Extended Compact Genetic Algorithms and Learning Classifier Systems for Dimensionality Reduction: a Protein Alphabet Reduction Study Case

Extended Compact Genetic Algorithms and Learning
Classiﬁer Systems for Dimensionality Reduction: a
Protein Alphabet Reduction Study Case

Jaume Bacardit & Natalio Krasnogor

ASAP - Interdisciplinary Optimisation Laboratory
School of Computer Science

Centre for Integrative Systems Biology
School of Biology

Centre for Healthcare Associated Infections
Institute of Infection, Immunity & Inflammation

University of Nottingham

Ben-Gurion University of the Negev - June 23rd to July 5th 2009 - Distinguished Scientist Visitor Program - Beer Sheva, Israel 1 /73
Tuesday, 30 June 2009

Acknowledgements
(in no particular order) (in no particular order)
 Peter Siepmann
Contributors to the talks I will give at BGU

 Pawel Widera  School of Physics and Astronomy
 James Smaldon  School of Chemistry
 School of Pharmacy
 Azhar Ali Shah
 School of Biosciences
 Jack Chaplin
 School of Mathematics
 Enrico Glaab  School of Computer Science
 German Terrazas  Centre for Biomolecular Sciences
 Hongqing Cao  all the above at UoN
 Jamie Twycross
 Jonathan Blake Thanks also go to:
 Francisco Romero-Campero
 Maria Franco Ben Gurion University of the
 Adam Sweetman
 Linda Fiaschi
Negev’s Distinguished Scientists
Visitor Program
Funding From:
BBSRC, EPSRC, EU, ESF, UoN Professor Dr. Moshe Sipper

Outline
 Introduction to Learning Classifier Systems
and Extended Compact GA
 Problem Definition
 Methods (ECGA, LCS, Mutual Information)
 Results
 Conclusions and further work


Based on Various Papers
 J.Bacardit, M.Stout, J.D. Hirst, A.Valencia, R.E.Smith, and N.Krasnogor. Automated
alphabet reduction for protein datasets. BMC Bioinformatics, 10(6), 2009.
 J. Bacardit, M. Stout, J.D. Hirst, K. Sastry, X. Llora, and N. Krasnogor. Automated
alphabet reduction method with evolutionary algorithms for protein structure prediction.
In Proceedings of the 2007 Genetic and Evolutionary Computation Conference,
number ISBN 978-1-59593-697-4, pages 346-353. ACM Press, 2007. This paper won
the Bronze Medal in the THE 2007 “HUMIES” AWARDS FOR HUMAN-COMPETITIVE
RESULTS PRODUCED BY GENETIC AND EVOLUTIONARY COMPUTATION. J.
 J.Bacardit and N. Krasnogor. Performance and efficiency of memetic pittsburgh
learning classifier systems. Evolutionary Computation, 17(3):(to appear), 2009.
 J.Bacardit, E.K. Burke, and N.Krasnogor. Improving the scalability of rule-based
evolutionary learning. Memetic Computing, 1(1):(to appear), 2009
 J. Bacardit, M. Stout, and N. Krasnogor. A tale of human-competiveness in
bioinformatics. Newsletter of ACM Special Interest Group on Genetic and Evolutionary
Computation: SIGEvolution, 3(1):2-10, 2008.

All papers available from: www.cs.nott.ac.uk/~nxk/publications.html


 Learning Classifier Systems (LCS) are one of
the major families of techniques that apply
evolutionary computation to machine learning
tasks
 Machine learning: How to construct
programs that automatically improve with
experience [Mitchell, 1997]
 Classification task: Learning how to label
correctly new instances from a domain based
on a set of previously labeled instances
 LCS are almost as ancient as GAs, Holland
made one of the first proposals
 Two of the first LCS proposals are [Holland &
Reitman, 78] and [Smith, 80]


 Traditionally there have been two different
paradigms of LCS
 The Pittsburgh approach [Smith, 80]
 The Michigan approach [Holland & Reitman,
78]
 More recently: The Iterative Rule Learning
approach [Venturini, 93]

 Knowledge representations
 All the initial approaches were rule-based
 In recent years several knowledge
representations have been used in the LCS
field: decision trees, synthetic prototypes, etc.


