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Feature selection and transduction
for prediction of molecular bioactivity
for drug design
Bioinformatics Vol. 19 no. 6 2003 (Pages 764-771)
Reporter: Yu Lun Kuo (D95922037)
E-mail: sscc6991@gmail.com
Date: April 17, 2008
Abstract
• Drug discovery
– Identify characteristics that separate active
(binding) compounds from inactive ones.
• Two method for prediction of bioactivity
– Feature selection method
– Transductive method
• Improvement over using only one of the techniques
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Introduction (1/4)
• Discovery of a new drug
– Testing many small molecules for their ability to
bind to the target site
– The task of determining what separate the active
(binding) compounds from the inactive ones
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Introduction (2/4)
• Design new compounds
– Not only bind
– But also possess certain other properties
required for a drug
• The task of determination can be seen in a
machine learning context as one of feature
selection
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Introduction (3/4)
• Challenging
– Few positive examples
• Little information is given indicating positive correlation
between features and the labels
– Large number of features
• Selected from a huge collection of useful features
• Some features are in reality uncorrelated with the labels
– Different distributions
• Cannot expect the data to come from a fix distribution
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Introduction (4/4)
• Many conventional machine learning
algorithms are illequiped to deal with these
• Many algorithms generalize poorly
– The high dimensionality of the problem
– The problem size many methods are no longer
computationally feasible
– Most cannot deal with training and testing data
coming from different distributions
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Overcome
• Feature selection criterion
– Called unbalanced correlation score
• Take into account the unbalanced nature of the data
• Simple enough to avoid overfitting
• Classifier
– Takes into account the different distributions in
the test data compared to the training data
• Induction
• Transduction
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Overcome
• Induction
– Builds a model based only on the distribution of
the training data
• Transduction
– Also take into account the test data inputs
• Combining these two techniques we obtained
improved prediction accuracy
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KDD Cup Competition (1/2)
• We focused on a well studies data set
– KDD Cup 2001 competition
• Knowledge Discovery and Data Mining
• One of the premier meetings of the data mining
community
– http://www.kdnuggets.com/datasets/kddcup.html
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KDD Cup Competition (2/2)
• KDD Cup 2006
– data mining for medical diagnosis, specifically identifying
pulmonary embolisms from three-dimensional computed
tomography data
• KDD Cup 2004
– features tasks in particle physics and bioinformatics
evaluated on a variety of different measures
• KDD Cup 2002
– focus: bioinformatics and text mining
• KDD Cup 2001
– focus: bioinformatics and drug discovery
•
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KDD Cup 2001 (1/2)
• Objective
– Prediction of molecular bioactivity for drug
design -- binding to Thrombin
• Data
– Training: 1909 cases (42 positive), 139,351
binary features
– Test: 634 cases
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KDD Cup 2001 (2/2)
• Challenge
– Highly imbalanced, high-dimensional, different
distribution
• Approach
– Bayesian network predictive model
– Data PreProcessor system
– BN PowerPredictor system
– BN PowerConstructor system
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Data Set (1/3)
• Provided by DuPont Pharmaceuticals
– Drug binds to a target site on thrombin, a key
receptor in blood clotting
• Each example has a fixed length vector of
139,351 binary features in {0, 1}
– Which describe three-dimensional properties of
the molecule
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Data Set (2/3)
• Positive examples are labeled +1
• Negative examples are labeled -1
• In the training set
– 1909 examples, 42 of which bind
(rather unbalanced, positive is 2.2%)
• In the test set
– 634 additional compounds
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Data Set (3/3)
• An important characteristic of the data
– Very few of the feature entries are non-zero
(0.68% of the 1,909 X 139,351 training matrix)
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System Assessment
• Performance is evaluated according to a
weighted accuracy criterion
– The score of an estimate y’ of the labels y
1 #{ y': y  1^ y'  1} 1 #{ y': y  1^ y'  1}
lbal( y, y' )  (
) (
)
2
#{ y : y  1}
2
#{ y : y  1}
– Complete success is a score of 1
• Multiply this score by 100 as the percentage weighted
success rate
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Methodology
• Predict the labels on the test set by using a
machine learning algorithm
• The positively and negatively labeled training
examples are split randomly into n groups
– For n-fold cross validation such that as close to
1/n of the positively labeled examples are
present in each group as possible
• Called balanced cross validation
– As few positive examples
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Methodology
• The method is
– Trained on n-1 of groups
– Tested on the remaining group
– Repeated n times (different group for testing)
– Final score: mean of the n scores
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Feature Selection (1/2)
• Called the unbalanced correlation score
fj   Xij    Xij
yi 1
yi  1
– fj: the score of feature j
– X: training data as a matrix X where columns are
features and examples are rows
• Take λ very large in order to select features which
have non-zero entries (λ ≧3)
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Feature Selection (2/2)
• This score is an attempt to encode prior
information that
