ID.
distances plots distances (convergence diagnostics of the algorithm) between subsequent feature rankings obtained during the MCFS-ID experiment.
cv plots cross validation results based on top features.
cmatrix plots the confusion matrix obtained on all s \cdot t trees.
heatmap plots heatmap results based on top features. Only numeric features can be presented on the heatmap.
size
number of features to plot.
ri_permutations
if type = "ri" and ri_permutations = "max", then it additionally shows horizontal lines that correspond to max RI values obtained from each single permutation experiment.
diff_bars
if type = "ri" or type = "id" and diff_bars = T, then it shows difference values for RI or ID values.
features_margin
if type = "features", then it determines the size of the left margin of the plot.
cv_measure
if type = "cv", then it determines the type of accuracy shown in the plot: weighted or unweighted accuracy ("wacc" or "acc"). If target attribute is numeric it is possible to review one of the following prediction quality measures: ("pearson", "MAE", "RMSE", "SMAPE")
heatmap_norm
if type = "heatmap", then it defines type of input data normalization 'none' - without any normalization, 'norm' - normalization within range [-1,1], 'scale' - standardization/centering by mean and stdev.
heatmap_fun
if type = "heatmap", then it determines calculation 'mean' or 'median' within the class to be shown as heatmap color intensity.
color
it defines main color of the following type of plots: 'ri', 'id', 'heatmap', 'features' and 'cmatrix'.
gg
if gg = TRUE use ggplot2.
cex
size of fonts.
...
additional plotting parameters.
Examples
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## Not run: ###dontrunbegin
# Create input data.
adata <- artificial.data(rnd_features = 10)
showme(adata)
# Parametrize and run MCFS-ID procedure.
result <- mcfs(class~., adata, cutoffPermutations = 0, featureFreq = 10,
finalCV = FALSE, finalRuleset = TRUE, threadsNumber = 2)
# Plot & print out distances between subsequent projections.
# These are convergence MCFS-ID statistics.
plot(result, type = "distances")
print(result$distances)
# Plot & print out 50 most important features and show max RI values from
# permutation experiment.
plot(result, type = "ri", size = 50)
print(head(result$RI, 50))
# Plot & print out 50 strongest feature interdependencies.
plot(result, type = "id", size = 50)
print(head(result$ID, 50))
# Plot features ordered by RI. Parameter 'size' is the number of
# top features in the chart. By default it is set on cutoff_value + 10
plot(result, type = "features", cex = 1)
# Here we set 'size' at fixed value 10.
plot(result, type = "features", size = 10)
# Plot cv classification result obtained on top features.
# In the middle of x axis red label denotes cutoff_value.
# plot(result, type = "cv", measure = "wacc", cex = 0.8)
# Plot & print out confusion matrix. This matrix is the result of
# all classifications performed by all decision trees on all s*t datasets.
plot(result, type = "cmatrix")
## End(Not run)###dontrunend
Example output
Loading required package: rJava
########################
## rmcfs 1.2.15 ##
########################
If used please cite the following paper:
M. Draminski, J. Koronacki (2018),
rmcfs: An R Package for Monte Carlo Feature Selection and Interdependency Discovery,
Journal of Statistical Software, vol 85(12), 1-28, doi:10.18637/jss.v085.i12.