Classification task
 Classification task: Learning how to label correctly new
instances from a domain based on a set of previously labeled
instances

New Instance

Learning Inference
Training Set
Algorithm Engine

Class


Classification task

1
If (X<0.25 and
Y>0.75) or
(X>0.75 and
Y
Y<0.25) then 

0 1
X

Paradigms of LCS
 The Pittsburgh approach
 Each individual is a complete solution to
the classification problem
 Traditionally this means that each
individual is a variable-length set of rules
 GABIL [De Jong & Spears, 93] is a well-
known representative of this approach
 Fitness function is based on the rule set
accuracy on the training set (usually also
on complexity)

Paradigms of LCS
 The Pittsburgh approach
 Crossover operator
Parents Offspring

 Mutation operator: bit flipping
 Individuals are interpreted as a decision list: an ordered rule set

Instance 1 matches rules 2, 3 and 7  Rule 2 will be used
Instance 2 matches rules 1 and 8  Rule 1 will be used
1 2 3 4 5 6 7 8 Instance 3 matches rule 8  Rule 8 will be used
Instance 4 matches no rules  Instance 4 will not be
classified


Paradigms of LCS
 The Michigan approach
 Each individual is a single rule
 The whole population cooperates to solve
the classification problem
 A reinforcement system is used to identify
the good rules
 A GA is used to explore the search space
for more rules
 XCS [Wilson, 95] is the most well-known
Michigan LCS


Paradigms of LCS
 Working cycle


Paradigms of LCS
 The Iterative Rule Learning approach
 Each individual is a single rule
 Individuals compete as in a standard
GA  A single GA run generates one
rule
 The GA is run iteratively to learn all rules
that solve the problem
 Instances already covered by previous
rules are removed from the training set
of the next iteration


Paradigms of LCS
 The Iterative Rule Learning approach
 HIDER System [Aguilar, Riquelme & Toro, 03]

1. Input: Examples

2. RuleSet = Ø

3. While |Examples| > 0

1. Rule = Run GA with Examples

2. RuleSet = RuleSet U Rule

3. Examples = Examples Covered(Rule)

4. EndWhile

5. Output: RuleSet


Bioinformatics-oriented Hierarchical
Evolutionary Learning (BioHel)

 BioHEL [Bacardit et al., 07] is a recent learning
system that applies the Iterative Rule Learning
(IRL) approach to generate sets of rules
 IRL was first used in EC by the SIA system
[Venturini, 93]
 BioHEL is strongly inspired by GAssist
[Bacardit, 04], a Pittsburgh approach Learning
Classifier System


 BioHEL learning paradigm
 IRL has been used for many years in the ML
community, with the name of separate-and-conquer


BioHEL’s objective function
 An objective function based on the Minimum-
Description-Length (MDL) (Rissanen,1978) principle
that tries to promote rules with
 High accuracy: not making mistakes
 High coverage: covering as many examples as possible
without sacrificing accuracy. Recall (TP/(TP+FN)) will be
used to define coverage
 Low complexity: rules as simple and general as possible
 The objective function is a linear combination of the three
objectives above


BioHEL’s objective function
 Intuitively, we would like to have accurate rules
covering as many examples as possible.
 However, in complex and inconsistent domains it is
rare to obtain such rules
 In these cases, easier path for evolutionary search is to
maximize accuracy at the expense of coverage
 Therefore, we need to enforce that the evolved rules
cover enough examples


Methods: BioHEL’s objective function

 Three parameters define the shape of the function
 The choice of the coverage break is crucial for the proper performance of the
system
 Also, coverage term penalizes rules that do not cover a minimum percentage of
examples or that cover too many

BioHEL’s other characteristics
 Attribute list rule representation
 Automatically identifying the relevant attributes for a given rule and
discarding all the other ones
 The ILAS windowing scheme
 Efficiency enhancement method, not all training points are used for each
fitness computation
 An explicit default rule mechanism
 Generating more compact rule sets
 Iterative process terminates when it is impossible to evolve a rule where
the associated class is the majority class among the matched examples
 At this point, all remaining training instances are assigned to the default
class
 Ensembles for consensus prediction
 Easy way of boosting robustness


Knowledge representations
 Representation of XCS for binary problems:
ternary representation
 Ternary alphabet {0,1,#}
 If A1=0 and A2=1 and A3 is irrelevant  class 0
 01#|0
 Representation of XCS for real-valued attributes:
real-valued interval.
 XCSR [Wilson, 99]
 Interval is codified with two variables: center & spread: [center-
spread, center+spread]
 UBR [ Stone & Bull, 03]
 The two bounds of the interval are codified directly with two real-
valued variables. The variable with lowest value is the lower
bound, the variable with higher value is the upper bound

