Download ET4718 - Computer Programming 7

Studying the Protein Folding Problem by
Means of a New Data Mining Approach
by Huy N.A. Pham and
Triantaphyllou Evangelos
Department of Computer Science, Louisiana State University
298 Coates Hall, Baton Rouge, LA 70803
Email: [email protected] and [email protected]
ICDM 2005 Workshop on Temporal Data Mining: Algorithms, Theory
and Applications
November 27-30, 2005, Houston, TX
This research was done under the LBRN program (www.lbrn.lsu.edu)
1
Brief introduction
The structure prediction problem for proteins plays an
important role in understanding the protein folding
process.
This is an NP-problem.
This research proposes a novel classification approach
based on a new data mining technique.
This technique tries to balance the overfitting and
overgeneralization properties of the derived models.
2
Outline
Introduction to:
 Classification
 The Protein Folding Problem
Classification methods
The overfitting and overgeneralization problem
The Binary Expansion Algorithm (BEA)
Experimental evaluation
Summary
3
Introduction to Classification
We are given a collection of records that consist the
training set:
 Each record contains a set of attributes and the class
that it belongs to.
We are asked to find a model that describes the records of
each class as a function of the values of their attributes.
The goal is to use this model to classify new records for
which we do not know the class in which they belong to.
Typical Applications:
 Credit approval
 Target marketing
 Medical diagnosis
 Treatment effectiveness analysis
4
Introduction to the protein folding problem
At least two distinct, though related, tasks can be
stated:

Structure Prediction Problem (Protein Folding
Problem): given a protein amino acid sequence,
determine its 3D folded shape.

Pathway Prediction Problem: given a protein amino
acid sequence and its 3D structure, determine the
time-ordered sequence of folding events.
5
Introduction to the protein folding problem Cont'd
Protein folding is the problem of finding the 3D
structure of a protein from its amino acid sequence.
There are 20 different types of amino acids (labelled
with their initials as: A, C, G, ...) => A protein is a
sequence of amino acids (e.g. AGGCT... ).
The folding problem is to find how this amino acid
chain (1D structure) folds into its 3D structure.
=> Classification problem.
6
Introduction to the protein folding problem Cont'd
A protein is classified into one of four structural
classes [Levitt and Chothia, 1976] according to its
secondary structure components:
 all-α (α –helix)
 all-β (β – Strand)
 α/β
 α +β
7
Outline
Introduction to Classification and Protein folding
problem
Classification methods
The overfitting and overgeneralization problem
The Binary Expansion Algorithm - BEA
Experimental evaluation
Summary
8
Classification methods
Decision trees

A flow-chart-like tree structure.

An internal node denotes a test on an attribute.

A branch represents an outcome of the test.

Leaf nodes represent class labels or class distribution.

Use the decision tree to classify an unknown sample.
Bayesian classification

Calculate explicit probabilities for hypothesis, among the most
practical approaches to certain types of learning problems.
Genetic algorithms

Based on an analogy to biological evolution.
9
Classification methods - Cont'd
Fuzzy set approaches

Use values between 0.0 and 1.0 to represent the degree of
membership.

Attribute values are converted to fuzzy values.

Compute the truth values for each predicted category.
Rough set approaches

Approximately or “roughly” define equivalent classes.
K-Nearest Neighbor Algorithms

Calculate the mean values of the K-nearest neighbors.
10
Classification methods - Cont'd
Neural Networks (NNs)



A problem-solving paradigm modeled after the physiological
functioning of the human brain.
The firing of a synapse is modeled by input, output, and
threshold functions.
The network “learns” based on problems to which answers
are known and produces answers to entirely new problems of
the same type.
Support Vector Machines (SVMs)