X1 X2 X3 X4 X5 X6 X7
1 0.20274639 0.11598857 0.61478547 0.42402600 0.14691274 0.3236284 0.8001307
2 0.73928474 0.57860234 0.61486531 0.38133400 0.33880215 0.1292732 0.2453541
3 0.63103498 0.78679008 0.82438874 0.95815380 0.29065329 0.8079233 0.4660874
4 0.49468632 0.01079839 0.84465378 0.68775093 0.71638810 0.1435464 0.8322140
5 0.21478014 0.76021624 0.76233393 0.82596737 0.90614322 0.2186508 0.3729568
6 0.01792957 0.33310221 0.45889654 0.35253950 0.09473219 0.5895532 0.3774475
7 0.70883512 0.33131018 0.05235094 0.95805453 0.49311441 0.5956836 0.9795866
8 0.58961368 0.90688919 0.34141376 0.93895753 0.23073050 0.3482507 0.1696028
9 0.03917050 0.70926578 0.18136785 0.11804200 0.61835473 0.4444953 0.1753490
10 0.42077821 0.80953743 0.98001714 0.05287438 0.44337865 0.6824827 0.8374790
X8 X9 X10
1 0.9568731 0.10960519 0.96426010
2 0.6124745 0.91389510 0.98430731
3 0.4601556 0.59884861 0.78023657
4 0.1745020 0.01131831 0.78055051
5 0.6778638 0.47877982 0.14869384
6 0.1215115 0.90418703 0.68087372
7 0.2969220 0.27685542 0.44335726
8 0.9159207 0.14095074 0.26334868
9 0.6974066 0.80049172 0.09963931
10 0.4777905 0.11793562 0.72466045
X7 X8 X9 X10 A1 A2 B1 B2 C1 C2 class
60 0.67379483 0.224148397 0.8012928 0.24526872 0 0 B B 0 0 B
61 0.09043089 0.841599274 0.1409634 0.43970449 0 0 0 0 C C C
62 0.29398599 0.815386671 0.5796068 0.56613591 0 0 0 0 C C C
63 0.47855031 0.002660131 0.7085816 0.99932247 0 0 0 0 C C C
64 0.42547938 0.827036177 0.9966765 0.48032494 0 0 0 0 0 0 C
65 0.80997500 0.304217760 0.2671738 0.76005871 0 0 0 0 0 0 C
66 0.59737957 0.172429372 0.5357804 0.71559289 0 0 0 0 C C C
67 0.34165553 0.532795396 0.5213760 0.65944794 0 0 0 0 C C C
68 0.33499330 0.716705573 0.9691289 0.22773926 0 0 0 0 0 0 C
69 0.11139761 0.466204482 0.2114007 0.06602295 0 0 0 0 C C C
70 0.74393240 0.841848927 0.7438138 0.61254859 0 0 0 0 0 0 C
class: 'data.frame' size: 70 x 17Checking input data...
Exporting params...
Exporting input data...
Running MCFS-ID...
*****************************************
******** dmLab *******
*** ver. 2.2.1 2016.10.27 ***
*****************************************
Created by Michal Draminski [mdramins@ipipan.waw.pl]
http://www.ipipan.eu/staff/m.draminski/
Polish Academy of Sciences - Institute of Computer Science
**************************************************************************
'MCFS-ID' and 'ADX' are developed by Michal Draminski
'rmcfs' developed by Michal Draminski & Julian Zubek
'SLIQ' developed by Mariusz Gromada
**************************************************************************
If you want to use dmLab or 'MCFS-ID' in your work, please cite the paper:
M.Draminski, A.Rada-Iglesias, S.Enroth, C.Wadelius, J. Koronacki, J.Komorowski
'Monte Carlo feature selection for supervised classification', BIOINFORMATICS 24(1): 110-117 (2008)
**************************************************************************
Warning! Value of cutoffPermutations = 0 and cutoffMethod = 'permutations'. Using cutoffMethod = 'mean'.
**************************
*** MCFS-ID Experiment ***
**************************
Loading data: 'input.adx'...
attributes: 17 events: 70
Data loaded.
Nominal target detected - using J48 model.
MCFS-ID param: ID-Graph is ON
MCFS-ID param: finalRuleset is ON
MCFS-ID param: balance classes is AUTO
Classes = [B, C, A], Sizes = [20, 10, 40], classSizeRatio = 0.25, balanceValue = 1.0
Starting MCFS-ID Procedure: projectionSize(m) = 4, projections(s) = 40, splits(t) = 5
Start time: Sun Dec 15 19:25:31 UTC 2019
Running: 2 threads.
50% 75% 100%
All 2 threads are finished.
200 trees built in 1.0 s.
