Learning Classifier Systems
for Class Imbalance
Problems
Ester Bernadó-Mansilla
Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle
Universitat Ramon Llull
Barcelona, Spain

Aim
Enhance the applicability of LCSs
to knowledge discovery from datasets
Classification problems
Real-world domains
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Framework
model
LCS
Dataset
+
estimated
performance
• Representativity of the target
• Evolutionary pressures
concept
• Interpretability
• Geometrical complexity
• Domain of applicability
• Class imbalance
• Noise
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Class Imbalance
When one class is represented by a small number of

examples, compared to other class/es.
Usually the class of that describes the circumscribed

concept (positive class) is the minority class
Where?

Rare medical diagnoses

Fraud detection

Oil spills in satellite images

Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Class Imbalance and Classifiers
Is there a bias towards the majority class?

Probably, because…

Most classifier schemes are trained to minimize the global error

As a result

They classify accurately the examples from the majority class

They tend to misclassify the examples of the minority class,

which are often those representing the target concept.
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Measures of Performance
Confusion matrix
Prediction
A B
Actual A true positive (TP) false negative (FN)
B false positive (FP) true negative (TN)
Accuracy = (TP+TN)/(TP+FN+FP+TN)
TN rate = TN / (TN + FP)
TP rate = TP / (FN + TP)
ROC curves
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

The Higher Class Imbalance: the
Higher Bias?
Dataset 1 Dataset 2
concept: 15 concept: 15
counterpart: 150 counterpart: 45
ratio: 10:1 ratio: 3:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

XCS
XCS
class
input Set of
Rules
update
search
Genetic Reinforcement
Algorithms Learning
reward
Environment
Dataset
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Our Approach with XCS
Bounding XCS’s parameters for unbalanced datasets

Online identification of small disjuncts

Adaptation of parameters for the discovery of small

disjuncts
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

XCS’s Behavior in Unbalanced
Datasets
Unbalanced 11-multiplexer problem
ir=16:1 ir=32:1 ir=64:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

XCS’s Population
Most numerous rules, ir=128:1
Classifier P Error F Num
###########:0 1000 0.12 0.98 385
1.2 10-4
###########:1 0.074 0.98 366
estimated estimated too high
high
prediction:
overgeneral error: numerosity
fitness
992.24
classifiers 15.38
7.75
Test examples are classified as belonging to the majority class
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

How Imbalance Affects XCS
Classifier’s error

Stability of prediction and error estimates

Occurrence-based reproduction

Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Classifier’s Error in Unbalanced
Datasets
Will an overgeneral classifier be detected as inaccurate if the

imbalance ratio is high?
Bound for inaccurate classifier: !\"!0
Given the estimated prediction and error:
P = Pc (cl ) Rmax + (1 ! Pc (cl )) Rmin
\"=| P ! Rmax | Pc (cl )+ | P ! Rmin | (1 ! Pc (cl ))
We derive:
# \"o p 2 + 2 p ( Rmax # \"0 )# \"0 ! 0
where !\"!0
p =!C / C
For
Rmax = 1000 !0 = 1
we get maximum imbalance ratio:
irmax = 1998
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Prediction and Error Estimates and
Learning Rate
ir=128:1, ###########:0
Error
Prediction
β=0.2
β=0.002
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Occurrence-based Reproduction
Probability of occurrence (pocc)
Given ir=maj/min:
0,6
Classifier poccB poccI
0,5
1/2 1/2
########### :0
probability of occurrence
1/2 1/2
########### :1 0,4
0,3
0000#######:0 1/32
0,2
0001#######:1 1/32 0,1
0
1 2 4 8 16 32 64 128 256
imbalance ratio
22ir
p occB 00001######:1 00000######:0
ir + 1 ###########:0 ###########:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Occurrence-based Reproduction
Probability of reproduction (pGA)

1
pGA =
TGA
if Tocc < % GA
#% GA
where TGA $ \"
!Tocc otherwise
With θGA=20:

GA
Tocc
…
T (# # # # # # # # # # #: 0) ! \"
GA GA
θGA
Tocc
GA
…
T (0000# # # # # # #: 0) ! T 1
GA occ
θGA
1 Assuming non-overlapping
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Guidelines for Parameter Tuning
Rmax and є0 determine the threshold between negligible noise and

imbalance ratio
β determines the size of the moving window. The window should be

high enough to allow computing examples from both classes:
f min
! =k
f maj
θGA can counterbalance the reproduction opportunities of most frequent

(majority) and least frequent niches (minority):
1
! GA = k '
f min
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

XCS with Parameters Tuning
XCS with parameter tuning
XCS with standard settings
ir=16:1 ir=32:1 ir=64:1 ir=64:1 ir=256:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

XCS Tuning for Real-world Datasets
How we can estimate the niche frequency?