Data that are non-separable in N-dimensions have a higher
chance of being separable if mapped into a space of higher
dimension.
Use a linear hyperplane to partition the high dimensional
feature space.
11
Outline
Introduction to Classification and Protein
folding problem
Classification methods
The overfitting and overgeneralization
problem
The Binary Expansion Algorithm - BEA
Experimental evaluation
Summary
12
Overfitting and overgeneralization in Classification
Algorithms have resulted in classification and prediction
systems that are highly accurate or they are not so accurate
for no apparent reason.
A growing belief is that the root to that problem is the
overfitting and overgeneralization behavior of such systems.
Overfitting means that the extracted model describes the
behavior of known data very well but does poorly on new
data points.
Overgeneralization occurs when the system uses the
available data and then attempts to analyze vast amounts of
data that has not seen yet. For example:
 The generated tree may overfit the training data.
 The SVMs method may overgeneralize the training
data.
=> Develop an algorithm that balances overfitting and
overgeneralization.
13
A multi-class prediction method
One-vs-Others method (Dubchak et al 1999, Brown et
al 2000)





Partition the K classes into a two-class problem: one class
contains proteins in one “true” class, and the “others” class
combines all the other classes.
A two-class classifier is trained for this two-class problem.
Then partition the K classes into another two-class problem:
one class contains another original class, and the “others”
class contains the rest.
Another two-class classifier is trained.
This procedure is repeated for each of the K classes, leading
to K two-class trained classifiers.
14
Outline
Introduction to Classification and Protein folding
problem
Classification methods
The overfitting and overgeneralization problem
The Binary Expansion Algorithm - BEA
Experimental evaluation
Summary
15
Some basic concepts
A clause: a description of a small area of the state space covering
examples of a given class.
Homogenous Clause (HC): an area covering a set of examples of
a given class and unclassified examples uniformly.
Any clause of a given class may be partitioned into of a set of
smaller homogenous clauses.
A
Example: B, A1, A2 are homogenous clauses while A is a non-homogenous clause. A can be partitioned
into two smaller homogenous clauses A1 and A2. The example is a 2D representation. The high
dimension cases can be treated similarly.
=> Unclassified examples covered by clause B can more accurately be
assumed to belong to the same class than those in the original clause A.
16
Some basic concepts - Cont'd
Determining whether a clause is a homogenous clause can be
decided by using its standard deviation.
The clause is superimposed by a hyper-grid with sides of some
length h. If all cells have the same density, then it is a (perfectly)
homogenous clause.
x 
1

(


The density of a cell [Richard, 2001]: p( x) 
D
h
n
nh
where n = #(examples in the cell), D = #(dimensions), and
+
+
+
+
+
+
+
+
A
+
+
+
+
+
++
+
+
+
+
+
B
+
+
+
+
A is superimposed to a hyper-grid and the
density of all cells can be computed
+
+
=> standard deviation = 0
B is superimposed to a hyper-grid and the
density of all cells can be computed
m
D
xim
i 1 m 1
 = a kernel function
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
=> standard deviation > 0
+
+
+
+
+
+
+
+
+
+
+
Determine the homogenous values of clauses A and B.
17
)
Some basic concepts - Cont'd
The density: It expresses how many classified examples
exist in a given clause of the state space.
The density of a homogenous clause is the number of
examples of a given class per a unit area.
R_Unit
R_Unit
A
B
The Density of homogenous clause A > The density of homogenous clause B
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BEA
Main idea of the algorithm:
Input: positive and negative examples
Output: a suitable classification

Find positive and negative homogenous
clauses using any clustering algorithm.

Sort homogenous clauses based on their
densities.

For each homogenous clause, one or
more new areas are created by :
 If its density > a threshold then
 Expand it by:
G' s radius  C ' s radius 1
F ' s radius  C ' s radius 
x
2
D
F = expanded area, C = original area, and
G = enveloping area.
 Accept some noisy examples.
 Else
 Reduce it into smaller
homogenous clauses.