Confusion Matrix
predicted
class B C A other
B 1119.0 101.0 250.0 0.0
C 171.0 392.0 277.0 0.0
A 110.0 52.0 2778.0 0.0
other 0.0 0.0 0.0 0.0
Accuracy = 0.8169
WeightedAccuracy = 0.7242
True Positive Rate
B: 0.7612
C: 0.4666
A: 0.9448
False Positive Rate
B: 0.0743
C: 0.0346
A: 0.2281
Minimal (based on linear regression angle) RI = 0.0465030
Minimal (based on k-means clustering) RI = 0.4039356
Minimal important (mean based on cutoff methods) RI = 0.0465030
Size of important (mean based on cutoff methods) attributes set = 6
*** Building RIPPER ruleset on top 6 attributes ***
JRIP rules:
===========
(A1 = 0) and (B1 = 0) => class=C (12.0/2.0)
(A1 = 0) => class=B (18.0/0.0)
=> class=A (40.0/0.0)
Number of Rules : 3
RIPPER CV Result (10 folds repeated 3 times)
Confusion Matrix
predicted
class B C A
B 54.0 6.0 0.0
C 6.0 24.0 0.0
A 0.0 0.0 120.0
Accuracy = 0.9428
WeightedAccuracy = 0.9
True Positive Rate
B: 0.9
C: 0.8
A: 1.0
False Positive Rate
B: 0.04
C: 0.0333
A: 0.0
*** Saving filtered data ***
*** Calculations for input data: 'input' are finished! Processing time: 1.6 s. ***
Reading results...
Done.
projection distance commonPart mAvg beta1
1 30 0.625 1 0 0
2 40 0.500 1 0 0
position attribute projections classifiers nodes RI_norm
11 1 A1 13 56 56 0.750915770
12 2 A2 12 54 54 0.746437400
14 3 B2 13 65 65 0.493405730
13 4 B1 9 45 45 0.403935670
15 5 C1 10 37 37 0.230295510
16 6 C2 6 18 18 0.208132670
2 7 X2 14 39 67 0.046503060
3 8 X3 12 20 40 0.016226858
6 9 X6 10 19 29 0.015134501
5 10 X5 9 13 25 0.013276609
10 11 X10 11 10 13 0.010786221
9 12 X9 11 15 22 0.009913590
1 13 X1 11 15 17 0.008722575
4 14 X4 10 12 17 0.005713617
7 15 X7 6 5 6 0.003090629
8 16 X8 11 7 9 0.002973641
position edge_a edge_b weight
1 1 A1 B1 5.8667207
2 2 B2 C1 4.4847684
3 3 A2 B2 4.2930510
4 4 B1 C1 3.2717352
5 5 B1 C2 3.0316665
6 6 A2 B1 2.8349319
7 7 A1 C1 2.3182650
8 8 X4 X9 1.7246404
9 9 X6 X1 1.5309514
10 10 A1 X2 1.4965894
11 11 X6 X3 1.4152018
12 12 X2 X3 1.3423343
13 13 A1 B2 1.3263541
14 14 A2 X2 1.2538404
15 15 A2 C1 1.2396010
16 16 X3 X9 1.2111881
17 17 C1 X2 1.1298822
18 18 X2 X1 1.1089367
19 19 X2 X9 1.0154294
20 20 X5 X2 0.9870153
21 21 X6 X2 0.9807923
22 22 X8 X3 0.9502878
23 23 A2 C2 0.8949746
24 24 B2 X10 0.8338920
25 25 X2 X6 0.8311915
26 26 X3 X8 0.7551038
27 27 C1 B1 0.7397414
28 28 B2 A2 0.7111111
29 29 X5 X3 0.6887644
30 30 C2 B1 0.6780198
31 31 X2 X10 0.6702008
32 32 X3 X10 0.5207051
33 33 C1 X9 0.5171953
34 34 X4 X2 0.5090396
35 35 X1 X2 0.5000000
36 36 B2 X3 0.4437181
37 37 X2 X4 0.4320035
38 38 X6 X5 0.4110417
39 39 X4 X3 0.4109206
40 40 X3 X6 0.4108423
41 41 A2 X5 0.4100743
42 42 X3 X5 0.4061762
43 43 X1 X5 0.4002047
44 44 X7 X4 0.3833016
45 45 X3 X4 0.3677971
46 46 X4 X7 0.3566939
47 47 X7 X9 0.3509262
48 48 A1 X10 0.3494854
49 49 X5 X6 0.3453436
50 50 X5 X4 0.3387522
rmcfs documentation built on Sept. 18, 2021, 5:07 p.m.