Estimate from the ratio of majority class instances and minority

class instances
Problem:

• This may not be related to the distribution of niches in the feature
space
Take the approach to the small disjuncts problem

Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Online Identification of Small Disjuncts
We search for regions that promote

overgeneral classifiers
Estimate ircl based on the classifier’s

experience on each class:
exp max
ircl =
exp min
Adapt β and θGA according to ircl

ircl = 20 / 4
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Online Parameter Adaptation
ir=256:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

What about UCS?
Supervised XCS:

Needs less exploration

Avoids XCS’s fitness dilemma

More robust to parameter settings

Overgeneral classifiers also tend to overcome the

population
Their probability of occurrence depends on the imbalance ratio

Partially minimized with fitness sharing

Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

What about UCS?
ir=256:1
ir=512:1
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Are LCSs more error-prone to class imbalance
than other classifier schemes?
C4.5 SMO XCS
TP rate Bal2c1 0,00% ± 0,00% 0,00% ± 0,00% 0,00% ± 0,00%
Bal2c2 81,65% ± 6,83% 93,72% ± 4,64% 81,96% ± 6,00%
Bal2c3 81,90% ± 6,04% 93,77% ± 5,59% 83,99% ± 6,88%
bpa 42,95% ± 14,09% 0,00% ± 0,00% 61,38% ± 9,10%
gls2c1 80,00% ± 42,16% 0,00% ± 0,00% 50,00% ± 52,70%
gls2c2 35,00% ± 47,43% 15,00% ± 33,75% 55,00% ± 49,72%
gls2c3 30,00% ± 42,16% 0,00% ± 0,00% 5,00% ± 15,81%
gls2c4 75,00% ± 32,63% 81,67% ± 25,40% 81,67% ± 25,40%
gls2c5 77,14% ± 16,77% 10,00% ± 9,64% 84,29% ± 14,21%
gls2c6 59,82% ± 15,13% 0,00% ± 0,00% 81,79% ± 13,95%
h-s 75,83% ± 13,29% 80,00% ± 7,03% 80,00% ± 9,78%
pim 55,37% ± 13,27% 53,38% ± 6,42% 55,93% ± 9,75%
tao 95,23% ± 2,14% 84,11% ± 6,17% 92,58% ± 5,72%
thy2c1 90,00% ± 16,10% 76,67% ± 22,50% 90,00% ± 16,10%
thy2c2 94,17% ± 12,45% 54,17% ± 24,92% 90,83% ± 14,93%
thy2c3 90,95% ± 10,34% 33,81% ± 21,35% 90,71% ± 8,05%
wav2c1 75,74% ± 4,06% 88,51% ± 3,20% 87,24% ± 3,43%
wav2c2 72,34% ± 3,89% 84,57% ± 4,05% 78,72% ± 2,57%
wab2c3 77,64% ± 2,38% 89,97% ± 3,48% 87,86% ± 3,65%
wbdc 92,95% ± 3,42% 95,42% ± 5,36% 95,83% ± 5,89%
wdbc 92,47% ± 5,09% 94,81% ± 2,71% 93,83% ± 6,37%
wine2c1 89,00% ± 16,63% 100,00% ± 0,00% 100,00% ± 0,00%
wine2c2 95,00% ± 8,05% 98,33% ± 5,27% 98,33% ± 5,27%
wine2c3 90,18% ± 11,70% 97,14% ± 6,02% 98,57% ± 4,52%
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla
wpbc 41,00% ± 12,87% 9,50% ± 17,07% 30,50% ± 24,99%

How can we Minimize the Effects of
Small Disjuncts?
Resampling the dataset:
 Addresses small
disjuncts
Classical methods:

• Random oversampling
• Random undersampling Assumes that
clusterization will
Heuristic methods:

find small
• Tomek links
disjuncts and
• CNN match classifier’s
• One-sided selection approximation
• Smote
Cluster-based oversampling
 Could XCS
benefit from the
online
Cost-sensitive classifiers

identification of
small disjuncts?
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Domains of Applicability
Should we use some counterbalancing scheme?

Which learning scheme should we use?

Is there a combination of counterbalancing

scheme+learner that beats all others?
How can we know the presence of small

disjuncts?
Are there other complexity factors mixed up with

the small disjuncts problem?
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Domains of Applicability
Resampling/
Learn it! Classifier/
Resampling+classifier
Where are
LCSs
placed?
Dataset Dataset
Suggested
Prediction
characterization
approach
Type of dataset:
Geometrical distribution of classes
Possible presence of small disjuncts
Other complexity factors
Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Future Directions
Potential benefit of XCS to discover small disjuncts

…and learn from it online
Further analyze UCS

How do LCSs perform w.r.t. other classifiers for unbalanced

datasets?
Measures for small disjuncts identification

… and other possible complexity factors
What is noise and what is a small disjunct?

In which cases a LCS is applicable?

Learning Classifier Systems for Class Imbalance Problems Ester Bernadó-Mansilla

Learning Classifier Systems
for Class Imbalance
Problems
Ester Bernadó-Mansilla
Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle
Universitat Ramon Llull
Barcelona, Spain