Faulon J.L., Bender A. Handbook of Chemoinformatics Algorithms

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388 Handbook of Chemoinformatics Algorithms

chemoinformatics uses a much broader set of data types. Bioinformatics applications

use a huge variety of algorithms but are generally restricted to microarray (numerical)

and sequence (string) data. Chemoinformatics applications generally use two to three

clustering algorithms (Jarvis–Patrick, Ward clustering, and k-means) but use very

large datasets and a huge number of chemical descriptors (see Chapters 2–4) as their

input.

Clustering in both bioinformatics and chemoinformatics is fairly mature. Both

fields have standard approaches that work well for their data types and applications.

Cross-fertilization, however, is certain to benefit both areas of study. Bioinformat-

ics, for example, has spurred the development of many new alternative clustering

techniques, some of which work on large datasets. After adaptation to data types

from chemoinformatics, it seems likely that many of these algorithms will be useful.

Conversely, the diversity of data types in chemoinformatics and the general interest

of drug design in bioinformatics have spurred the development of new techniques,

including graph kernels in support vector machines (SVMs) (see Section 14.2.2) and

the inference of protein–chemical interaction networks (Section 14.2.3).

14.2 APPLICATIONS OF CLASSIFICATION AND REGRESSION

In this section, we consider applications of methods in classification and regression to

problems in bioinformatics and chemoinformatics. In the previous section (Equation

14.1), we saw that the choice of clustering algorithm varied widely between the two

fields. This is due to historical reasons, as well as dataset size and type differences

between biology and chemistry. In contrast, the choice of algorithm in classifica-

tion and regression is fairly uniform between bioinformatics and chemoinformatics.

Instead, most of the difference lies in the choice of data description. In bioinformatics,

descriptors are often based on sequence (largely due to the vast amount of sequence

data available), while in chemoinformatics, descriptors are typically tied more directly

to structure.

Classification and regression are both methods for correlating elements in a dataset

with properties of those elements. In classification, elements are correlated with dis-

crete properties, as in the case of the classification of a molecule according to its

activity(e.g., activeor inactive).In regression, elements are correlated with continuous

properties, as in the case of relating molecular structure to boiling point or log P.

There are many available algorithms for use in both classification and regression. In

classification, popular algorithms include k-nearest neighbors [41], neural networks

[42], SVMs [43], and numerous statistical methods [44,45]. In regression, popular

algorithms include linear and multiple regression, principal component regression,

and partial least squares [46,47]. In addition, there are several algorithms that can be

used for both classification and regression, including neural networks and SVMs.

Since techniques in classification and regression are applied fairly uniformly in

both bioinformatics and chemoinformatics, we focus our discussion on SVMs. SVMs

can be used for classification [43,48], regression [49], and even clustering [50]. We

highlight data-type differences between bioinformatics and chemoinformatics and

how these differences can be accommodated using SVMs.

Machine Learning–Based Bioinformatics Algorithms 389

FIGURE 14.3 A linear SVM. The SVM decision boundary is defined by the support vectors,

which are the examples falling on the dotted lines. The distance between the dotted lines is

known as the margin and is maximized to obtain the SVM decision boundary, shown as the

solid line separating the circles (class 1) from the x marks (class −1).

At its core, an SVM is a linear binary classifier. Suppose that we have a dataset

}⊆R

and that each point x

in our dataset has a corresponding class label

∈{±1}. Our goal is to separate the points in our dataset according to their class

label. Since there are two classes, this is known as binary classification. An SVM

attempts this classification by using a linear hyperplane w

x +b, w = 0, as shown

in Figure 14.3.

Assuming that our dataset is in fact linearly separable, there will in general be

many possible hyperplanes that can achieve the separation. An SVM uses an optimal

separating hyperplane known as the maximal margin hyperplane. The hyperplane

margin is twice the distance from the separating hyperplane to the nearest point in

one (or the other) of the two classes. In Figure 14.3, this is the distance between the

two dotted lines. The SVM hyperplane is found by solving the quadratic programming

problem [51,52]:

max



i,j

−



s.t.



= 0, 0 ≤ α

≤ C,

(14.2)

where w =



is the normal to the SVM hyperplane. Using w we form the

SVM decision function f (x) = sign(w

x +b), where b is obtained implicitly [51,52].