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Description Usage Arguments Examples
Description
Plots various aspects of the MCFS-ID result.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 | ## S3 method for class 'mcfs'
plot(x, type = c("features", "ri", "id", "distances", "cv", "cmatrix", "heatmap"),
size = NA,
ri_permutations = c("max", "all", "sorted", "none"),
diff_bars = TRUE,
features_margin = 10,
cv_measure = c("wacc", "acc", "pearson", "MAE", "RMSE", "SMAPE"),
heatmap_norm = c('none', 'norm', 'scale'),
heatmap_fun = c('median', 'mean'),
color = c('darkred'),
gg = TRUE,
cex = 1, ...)
|
Arguments
x |
'mcfs' S3 object - result of the MCFS-ID experiment returned by |
type |
|
size |
number of features to plot. |
ri_permutations |
if |
diff_bars |
if |
features_margin |
if |
cv_measure |
if |
heatmap_norm |
if |
heatmap_fun |
if |
color |
it defines main color of the following type of plots: 'ri', 'id', 'heatmap', 'features' and 'cmatrix'. |
gg |
if |
cex |
size of fonts. |
... |
additional plotting parameters. |
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | ## Not run: ###dontrunbegin
# Create input data.
adata <- artificial.data(rnd_features = 10)
showme(adata)
# Parametrize and run MCFS-ID procedure.
result <- mcfs(class~., adata, cutoffPermutations = 0, featureFreq = 10,
finalCV = FALSE, finalRuleset = TRUE, threadsNumber = 2)
# Plot & print out distances between subsequent projections.
# These are convergence MCFS-ID statistics.
plot(result, type = "distances")
print(result$distances)
# Plot & print out 50 most important features and show max RI values from
# permutation experiment.
plot(result, type = "ri", size = 50)
print(head(result$RI, 50))
# Plot & print out 50 strongest feature interdependencies.
plot(result, type = "id", size = 50)
print(head(result$ID, 50))
# Plot features ordered by RI. Parameter 'size' is the number of
# top features in the chart. By default it is set on cutoff_value + 10
plot(result, type = "features", cex = 1)
# Here we set 'size' at fixed value 10.
plot(result, type = "features", size = 10)
# Plot cv classification result obtained on top features.
# In the middle of x axis red label denotes cutoff_value.
# plot(result, type = "cv", measure = "wacc", cex = 0.8)
# Plot & print out confusion matrix. This matrix is the result of
# all classifications performed by all decision trees on all s*t datasets.
plot(result, type = "cmatrix")
## End(Not run)###dontrunend
|
Example output
Loading required package: rJava
########################
## rmcfs 1.2.15 ##
########################
If used please cite the following paper:
M. Draminski, J. Koronacki (2018),
rmcfs: An R Package for Monte Carlo Feature Selection and Interdependency Discovery,
Journal of Statistical Software, vol 85(12), 1-28, doi:10.18637/jss.v085.i12.
