Classifying Nucleotide Sequences and their Positions
of Influenza A Viruses through Several Kernels
∗
Issei Hamada
1
, Takaharu Shimada
1†
, Daiki Nakata
1
, Kouichi Hirata
1
and Tetsuji Kuboyama
2
1
Kyushu Institute of Technology, Kawazu 680-4, Iizuka 820-8502, Japan
2
Gakushuin University, Mejiro 1-5-1, Toshima, Tokyo 171-8588, Japan
Keywords:
Kernels, Nucleotide Sequences, Positions in Nucleotide Sequences, Phylogenetic Trees.
Abstract:
In this paper, we classify nucleotide sequences and their positions of influenza A viruses by using both nu-
cleotide sequence kernels and phylogenetic tree kernels. In the nucleotide sequence kernel, we regard a nu-
cleotide sequence as a vector, a multiset and a string. In the phylogenetic tree kernel, we use a relabeled
phylogenetic tree obtained by replacing the labels of leaves that are indices of nucleotide sequences in the
reconstructed phylogenetic tree from a set of nucleotide sequences with the nucleotides at a fixed position and
trimmed phylogenetic trees obtained by trimming the branches in the relabeled phylogenetic tree with same
leaves as possible. Then, we observe which of kernels are effective the classification of nucleotide sequences
as analyzing pandemic occurrences and regions and the classification of positions in nucleotide sequences as
analyzing positions in packaging signals.
1 INTRODUCTION
In this paper, we classify nucleotide sequences and
their positions of influenza A viruses by using nu-
cleotide sequence kernels and phylogenetic tree ker-
nels through LIBSVM (Chang and Lin, 2013).
In the nucleotide sequence kernels, we use a na
¨
ıve
kernel, a multiset kernel (G¨artner, 2008) and a spec-
trum string kernel (Leslie et al., 2002) by regarding
a nucleotide sequence as a vector, a multiset and a
string, respectively.
On the other hand, in the phylogenetic tree ker-
nels, we prepare relabeled phylogenetic trees ob-
tained by replacing the labels of leaves that are indices
of nucleotide sequences in the reconstructed phyloge-
netic tree from a set of nucleotide sequences with the
nucleotides at a fixed position, and trimmed phyloge-
netic trees obtained by trimming the branches in the
relabeled phylogenetic tree with same leaves as pos-
sible. Then, we use an agreement subtree mapping
kernel (Hamada et al., 2013) and a leaf-path kernel to
classify relabeled or trimmed phylogenetic trees.
As the target of classification of nucleotide se-
∗
This work is partially supported by Grant-in-Aid
for Scientific Research 24240021, 24300060, 25540137,
26280085, 26280090 and 26370281 from the Ministry of
Education, Culture, Sports, Science and Technology, Japan.
†
Current Affilication: Mazda Motor Corporation.
quences, we classify nucleotide sequences of pan-
demic viruses from ones of non-pandemic viruses,
called pandemic classification, and nucleotide se-
quences at one region from ones at other regions,
called regional analysis, for influenza A (H1N1)
viruses as similar as (Hamada et al., 2013; Makino
et al., 2012b; Shimada et al., 2013). As the target of
classification of positions in nucleotide sequences, we
classify positions in packaging signals from ones not
in packagingsignals, called packagingsignal analysis
for influenza A (H3N2) viruses as similar as (Makino
et al., 2012a; Shimada et al., 2012).
Hence, we observe that both the nucleotide se-
quence kernels and the phylogenetic tree kernels are
effective to the pandemic classification. Also the nu-
cleotide sequence kernels and the leaf-path kernel are
effective to the packaging signal analysis. Further-
more, the phylogenetic tree kernels but none of nu-
cleotide sequence kernels are effective to the regional
analysis.
2 NUCLEOTIDE SEQUENCE
KERNELS
Let Σ be {A,C,G,T} with an alphabetical order .
Throughout of this paper, we assume that a nucleotide
sequence is a sequence on Σ and every sequence in a
342
Hamada I., Shimada T., Nakata D., Hirata K. and Kuboyama T..
Classifying Nucleotide Sequences and their Positions of Influenza A Viruses through Several Kernels.
DOI: 10.5220/0005251103420347
In Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM-2015), pages 342-347
ISBN: 978-989-758-076-5
Copyright
c
 2015 SCITEPRESS (Science and Technology Publications, Lda.)