 Representation of GABIL for nominal attributes
 Predicate → Class
 Predicate: Conjunctive Normal Form (CNF) (A1=V11∨..
∨ A1=V1n) ∧.....∧ (An=Vn2∨.. ∨ An=Vnm)
 Ai : ith attribute
 Vij : jth value of the ith attribute
 The rules can be mapped into a binary string, e.g., 3
attributes with {3,5,2} values each respectively:
 (A1=V11∨ A1=V13) ∧ (A2=V22 ∨ A2=V24 ∨ A2=V25) ∧
(A3=V31) 101|01011|10


 Pittsburgh representations for real-valued attributes:
 Rule-based: Adaptive Discretization Intervals (ADI)
representation [Bacardit, 04]
 Intervals in ADI are build using as possible
bounds the cut-points proposed by a
discretization algorithm
 Search bias promotes maximally general
intervals
 Several discretization algorithms are used at the
same time to reduce bias


 Pittsburgh representations for real-valued attributes:
 Decision trees [Llorà, 02]
 Nodes in the trees can use orthogonal or oblique criteria


 Pittsburgh representations for real-valued attributes
 Synthetic prototypes [Llorà, 02]
 Each individual is a set of synthetic instances
 These instances are used as the core of a nearest-neighbor
classifier

?


Extended Compact Genetic
Algorithm (ECGA)
 ECGA belongs to a class of Evolutionary
Algorithms called Estimation of Distribution
Algorithms (EDA)
 no crossover or mutation!
 instead a probabilistic model of the
structure of the problem is kept
 individuals are sampled from this probability
distribution model


Taken from: Linkage Learning via Probabilistic Modeling in the Extended Compact
Genetic Algorithm (ECGA) by Georges R. Harik, Fernando G. Lobo and Kumara
Sastry. Studies in Computational Intelligence, Volume 33/2006, Springer, 2007.

Text

Text

Key Idea Behind Compact GA (CGA)



 Genes Interactions must be accounted for
 Approximates complex distributions by
Marginal Distribution Models (i.e. genes
partitions)
 Selects amongst alternative models by
means of the MDL:


Outline
 Results


Protein Structure Prediction (PSP) has as goal to predict
the 3D structure of a protein based on its primary
sequence

Primary Sequence 3D Structure


 PSP is a very costly process
 As an example, one of the best PSP
methods in the last CASP meeting,
Rosetta@Home used up to 104
computing years to predict a single
protein’s 3D structure
 Ways to alleviate computational burden:
 to simplify the problem
 to simplify the representation used to
model the proteins

From Full PSP to CN prediction
 Two residues of a chain are said to be in contact if
their distance is less than a certain threshold

Primary Contact Native State
Sequence

 CN of a residue : number of contacts that a certain
residue has
 In this specific case we predict, e.g., whether the
CN of a residue is smaller or higher than the
middle point of the CN domain

From Full PSP to SA prediction
 Solvent Accessibility:
Amount of surface of
each residue that is
exposed to the solvent
(e.g. water)
 Metric is normalised for
each AA type
 Problem is to predict
whether SA is lower or
higher than 25%


 PSP is a very costly process
 As an example, one of the best PSP
methods in the last CASP meeting,
Rosetta@Home used up to 104
computing years to predict a single
protein’s 3D structure
 Ways to alleviate computational burden:
 to simplify the problem
 to simplify the representation used to
model the proteins

 Primary Sequence of a protein (the amino acid
type of the elements of a protein chain) is an usual
target for such simplification
 It is composed of a quite high cardinality
alphabet of 20 symbols
 One example of reduction widely used in the
community is the hydrophobic-polar (HP)
alphabet, reducing these 20 symbols to just two
 HP representation usually is too simple,
information is lost in the reduction process
 M. Stout, et al. Prediction of residue exposure and contact number for simplified hp lattice model proteins using
learning classifier systems. In Proceedings of the 7th International FLINS Conference on Applied Artificial Intelligence,
pages 601-608. World Scientific, August 2006.
 M. Stout, J. Bacardit, J.D. Hirst, N. Krasnogor, and J. Blazewicz. From hp lattice models to real proteins: coordination
number prediction using learning classifier systems. In 4th European Workshop on Evolutionary Computation and
Machine Learning in Bioinformatics, volume 3907 of Springer Lecture Notes in Computer Science, page 208–220,
Budapest, Hungary, April 2006. Springer. ISBN 978-3-540-33237-4.
 papers at: http://www.cs.nott.ac.uk/~nxk/publications.html


 Research Question:

 Are there “simplified” alphabets that
retain key information content while
simplifying interpretation,processing
time, etc?
 If yes, are these alphabet general for
any problem domain or domain
specific?
 Can we automatically generate these
alphabets and tailor them to the
specific domain we are predicting?