X1 X2 X3 X4 X5 X6 X7
1 0.20274639 0.11598857 0.61478547 0.42402600 0.14691274 0.3236284 0.8001307
2 0.73928474 0.57860234 0.61486531 0.38133400 0.33880215 0.1292732 0.2453541
3 0.63103498 0.78679008 0.82438874 0.95815380 0.29065329 0.8079233 0.4660874
4 0.49468632 0.01079839 0.84465378 0.68775093 0.71638810 0.1435464 0.8322140
5 0.21478014 0.76021624 0.76233393 0.82596737 0.90614322 0.2186508 0.3729568
6 0.01792957 0.33310221 0.45889654 0.35253950 0.09473219 0.5895532 0.3774475
7 0.70883512 0.33131018 0.05235094 0.95805453 0.49311441 0.5956836 0.9795866
8 0.58961368 0.90688919 0.34141376 0.93895753 0.23073050 0.3482507 0.1696028
9 0.03917050 0.70926578 0.18136785 0.11804200 0.61835473 0.4444953 0.1753490
10 0.42077821 0.80953743 0.98001714 0.05287438 0.44337865 0.6824827 0.8374790
X8 X9 X10
1 0.9568731 0.10960519 0.96426010
2 0.6124745 0.91389510 0.98430731
3 0.4601556 0.59884861 0.78023657
4 0.1745020 0.01131831 0.78055051
5 0.6778638 0.47877982 0.14869384
6 0.1215115 0.90418703 0.68087372
7 0.2969220 0.27685542 0.44335726
8 0.9159207 0.14095074 0.26334868
9 0.6974066 0.80049172 0.09963931
10 0.4777905 0.11793562 0.72466045
X7 X8 X9 X10 A1 A2 B1 B2 C1 C2 class
60 0.67379483 0.224148397 0.8012928 0.24526872 0 0 B B 0 0 B
61 0.09043089 0.841599274 0.1409634 0.43970449 0 0 0 0 C C C
62 0.29398599 0.815386671 0.5796068 0.56613591 0 0 0 0 C C C
63 0.47855031 0.002660131 0.7085816 0.99932247 0 0 0 0 C C C
64 0.42547938 0.827036177 0.9966765 0.48032494 0 0 0 0 0 0 C
65 0.80997500 0.304217760 0.2671738 0.76005871 0 0 0 0 0 0 C
66 0.59737957 0.172429372 0.5357804 0.71559289 0 0 0 0 C C C
67 0.34165553 0.532795396 0.5213760 0.65944794 0 0 0 0 C C C
68 0.33499330 0.716705573 0.9691289 0.22773926 0 0 0 0 0 0 C
69 0.11139761 0.466204482 0.2114007 0.06602295 0 0 0 0 C C C
70 0.74393240 0.841848927 0.7438138 0.61254859 0 0 0 0 0 0 C
class: 'data.frame' size: 70 x 17Checking input data...
Exporting params...
Exporting input data...
Running MCFS-ID...
*****************************************
******** dmLab *******
*** ver. 2.2.1 2016.10.27 ***
*****************************************
Created by Michal Draminski [mdramins@ipipan.waw.pl]
http://www.ipipan.eu/staff/m.draminski/
Polish Academy of Sciences - Institute of Computer Science
**************************************************************************
'MCFS-ID' and 'ADX' are developed by Michal Draminski
'rmcfs' developed by Michal Draminski & Julian Zubek
'SLIQ' developed by Mariusz Gromada
**************************************************************************
If you want to use dmLab or 'MCFS-ID' in your work, please cite the paper:
M.Draminski, A.Rada-Iglesias, S.Enroth, C.Wadelius, J. Koronacki, J.Komorowski
'Monte Carlo feature selection for supervised classification', BIOINFORMATICS 24(1): 110-117 (2008)
**************************************************************************
Warning! Value of cutoffPermutations = 0 and cutoffMethod = 'permutations'. Using cutoffMethod = 'mean'.
**************************
*** MCFS-ID Experiment ***
**************************
Loading data: 'input.adx'...
attributes: 17 events: 70
Data loaded.
Nominal target detected - using J48 model.
MCFS-ID param: ID-Graph is ON
MCFS-ID param: finalRuleset is ON
MCFS-ID param: balance classes is AUTO
Classes = [B, C, A], Sizes = [20, 10, 40], classSizeRatio = 0.25, balanceValue = 1.0
Starting MCFS-ID Procedure: projectionSize(m) = 4, projections(s) = 40, splits(t) = 5
Start time: Sun Dec 15 19:25:31 UTC 2019
Running: 2 threads.
50% 75% 100%
All 2 threads are finished.
200 trees built in 1.0 s.