– The data is unbalanced
– Large number of features
– Only positive correlations are likely to be useful
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Justification
• Justify the unbalanced correlation score
using methods of information theory
– Entropy: higher  non-regular
 pi ln( pi )
• Pi: the probability of appearance of event i
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Entropy
• The probability of random appearance of a
feature with an unbalanced score of N=Np-Nn
Np  Nn 1
Nn 1
i 0
i 0
Np  Nn
P1(Tp, Tn, Np, Nn)  (
)  (Tp  i)  (Tn  i)
Np
– Np= number of one entries associated to +1
– Nn= number of one entries associated to -1
– Tp= total number of positive labels in training set
– Tn= total number of negative labels in training set
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Entropy
• Need to compute the probability that a
certain N might occur randomly
1 min( Tp  N ,Tn  N )
P 2(Tp, Tn, N ) 
P1(Tp, Tn, max( 0, N )  i, max( 0, N )  i)

Tp  Tn
i 0
• Finally, compute the entropy for each feature
 P1P 2 log( P1P 2)
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Entropy and unbalanced score
• The entropy and unbalanced score will not
reach the same feature
– Because the unbalanced correlation score will
no select samples with low negative
• In this particular problem
– Reach a similar ranking of the features
• Due to the unbalanced nature of the data
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Entropy and unbalanced score
• The first 6 features for both scores
– 5 out of 6 are the same ones
– For 16 features, 12 coincide
– Pay more attention to positive correlations
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Multivariate unbalanced
correlation
• The feature selection algorithm described so
far is univariate
– Reduces the chance of overfitting
– Between the inputs and targets are too complex
this assumption may be to restrictive
• We extend our criterion to assign a rank to a
subset of feature
– Rather than just a single feature
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Multivariate unbalanced
correlation
• By computing the logical OR of the subset of
features S (as they are binary)
Xi(S )  1   (1  Xij )
jS
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Fisher Score
( j (  )  j (  ))
fj 
2
2
(j (  ))  (j (  ))
2
– μ(+): the mean of the feature values for positive
– μ(-): the mean of the feature values for negative
– σ(+): standard deviations
– σ(-): standard deviations
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• In each case, the algorithms are evaluated
for different numbers of features d
– The range d = 1, …, 40
• Choose a small number of features in order to render
interpretability of the decision function
• It is anticipated that a large number of features are
noisy and should not be selected
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Classification algorithms
(Inductive)
• The task may not simply be just to identify
relevant characteristics via feature selection
– But also to provide a prediction system
• Simplest of classifiers

d
f ( x)  1, if
i 1
x(i )
d
 1, otherwise
0
– We call this a logical OR classifier
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Comparison Techniques
• We compared a number of rather more
sophisticated classification
– Support vector machines (SVM)
– SVM*
• Make a search over all possible values of the
threshold parameter in the linear model after training
– K-nearest neighbors (K-NN)
– K-NN* (parameter γ)
– C4.5 (decision tree learner)
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Transductive Inference
• One is given labeled data from which builds
a general model
– Then applies this model to classify previously
unseen (test) data
• Takes into account not only the given
(labeled) training set but also unlabeled data
– That one wishes to classify
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Transductive Inference
• Different models can be built
– Trying to classify different test sets
– Even if the training set is the same in all cases
• It is this characteristic which help to solve
problem 3
– The data we are given has different distribution
in the training and test sets
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Transductive Inference
• Transduction is not useful in all tasks
– In drug discovery in particular we believe it is
useful
• Developers often have access to huge
databases of compounds
– Compounds are often generated using virtual
Combinatorial Chemistry
– Compound descriptors can be computed even
though the compounds have not been
synthesized yet
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Transductive Inference
• Drug discovery is an iterative process
– Machine learning method is to help choose the
next test set
– Step in a two-step candidate selection procedure
• After candidate test set has been produced
• Its result is the final test set
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Transductive algorithm
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Results (with unbalanced
correlation score)
• C4.5 gave only 50% success rate for all
The tansductive algorithm is consistently selecting
more relevant features than the inductive one
the Fisher score
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Further Results
• We also tested some more sophisticated
multivariate feature selection methods
– Not as good as using the unbalanced criterion
score
• Using non-linear SVMs
– Not improve results (50% success)
• SVMs as a base classifier for our
transduction
– Improvement over using SVMs
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Further Results
• Also tried training the classifiers with larger
numbers of features
– Inductive methods
• failed to learn anything after 200 features
– Transductive methods
• Exhibit generalization behavior up to 1000 features
• (TRANS-Orcub:58% success with d=1000,77% with
d=200)
– KDD champion
• Success rate 68.4% (7% of entrants higher than 60%)
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Thanks for your attention
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