Outline
 Results


 Use an (automated) information theory-driven pipeline to
reduce alphabet for PSP datasets
 Use the Extended Compact Genetic Algorithm (ECGA) to find
a dimensionality reduction policy (guided by a fitness function
based on the Mutual Information (MI) metric)
 Two PSP datasets will be used as testbed:
 Coordination Number (CN) prediction
 Relative Solvent Accessibility (SA) prediction
 Verify the optimized reduction policies with BioHEL, an
evolutionary-computation based rule learning system
J.Bacardit, M.Stout, J.D. Hirst, A.Valencia, R.E.Smith, and N.Krasnogor. Automated alphabet reduction for
protein datasets. BMC Bioinformatics, 10(6), 2009.
J. Bacardit, M. Stout, and N. Krasnogor. A tale of human-competiveness in bioinformatics. Newsletter of
ACM Special Interest Group on Genetic and Evolutionary Computation: SIGEvolution, 3(1):2-10, 2008.
J. Bacardit, M. Stout, J.D. Hirst, K. Sastry, X. Llora, and N. Krasnogor. Automated alphabet reduction
method with evolutionary algorithms for protein structure prediction. In Proceedings of the 2007 Genetic
and Evolutionary Computation Conference, number ISBN 978-1-59593-697-4, pages 346-353. ACM Press,
2007.

All papers at: http://www.cs.nott.ac.uk/~nxk/publications.html

 Protein dataset proposed by [Kinjo et al., 05]
 1050 proteins
 259768 residues
 Proteins were selected from PDB-REPRDB using
these conditions:
 Less than 30% sequence identity
 More than 50 residues
 Resolution better than 2Å
 No membrane proteins, no chain breaks, no non-
standard residues
 Crystallographic R-factor better than 20%
 Dataset is partitioned into training/test sets using ten-
fold cross-validation

Instance Representation

AAi-5 AAi-4 AAi-3 AAi-2 AAi-1 AAi AAi+1 AAi+2 AAi+3 AAi+4 AAi+5
CNi-5 CNi-4 CNi-3 CNi-2 CNi-1 CNi CNi+1 CNi+2 CNi+3 CNi+4 CNi+5

AAi-1,AAi,AAi+1  CNi
AAi,AAi+1,AAi+2  CNi+1
AAi+1,AAi+2,AAi+3  CNi+2


Taken from: J. Bacardit, M. Stout, J.D. Hirst, K. Sastry, X. Llora, and N. Krasnogor.
Automated alphabet reduction method with evolutionary algorithms for protein
structure prediction. In Proceedings of the 2007 Genetic and Evolutionary
Computation Conference, number ISBN 978-1-59593-697-4, pages 346-353. ACM
Press, 2007.


General Workflow of the Alphabet Reduction Pipeline

Size = N Test set

Dataset ECGA Dataset BioHEL Ensemble
|∑|=20 |∑|=N of rule sets

Accuracy
Mutual
Information


Methods: alphabet reduction
strategies
 Three strategies were evaluated
 They represent progressive levels of
sophistication
 Mutual Information (MI)
 Robust Mutual Information (RMI)
 Dual Robust Mutual Information (DualRMI)
 Thus MI, RMI, DualRMI were used in
separate experiments as the “fitness”
function for the ECGA tournament phase.