Use expanded homogenous clauses for
the new testing data.
F’s radius = C’s radius + (G’s
radius – C’s radius)/(2 *D)
-
G
-
-
C
-
+ +
+ +
++
-
-
D=6
Stopping conditions for expansion:
F’s radius ≤ D * C’s radius
#(Noisy points) ≤ (D * n) / 100
19
BEA - Cont'd
Main Algorithm:
Input: positive and negative examples
Output: a suitable classification
Step 1: Find positive and negative clauses using the k-means clusteringbased approach with the Euclidean distance.
Step 2: Find positive and negative homogenous clauses from positive and
negative clauses respectively.
Step 3: Sort positive and negative homogenous clauses on densities.
Step 4: FOR each homogenous clause C DO
If (its density > a threshold = (max – min)/2 of densities) then
Else
- Expand C using its density D.
- Accept (D*n)/100 noisy examples where n=#(its examples).
Reduce C into smaller homogenous clauses by considering
each cell of its hyper-grid as a new homogenous clause.
20
BEA - Cont'd
Example: BEA in 2D
Positive
Clauses
Expand
Homogenous Clauses
Extended HC
21
Correctness of improvement
Definition: e is improved by e’, e > e’, if for all
contexts C such that C[e] and C[e’] are closed, and if
C[e] converges in n steps then C[e’] also converges in
k steps where k ≤ n, [Sands, 2001].
BEA:



Use k-means clustering based approach to find positive and
negative sets.
Let e denotes results obtained from k-means clustering based
approach and e’ denote results obtained from BEA. Certainly
C[e] and C[e’] are closed. Moreover C[e’] can accept more
examples since all homogenous clauses are expanded from e.
Accept noisy examples.
 e is improved by e’
or e is refined to e’.
22
Outline
Introduction to Classification and Protein folding
problem
Classification methods
The overfitting and overgeneralization problem
The Binary Expansion Algorithm - BEA
Experimental evaluation
Summary
23
Accuracy measures for multi-class classification
The accuracy of two-class problems involves
calculating true positive rates and false positive rates.
The accuracy, Q, of multi-class problems can be
determined as true class rates, [Rost & Scander, 1993,
Baldi et al, 2000], by:
Q
k
wq
i 1
i
i
qi = ci/ni where ni = #(examples in class ith)
and ci = #(true examples in class ith).
wi=ni/N where N = Total of examples of a given class.
24
Experiments
Assess the algorithm for two-class problems. Source:
http://www.csie.ntu.edu.tw/~cjlin/methods/guide/data/
Training set
Testing set
# Atts
C.J.Lin’s SVMs
Train_1(3089 exps)
Test_1 (4000 exps)
4
96.9%
Train_2(391 exps)
Train_2 (391 exps)
Cross validation
Test_3 (41 exps)
20
85.2%
21
87.8%
Train_3(1243 exps)
BEA
Training set
Testing set
#Fail Positive
#Fail Negative
Q
Train_1
Test_1
Train_2
Test_3
22
(200 negative exps)
0
0
(0 negative exps)
99,25%
Train_2
Train_3
9
(2000 positive exps)
0
0
(41 positive exps)
100%
100%
25
Experiments - Cont'd
100.0%
95.0%
90.0%
85.0%
C.J.Lin's SVMs
BEA
80.0%
75.0%
Train_1 & Train_2 with Train_3 &
Test_1
cross
Test_3
validation
The BEA provides 15.5% improvement in the
classification accuracy vs. C.J.Lin’s SVMs.
26
Experiments - Cont'd
Assess the algorithm for two-class problems. Source:
http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/binary
Train
Test
Train
Test
Data
#atts
#exps
Q
w1a
w2a
w3a
w4a
w5a
w6a
300
300
300
300
300
300
2477
3470
4912
7366
9888
17188
Data
a3a
#atts
Q
122
#exps
3185
a4a
122
4781
90,17%
a5a
122
6414
86,47
a6a
122
11220
82,17
a7a
122
16100
79,99
Train
85,97 %
85,40
85,08
84,64
84,18
Test
Train
Test
Data
w4a
w1a
w2a
w3a
w5a
w6a
#exps
7366
2477
3470
4912
9888
17188
Q
Data
a7a
a3a
#exps
16100
3185
94,98%
a4a
4781
94,92
a5a
6414
94,92
a6a
11220
96,95
85,79%
86,57
86,16
85,41
84,83
Q
27
Experiments - Cont'd
A test bed of the algorithm for the protein folding problem

Source of data sets: http://www.nersc.gov/~cding/protein by Ding and
Dubchak, 2001.
Data types
#atts
# training exps
# testing exps
A.A.Composition (C)
Secondary struc. (S)
21
22
605
605
385
385
Polarity (P)
22
605
385
Polarizability (Po)
22
605
385
Hydrophobicity (H)
22
605
385

Volume (V)
22
605
Six parameter datasets extracted from protein sequences.