We note that α

= 0 only when x

is a support vector.

The SVM problem given in Equation 14.2 only applies to datasets {x

}⊆R

. Often,

however, we want to use an SVM on a dataset that is not a subset of R

. This occurs

in the case of biology and chemistry problems when we are likely to use amino acid

sequences or chemical structures to describe our data. Fortunately, there is a ready

solution to this problem, formalized in the use of kernel functions.

390 Handbook of Chemoinformatics Algorithms

Suppose that our data {x

}⊆S, where S might be the set of all finite length protein

sequences or all finite diameter chemical graphs. We can then define a kernel function

as a map k : S ×S → R such that

k(x

, x

) = Φ(x

)

Φ(x

), (14.3)

where Φ: S → F is a map from our original data space S into a space F with a defined

dot product such as R

Once we have defined a kernel function, we simply replace the dot product x

Equation 14.2 with the kernel k(x

, x

) to obtain the full SVM quadratic programming

problem. A similar procedure can be used for any method that is written in terms of

dot products, thus giving rise to the moniker kernel methods.

SVMs have a number of advantages over competing methods, including a unique

solution of a fairly straightforward quadratic programming problem (compared to a

nonunique solution for a neural network), ability to employ nonlinearity by choice

of kernel, and widespread availability of software [53,54]. On the other hand, SVMs

can be memory intensive O(n

) and the flexibility in choice of kernel can make

SVMs difficult for beginners. Neither of these disadvantages, however, has slowed

the widespread use of SVMs in both bioinformatics and chemoinformatics.

14.2.1 APPLICATIONS IN BIOINFORMATICS

The central applications of classification and regression methods in bioinformatics

are to protein function prediction [55] and protein interaction prediction [56]. These

two topics are not unrelated and are often approached using the same basic methods.

In particular, both protein function and protein interaction prediction have benefited

from the application of classification and regression methods.

The success of function and interaction prediction often depends more on the

formulation of the problem than on the algorithm used for the classification or regres-

sion. For proteins, this means the use of either sequence or structure and the particular

assumptions used when the data are put into the algorithm. For sequence data, pre-

dictions are often made by comparing proteins using sequence similarity (homology)

across organisms [24,57], using subsequence motifs or identifying motifs and using

them to predict either function or interaction [58,59] and by using amino acid residue-

specific features such as van der Waals volume, polarity, hydrophobicity, charge, and

so on to represent a sequence as a vector [60,61]. For structural data, predictions can

be made by comparing proteins based on geometric considerations such as amino

acid proximity and similarity of 3D ball protein models [62].

In terms of SVMs, data types used to predict function include gene expression

data [63], motif-based subsequences [58], and feature vectors based on sequence [61]

and structure [62]. Data used to predict interactions include generalized subsequences

[64], feature vectors [60], and combinations of sequence and structure [65,66].

The success of classification and regression methods has been widespread in bioin-

formatics, due largely to the availability of vast amounts of sequence data. Although

many different algorithms have been applied in the field, SVMs have been a favorite

for a variety of data types. One reason that SVMs are popular is that SVMs encourage

Machine Learning–Based Bioinformatics Algorithms 391

a very useful separation between data and method. A computer scientist interested

in developing algorithms or methods can take as a starting point a kernel of the

type described in Equation 14.3, while a biologist or chemist interested in a particular

problem needs only provide a pairwise kernel similarity in order to apply the methods

developed by the computer scientist.

To illustrate the use of an SVM kernel in bioinformatics, we briefly describe

the subsequence kernel used for predicting protein interaction used by Martin et al.

[64]. Suppose that we have two protein sequences that we would like to compare.

In mathematical terms, a protein sequence is a finite length string over an alphabet

of 20 letters corresponding to the 20 possible amino acid residues. To calculate the

similarity between two proteins we must calculate the similarity between two strings.

Hence we use a string kernel.