Methods: MI strategy
 There are 21 symbols (20AA+end of chain) in the
alphabet
 Each symbol will be assigned to a group in the
chromosome used by ECGA


Methods: MI stragegy
 Objective function for MI strategy: Mutual Information
 Mutual Information is a measure that quantifies the
interrelationship that two discrete variables have
among each other

 X is the reduced representation of the window of
residues around the target.
 Y is the two-state definition fo CN or SA


 Steps of objective function computation for the
MI strategy
1. Reduction mappings are extracted from the
chromosome
2. Instances of the training set are transformed into the
lower cardinality alphabet
3. Mutual information between the class attribute and
the string formed by concatenating the input
attributes is computed
4. This MI is assigned as the result of the evaluation
function


 Problem of MI strategy
 Mutual Information needs redundancy in order to become a good
estimator
 That is, each possible pattern in X and Y should be well represented in
the dataset
 Patterns in Y are always well represented. What happens with patterns in
X in our dataset?
 Our sample, despite having almost 260000 residues is too small

#letters Represented patterns
2 100%
3 97.8%
4 57.6%
5 11.3%
20 3.1E-07

Methods: RMI strategy
 In order to solve the sample size problem of the MI strategy, we use
a robust MI estimator proposed by [Cline et al., 02]
 Pairs of (x,y) in the dataset are scrambled
 That is, each x in the dataset is randomly joined to an y but the
distribution of x and y remains equal
 MI is computed for the scrambled dataset
 This process is repeated N time, and the average scrambled MI is
computed

 Finally, the value for the objective function is MI – Mis
 Mis is an estimation of the sampling bias in the data. By subtracting
it from the original MI metric we obtain a less biased objective
function


Methods: DualRMI strategy
 The next strategy is based on some observations we
did in previous work [Bacardit et al., 06]
 Example of a rule set for prediction CN from primary
sequence

 Predicate associated to the target residue (AA) is
very different from the predicates associated to the
other window positions

Methods: DualRMI strategy
 Why not generating two reduced alphabets
at the same time?
 One for the target residue
 One for the other residues in the window
 Objective function remains unchanged


Outline
 Results


Experimental design
 For each problem (CN, SA)
 For each reduction strategy (MI, RMI, DualRMI)
 ECGA was run to generate alphabets of two, three,
four and five letters
 Afterwards, BioHEL was trained over the reduced
datasets to determine the prediction accuracy that
could be obtained from each alphabet size
 Comparisons are drawn


Reduced alphabets for CN
Amino acids that remain always in the same group
are marked with solid rectangles


Alphabets for CN
 The two-letter alphabet divides the amino-acids between
hydrophobic and polar
 RMI could not find a five-letter alphabet
 DualRMI did, but only for the target residue
 RMI and DualRMI have a much larger number of framed
residues, showing more robustness
 For DualRMI we can observe small groups of hydrophobic
residues, while all polar ones are in the same group
 We can also observe a strange group, GHTS, that mixes
different kind of physico-chemical properties
 Not explained by properties but by inherent distribution in
datasets


 A retrospective
analysis of the dataset
reveals why GHTS
are clustered together
 We computed the
proportion of residues
for each amino acid
type with high CN
 These four residues
have very similar
average behavior in
relation to CN


Accuracy of CN prediction Using Biohel
 Accuracy difference
between the AA
representation and the
best reduced
alphabets is 0.7%
 Difference in non-
significant according to
t-tests
 RMI and DualRMI
perform similarly


Reduced alphabets for SA


Reduced alphabets for SA
 Even though SA and CN are somewhat related
structural features, the resulting alphabets are
different
 These alphabets contain more groups of polar
residues, and less groups of hydrophobic ones (in
contrast with CN)
 In DualRMI and 5 letters we can observe very small
groups
 A, EK for the target alphabet
 G,X for the other residues alphabet
 Again, the GHTS group appears

 Analysis of
average SA
behavior for
each AA type
 The reduced
alphabet
matched
perfectly the
properties of the
SA features


Accuracy of SA prediction with BioHel
 Accuracy of reduced
alphabets for SA
prediction
 Only DualRMI
managed to give a
performace
statistically similar to
the original AA
representation
 Accuracy difference
is 0.4%


Comparison to Other Reduced Alphabets from the
Literature and Expert-Designed Alphabets Based on
Physico-Chemical Properties
Alphabet Letters CN acc. SA acc. Diff. Ref.
AA 20 74.0±0.6 70.7±0.4 --- ---

DualRMI 5 73.3±0.5 70.3±0.4 0.7/0.4 This work

WW5 6 73.1±0.7 69.6±0.4 0.9/1.1 [Wang & Wang, 99]

Alphabets from
the literature
SR5 6 73.1±0.7 69.6±0.4 0.9/1.1 [Solis & Rackovsky, 00]

MU4 5 72.6±0.7 69.4±0.4 1.4/1.3 [Murphy et al., 00]