set of nucleotide sequences has the same length.
First, we regard a nucleotide sequence as a vector
on Σ. For x, y ∈ Σ, we define δ
1
(x,y) = 1 if x = y; 0
otherwise. Also we define δ
2
(x,y) = 1 if x = y; 1/2 if
(x,y) = (A,T),(T,A),(C,G),(G,C) (that is, base pairs
are weighted); 0 otherwise. Then, we define a na
¨
ıve
kernel K
j
(j = 1,2) for two vectors X = (x
1
,...,x
n
)
and Y = (y
1
,...,y
n
) (x
i
,y
i
∈ Σ) on Σ as follows.
K
j
(X,Y) =
1
n
n
∑
i=1
δ
j
(x
i
,y
i
).
Next, we regard a nucleotide sequence as a multi-
set. We call X ⊆ Σ× N a multiset on Σ. For a multiset
X, let Γ
X
(x) denote an n such that (x,n) ∈ X. Then,
we define a multiset product kernel K
×
and a multiset
intersection kernel K
∩
for two multisets X and Y on Σ
as follows.
K
×
(X,Y) =
∑
a∈Σ
Γ
X
(a) · Γ
Y
(a),
K
∩
(X,Y) =
∑
a∈Σ
min{Γ
X
(a),Γ
Y
(a)}.
Finally, we regard a nucleotide sequence as a
string on Σ. For a string X ∈ Σ
∗
and a substring s ∈ Σ
∗
of X, let Γ
X
(s) be the number of occurrences of s in
X. Also, for k ∈ N, let Σ
k
be {s ∈ Σ
∗
| |s| = k}. Then,
we define a spectrum string kernel K
k
S
for two strings
X and Y on Σ as follows.
K
k
S
(X,Y) =
∑
s∈Σ
k
Γ
X
(s) · Γ
X
(s).
3 PHYLOGENETIC TREE
KERNELS
A tree is a connected graph without cycles. For a tree
T = (V,E), we denote V by V(T) and v ∈ V(T) by
v ∈ T. A rooted tree is a tree with one node r chosen
as its root.
For each node v in a rooted tree with the root r,
let UP
r
(v) be the unique path from r to v. The parent
of v(6= r), which we denote by par(v), is its adjacent
node on UP
r
(v) and the ancestors of v(6= r) are the
nodes on UP
r
(v) − {v}. We say that u is a child of v
if v is the parent of u, and u is a descendant of v if v is
an ancestor of u.
In this paper, we use the ancestor orders < and ≤,
that is, u < v if v is an ancestor of u and u ≤ v if u < v
or u = v. We say that w is the least common ancestor
of u and v, denoted by u⊔v, if u ≤ w, v ≤ w, and there
exists no w
′
such that w
′
< w, u ≤ w
′
and v ≤ w
′
.
Two nodes with the common parent are called sib-
lings. A leaf is a node having no children. We denote
the set of leaves of a rooted tree T by lv(T). For nodes
v, w ∈ V, we denote a path between v and w by p(v,w).
Also we denote the number of edges in a path p(v, w)
by ne(v,w). It is obvious that ne(v,v) = 0.
A rooted tree is unordered if an order between sib-
lings is ignored. A rooted tree is leaf-labeled if just
leaves are labeled by some symbols drawn from Σ and
full binary if every internal node has just two chil-
dren. We denote the label of a leaf v in Σ by l(v). We
call a rooted unordered leaf-labeled full binary tree
a phylogenetic tree. As a reconstruction of a phylo-
genetic tree from a set of nucleotide sequences, we
adopt a neighbor joining method (cf., (Durbin et al.,
1998; Sung, 2009)) based on the Hamming distance
between nucleotide sequences.
Let S be a set of nucleotide sequences with length
n and T a phylogenetic tree reconstructed from S.
Then, we can obtain n phylogenetic trees by relabel-
ing an index of S assigned to the leaves in T with
the i-th nucleotide in S (1 ≤ i ≤ n), which we call
a relabeled phylogenetic tree at the position i. Fur-
thermore, we call the phylogenetic tree obtained by
applying the label-based closest-neighbor trimming
method (Makino et al., 2012b; Makino et al., 2012a)
to the relabeled phylogenetic tree at the position i the
trimmed phylogenetic tree at the position i.
In the remainder of this section, we introduce an
agreement subtree mapping kernel and a leaf-path
kernel as phylogenetic tree kernels.
Let T
1
and T
2
be phylogenetic trees. Then, we say
that M ⊆ V(T
1
) ×V(T
2
) is a mapping between T
1
and
T
2
if M satisfies the following conditions.
1. ∀(v
1
,w
1
),(v
2
,w
2
) ∈ M