Use One-vs-Others method for the fourth-classes problem.

Use the Independent Test method in experiments.

385
BEA represents a protein as a n dimensional vector corresponding to the
composition of the n amino acids in the protein.
28
Experiments - Cont'd
The average results obtained from [Ding and Dubchak, 2001] and
[Zerrin, 2004] for the dataset with 27-class:
Data types
Q1
Q2
Q3
Q4
A.A.Composition
43.5%
20.5%
71.44%
66.66%
Secondary struc.
43.2
36.8
Hydrophobicity
45.2
40.6
Polarity
43.2
41.1
volume
44.8
41.2
Polarizability
44.9
41.8
Q1: The average accuracy of the SVMs with the independent test method in [Ding and
Dubchack, 2001, Table 6, p11].
Q2: The average accuracy of the Neural Networks with the independent test method
in [Ding and Dubchack, 2001, Table 6, p11].
Q3: The average accuracy of the SVMsAAC method in [Zerrin, 2004].
Q4: The average accuracy of the SVMstrio AAC method in [Zerrin, 2004].
29
Experiments - Cont'd
Results obtained from BEA for 4-class:
Data types
all-α
all-β
α/β
α+β
Q5
A.A.Composition
87.27%
74.81%
71.43%
91.95%
81.37%
Secondary struc.
87.23
72.21
66.75
91.17
79.34
Hydrophobicity
86.75
74.55
71.17
91.69
81.04
Polarity
87.27
73.51
70.13
91.95
80.72
Volume
87.01
74.29
71.43
91.95
81.17
Polarizability
86.75
74.29
70.13
91.95
80.78
30
Experiments - Cont'd
90.0%
Ding's Neural
Networks for 27-class
80.0%
70.0%
Ding's S VMs for 27class
60.0%
50.0%
S VMs-TrioAAC for
27-class
40.0%
30.0%
S VMs-AAC for 27class
20.0%
10.0%
BEA for 4-class
0.0%
C
S
P
Po
H
V
The BEA provides:
10% improvement in classification accuracy as the SVMsAAC method at the data
type of Amino Acid Composition.
•
• Approximately 36% improvement as Ding’s SVM.
31
Summary
This research was done to:
 Enhance our understanding of the performance of a new data
mining algorithm.
 Propose a new approach based on balancing overfitting and
overgeneralization properties to enhance the performance of
data mining algorithms.
 Make a contribution in a hot area in pure Bioinformatics by
achieving highly accurate results in predicting protein folding
properties.
Future work to focus on:
 Test the BEA with other applications.
 Improve the performance of the approach by:
 Improving the accuracy of the algorithm by finding a
suitable density for homogenous clauses.
 Decreasing the execution time by using parallel computing
techniques.
 Studying a multi-class classification algorithm.
32
References
Zerrin Isik et al, “Protein Structural Class Determination Using Support Vector Machines”,
Lecture Notes in Computer Science-ISCIS 2004, vol: 3280, pp. 82, Oct. 2004.
http://people.sabanciuniv.edu/~berrin/methods/fold-classification-iscis04.pdf
A.C.Tan et al, “Multi-Class Protein Fold Classification Using a New Ensemble Machine Learning
Approach”, Genome Informatics 14: 206–217, 2003.
http://www.brc.dcs.gla.ac.uk/~actan/methods/actanGIW03.pdf
Chris H.Q.Ding et al, “Multi-class protein fold recognition using Support Vector Machines and
Neural Networks”, Bioinformatics, 17:349-358, 2001.
http://www.kernel-machines.org/methods/upload_4192_bioinfo.ps
D. Sands.: Improvement theory and its applications. In A. D. Gordon and A. M. Pitts, editors,
Higher Order Operational Techniques in Semantics, Publications of the Newton Institute, pp
275-306. Cambridge University Press, 1998.
33
Thank you!
Any questions?
34