MM5 6 73.1±0.6 69.3±0.3 0.9/1.4 [Melo & Marti-Renom, 06]

Expert designed
HD1 7 72.9±0.6 69.3±0.4 1.1/1.4 This work

alphabets
HD2 9 73.0±0.6 69.3±0.4 1.0/1.4 This work

HD3 11 73.2±0.6 69.9±0.4 0.8/0.8 This work


Reduced Alphabets Comparison
 Automatically reduced alphabets obtain better accuracy,
but how different are the alphabets themselves?
 We applied again the AA-wise high CN/SA analysis
 Two metrics were computed
 Transitions: how many times does the group index change
through the list of sorted AA.
 The less number of changes, the more homogenous the groups are
 Average range: The range of a reduction group is the
difference between the minimum and maximum CN/SA of the
AAs belonging to that group
 The smaller the average range, the more focused the reduction
groups are in relation to that structural property


Reduced Alphabets Comparison (CN)


Reduced Alphabets Comparison (SA)


Additional Results

 Are the alphabets interchangeable across
problems?
 Can these reduced alphabets be applied to
an evolutionary information-based
representation?


Results: Are the alphabets interchangeable?
 We applied the alphabet optimized for CN to SA and vice
versa

 SA alphabet is good for predicting CN, but CN alphabet
obtains poor performance on SA
 Reduced alphabets must always be tailored to the
domain at hand

Results
 Application of the reduced alphabets to an evolutionary
information-based representation
 So far we have used only the simple primary sequence
representation
 Can this process be applied to much richer (and complex)
representations?
 We computed the position-specific scoring matrices (PSSM)
representation of our dataset using PSI-BLAST. Each
instance (9 window positions) is represented by 180
continuous variables (rather than 20+1 as originally done)
 Then, we reduced this representation using our alphabets
 The values of each PSSM profile corresponding to amino acids in
the same reduction group are averaged


Results

 Application of
reduced
alphabets to a
PSSM
representation
 Thus, we
reduced the
representation
from 180
attributes to 45


Results
 Results of learning from the reduced PSSM
representation

 Accuracy difference is still less than 1%
 Obtained rules sets are simpler and training process
is much faster
 Performance levels are similar to recent works in the
literature [Kinjo et al., 05][Dor and Zhou, 07]

Conclusions
 We have proposed an automated alphabet reduction protocol
for protein datasets
 Protocol does not use any domain knowledge
 It automatically tailors the reduced datasets to the domain at hand
 Our experiments show that it is possible to obtain quite
reduced alphabets (5 letters) with similar performance than
the original AA alphabet
 Our reduced alphabets are better at CN and SA prediction
than other alphabet from the literature, as they are better
suited for these tasks
 The findings from the protocol can be used in state-of-the-art
protein representations as PSSM profiles
 We found some unexpected reduction groups (GHTS) but the
properties of the data showed us that this is not an artifact


Future work
 Explore alternative objective evaluation functions
 Other robust MI estimation
 Explore slightly higher cardinality alphabets
 Is it possible to close the accuracy gap even more?
 Apply this protocol to other kind of datasets
 E.g. protein mutations
 Structural aspects defined as continuous variables, not
just discrete ones


Acknowledgements
(in no particular order) (in no particular order)
 Peter Siepmann
Contributors to the talks I will give at BGU

 Pawel Widera  School of Physics and Astronomy
 James Smaldon  School of Chemistry
 School of Pharmacy
 Azhar Ali Shah
 School of Biosciences
 Jack Chaplin
 School of Mathematics
 Enrico Glaab  School of Computer Science
 German Terrazas  Centre for Biomolecular Sciences
 Hongqing Cao  all the above at UoN
 Jamie Twycross
 Jonathan Blake Thanks also go to:
 Francisco Romero-Campero
 Maria Franco Ben Gurion University of the
 Adam Sweetman
 Linda Fiaschi
Negev’s Distinguished Scientists
Visitor Program
Funding From:
BBSRC, EPSRC, EU, ESF, UoN Professor Dr. Moshe Sipper

Extended Compact Genetic Algorithms and Learning Classifier Systems for Dimensionality Reduction: a Protein Alphabet Reduction Study Case

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Extended Compact Genetic Algorithms and Learning Classifier Systems for Dimensionality Reduction: a Protein Alphabet Reduction Study Case