To define a string kernel, we first define a map Φ

: {finite length amino acid

strings} → Z

, where N

is the number of possible amino acid sequences of length

l. If we denote by z

the bases of Z

where each basis vector z

corresponds to an

amino acid sequence of length l, then Φ

is given by



, (14.4)

where P

is a finite length amino acid string and σ

is the number of times that the

amino acid string corresponding to z

occurs in the string P

. We then define the string

kernel k

, P

) between two proteins P

and P

, P

) = Φ

)

). (14.5)

As an example, suppose that we have amino acid strings LVMLVM and LVMTTM.

We want to calculate Φ

(LVMLVM), Φ

(LVMMTT), and k

(LVMLVM, LVMTTM).

There are four substrings of length 3 (also known as trimers) in LVMLVM, namely

LVM, VML, MLV, and LVM. There are also four substrings of length 3 in LVMTTM,

namely LVM, VMT, MTT, and TTM. Suppose that z

corresponds to LVM, z

corre-

sponds to VML, z

corresponds to MLV, z

corresponds to VMT, z

corresponds to

MTT, and z

corresponds to TTM. We see that Φ

(LVMLVM) = (2, 1, 1, 0, 0, 0)

and

(LVMMTT) = (1, 0, 0, 1, 1, 1)

, so that k

(LVMLVM, LVMMTT) = 2. A visual

demonstration arriving at Φ

(LVMLVM) is shown in Figure 14.4.

14.2.2 APPLICATIONS IN CHEMOINFORMATICS

The main application of classification and regression in chemoinformatics is to the

development of QSARs and QSPRs. We refer to both QSARs and QSPRs using the

term “QSAR” only. The use of QSAR is widespread in chemoinformatics, occur-

ring historically in the study of drugs [29] and theoretical organic chemistry (see

Refs. [67,68]). Pioneering work was conducted by Hansch and Fujita [69] and Free

and Wilson [70] and substantial continuing research is ongoing in the area of drug dis-

covery [29,30]. The use of SVMs in the field of QSAR has occurred more recently and

includes applications to various chemical properties [71–73], drug activity [74,75],

and mutagenicity prediction [76,77].

392 Handbook of Chemoinformatics Algorithms

. . .

+ 1 + 1 + 0 +

. .

LVM VML MLV VMT

(LVMLVM) = ∑

= 2

FIGURE 14.4 Representing an amino acid string as a vector. Here we show how a finite

length amino acid string can be represented as a vector. The string VLMVLM is mapped to a

vector Φ

(VLMVLM) by counting the number of occurrences of different (trimer) substrings

of length 3.

There are as many different algorithms for QSAR as there are applications of

the QSARs themselves. As in bioinformatics, the success of a given QSAR often

depends more on the formulation of the problem than on the algorithm used for the

classification or regression. In the case of QSAR, this boils down to the choice of the

molecular descriptor.

Molecular descriptors used in QSAR are numerous and include examples discussed

earlier in this book such as topological indices, fragmental descriptors and pharma-

cophores (Chapters 2 through 4). Any descriptor may be used in an SVM-based

QSAR, although SVMs are particularly well suited for complex high-dimensional

descriptors such as fragments of labeled graphs that may not be handled as easily

using other methods (e.g., multiple linear regression).

To illustrate the use of labeled graph fragments in SVM-based QSARs, we describe

a simplified version of the method developed by Mahe et al. [77]. The method we

describe here is based on work done to predict protein–chemical interactions [78,79].

Suppose we have two molecular structures that we would like to compare, both given

as labeled graphs, where vertices correspond to atoms and edges correspond to bonds.

Mathematically, we represent such a molecular graph using a vector counting the

number of subgraphs in our original graph. This representation is known as molecular

signature [80–82].

Formally, we definea map Φ

: {molecular graphs} → Z

, where N

is the number

of possible atomic signatures of height h. As in Section 14.2.1, we denote by z

the

bases of Z

where each basis vector z

corresponds to a height h subgraph of a

molecular graph. If M

denotes a molecular graph, then Φ

is given by

) =



, (14.6)

where σ

is the number of times that the molecular subgraph corresponding to z

occurs in M

. Now we define a graph kernel just like we defined the string kernel.