Confusion Matrix
predicted
class B C A other
B 1119.0 101.0 250.0 0.0
C 171.0 392.0 277.0 0.0
A 110.0 52.0 2778.0 0.0
other 0.0 0.0 0.0 0.0
Accuracy = 0.8169
WeightedAccuracy = 0.7242
True Positive Rate
B: 0.7612
C: 0.4666
A: 0.9448
False Positive Rate
B: 0.0743
C: 0.0346
A: 0.2281
Minimal (based on linear regression angle) RI = 0.0465030
Minimal (based on k-means clustering) RI = 0.4039356
Minimal important (mean based on cutoff methods) RI = 0.0465030
Size of important (mean based on cutoff methods) attributes set = 6
*** Building RIPPER ruleset on top 6 attributes ***
JRIP rules:
===========
(A1 = 0) and (B1 = 0) => class=C (12.0/2.0)
(A1 = 0) => class=B (18.0/0.0)
=> class=A (40.0/0.0)
Number of Rules : 3
RIPPER CV Result (10 folds repeated 3 times)
Confusion Matrix
predicted
class B C A
B 54.0 6.0 0.0
C 6.0 24.0 0.0
A 0.0 0.0 120.0
Accuracy = 0.9428
WeightedAccuracy = 0.9
True Positive Rate
B: 0.9
C: 0.8
A: 1.0
False Positive Rate
B: 0.04
C: 0.0333
A: 0.0
*** Saving filtered data ***
*** Calculations for input data: 'input' are finished! Processing time: 1.6 s. ***
Reading results...
Done.
projection distance commonPart mAvg beta1
1 30 0.625 1 0 0
2 40 0.500 1 0 0
position attribute projections classifiers nodes RI_norm
11 1 A1 13 56 56 0.750915770
12 2 A2 12 54 54 0.746437400
14 3 B2 13 65 65 0.493405730
13 4 B1 9 45 45 0.403935670
15 5 C1 10 37 37 0.230295510
16 6 C2 6 18 18 0.208132670
2 7 X2 14 39 67 0.046503060
3 8 X3 12 20 40 0.016226858
6 9 X6 10 19 29 0.015134501
5 10 X5 9 13 25 0.013276609
10 11 X10 11 10 13 0.010786221
9 12 X9 11 15 22 0.009913590
1 13 X1 11 15 17 0.008722575
4 14 X4 10 12 17 0.005713617
7 15 X7 6 5 6 0.003090629
8 16 X8 11 7 9 0.002973641
position edge_a edge_b weight
1 1 A1 B1 5.8667207
2 2 B2 C1 4.4847684
3 3 A2 B2 4.2930510
4 4 B1 C1 3.2717352
5 5 B1 C2 3.0316665
6 6 A2 B1 2.8349319
7 7 A1 C1 2.3182650
8 8 X4 X9 1.7246404
9 9 X6 X1 1.5309514
10 10 A1 X2 1.4965894
11 11 X6 X3 1.4152018
12 12 X2 X3 1.3423343
13 13 A1 B2 1.3263541
14 14 A2 X2 1.2538404
15 15 A2 C1 1.2396010
16 16 X3 X9 1.2111881
17 17 C1 X2 1.1298822
18 18 X2 X1 1.1089367
19 19 X2 X9 1.0154294
20 20 X5 X2 0.9870153
21 21 X6 X2 0.9807923
22 22 X8 X3 0.9502878
23 23 A2 C2 0.8949746
24 24 B2 X10 0.8338920
25 25 X2 X6 0.8311915
26 26 X3 X8 0.7551038
27 27 C1 B1 0.7397414
28 28 B2 A2 0.7111111
29 29 X5 X3 0.6887644
30 30 C2 B1 0.6780198
31 31 X2 X10 0.6702008
32 32 X3 X10 0.5207051
33 33 C1 X9 0.5171953
34 34 X4 X2 0.5090396
35 35 X1 X2 0.5000000
36 36 B2 X3 0.4437181
37 37 X2 X4 0.4320035
38 38 X6 X5 0.4110417
39 39 X4 X3 0.4109206
40 40 X3 X6 0.4108423
41 41 A2 X5 0.4100743
42 42 X3 X5 0.4061762
43 43 X1 X5 0.4002047
44 44 X7 X4 0.3833016
45 45 X3 X4 0.3677971
46 46 X4 X7 0.3566939
47 47 X7 X9 0.3509262
48 48 A1 X10 0.3494854
49 49 X5 X6 0.3453436
50 50 X5 X4 0.3387522
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