Namely, the graph kernel k

, M

) between two molecules M

and M

is given by

, M

) = Φ

)

). (14.7)

Machine Learning–Based Bioinformatics Algorithms 393

1 C(OHCC)

2 C(OHHC)

5 H(C)

1 H(O)

4 O( N)

1 O(HC)

2 O(NC)

2 N(O O O)

1 C(OHCC)

2 C(OHHC)

5 H(C)

3 O(NC)

3 N(O O O)

6 O( N)

Nitroglycerine 1,2-Dinitroglycerine

(3,6,3,5,2,1,0,0)

(2,4,2,5,2,1,1,1)

FIGURE 14.5 Height-1 signature representations of nitroglycerine (left) and 1,2-

dinitroglycerine (right). Proceeding from the top to the bottom we show (top row) the molecular

graph representations of the two molecules, (middle row) the number of occurrences of height-

1 atomic signatures and (bottom row) the signature vector representation of the two molecules.

The atomic signature occurrences give the number of times a given chemical fragment occurs in

the molecules. In the case of nitroglycerine, we have three oxygen atoms bonded to a nitrogen

atom and a carbon atom [shown as 3 O(NC)], six oxygen atoms double bonded to a nitrogen

atom [shown as 6 O(

N)], three nitrogen atoms bonded to an oxygen atom and double bonded

to two other oxygen atoms [shown as 3 N(O

O)], and so on.

To provide an example, consider the two molecules shown in Figure 14.5. Both

molecules, nitroglycerine and 1,2-dinitroglycerine, are represented as undirected

edge- and vertex-labeled molecular graphs (carbons and hydrogens are implicit). To

obtain vectors from these graphs, we first visit each node in each graph and record the

subgraph formed by that node and its neighbors. This is known as a height 1 atomic

signature. If we wanted to compute height 2 signature, we would have to visit the

neighbors of the neighbors.

The atomic signatures are recorded as strings A

...), where A

is the

vertex type of the root node (the node we are visiting), A

is a neighbor of A

with bond

type b

is a neighbor of A

with bond type b

, and so on. If b

, b

, ...are single

bonds, then they are omitted. This representation is canonical if we alphabetize the

list (b

, b

, ...) of bonds and atoms [81]. In Figure 14.5, we have written oxygen

bonded to nitrogen and carbon as O(NC) and oxygen double bonded to nitrogen as

N).

After visiting each node of each molecular graph, we obtain a list of atomic signa-

ture string representations. This list is identified with a set z

, z

, ...of basis vectors.

394 Handbook of Chemoinformatics Algorithms

In Figure 14.5, we have identified O(NC) with z

and O(

N) with z

. Using these

basis vectors, we record the number of times a given atomic signature subgraph occurs

in a molecular graph to obtain our molecular signature vector representation. Since

O(NC) occurs three times in nitroglycerine and O(

N) occurs six times, the first two

entries of our signature vector for nitroglycerine are 3 and 6. The full vector is (3, 6,

3, 5, 2, 1, 0, 0, 0)

. This analysis is also performed on 1,2-dinitroglycerine to get the

signature vector (2, 4, 2, 5, 2, 1, 1, 1)

Once we have molecular signature vectors for the various molecular graphs

in our dataset, it is a simple matter to compute kernel similarities by taking dot

products of signature vectors. Using the signature vectors for nitroglycerine and 1,2-

dinitroglycerine, we compute a similarity of (3, 6, 3, 5, 2, 1, 0, 0)

· (2, 4, 2, 5, 2, 1,

1, 1)

= 66.

14.2.3 COMPARISONS

The use of classification and regression are fairly mature in both bioinformatics

and chemoinformatics. The two fields, however, are again benefiting from cross-

fertilization, this time in terms of problem formulation and molecular descrip-

tion. A motivating example is drug design, where we are interested in predicting

protein–chemical interaction [78,83].

One of the standard chemoinformatic approaches to drug design is the use of

virtual screening, where a library of chemicals is examined (e.g., using QSAR)

for a certain activity. In this approach, the corresponding protein is usually fixed

and all attention is focused on the drug. In bioinformatics, it is more com-

mon to consider a network of interactions, as in the case of a protein–protein

interaction network [56]. If we combine both types of approaches, we arrive

at the prospect of predicting a protein–chemical interaction network [78,83].

[Although the general area of large-scale (informatics-based) protein–chemical inter-

action prediction is relatively unexplored, both approaches mentioned here use

SVMs.]

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