v
1
= v
2
⇐⇒ w
1
= w
2

.
2. ∀(v
1
,w
1
),(v
2
,w
2
) ∈ M

v
1
≤ v
2
⇐⇒ w
1
≤ w
2

.
Let T
1
and T
2
be phylogenetic trees and M a map-
ping between T
1
and T
2
. Also let M
lv
be M∩(lv(T
1
)×
lv(T
2
)). Then, we say that M is an agreement subtree
mapping (Hamada et al., 2013) if M satisfies the fol-
lowing conditions.
1. ∀(v,w) ∈ M

v ∈ lv(T
1
) ⇐⇒ w ∈ lv(T
2
)

.
2. ∀(v,w) ∈ M
lv

l(v) = l(w)

.
3. ∀(v
1
,w
1
),(v
2
,w
2
) ∈ M
lv

(v
1
⊔v
2
,w
1
⊔w
2
) ∈ M

.
4. ∀(v,w) ∈ M − M
lv
∃(v
1
,w
1
),(v
2
,w
2
) ∈ M
lv

(v = v
1
⊔ v
2
) ∧(w = w
1
⊔ w
2
)

.
Definition 1. Let T
1
and T
2
be phylogenetic trees.
Then, an agreement subtree mapping kernel is the
number of all of the agreement subtree mappings be-
tween T
1
and T
2
and denote it by K
AM
(T
1
,T
2
).
ClassifyingNucleotideSequencesandtheirPositionsofInfluenzaAVirusesthroughSeveralKernels
343

For example, consider the tree T illustrated in Fig-
ure 1 (left). Then, Figure 1 (right) illustrates all of
the agreement subtree mappings between T and T.
Hence, it holds that K
AM
(T,T) = 6.
T
Figure 1: The tree T (left) and all of the agreement subtree
mappings between T and T (right).
For a phylogenetic tree T and v,w ∈ lv(T), we de-
note the frequency of a path p(v, w) such that l(v) = a,
l(w) = b and ne(v,w) = k by f
T
(a,b,k).
Definition 2. Let T
1
and T
2
be phylogenetic trees la-
beled by Σ. Then, the leaf-path kernel K
LP
(T
1
,T
2
)
between T
1
and T
2
is defined as follows, where ∆ =
2· max{dep(T
1
),dep(T
2
)}.
K
LP
(T
1
,T
2
) =
∑
a∈Σ
∑
b∈Σ,ab
∆
∑
k=0
f
T
1
(a,b,k) · f
T
2
(a,b,k).
For example, consider the trees T
1
and T
2
in
Figure 2 (upper). Then, we obtain f
T
1
(a,b,k) and
f
T
2
(a,b,k) as Figure 2 (lower). Hence, it holds that
K
LP
(T
1
,T
2
) = 16.
T
1
T
2
a b k f
T
1
f
T
2
A A 0 3 2
A A 2 1 0
A A 4 2 1
A C 2 1 2
A C 4 2 2
C C 0 1 2
C C 4 0 1
Figure 2: Trees T
1
and T
2
(left) and f
T
1
(a,b,k) and
f
T
2
(a,b,k) (right).
We denote an agreement subtree mapping kernel
(resp., a leaf-path kernel) for trimmed and relabeled
phylogenetic trees by K
t
AM
and K
r
AM
(resp., K
t
LP
and
K
r
LP
), where we use K
r
AM
just in Table 2.
4 CLASSIFICATION OF
NUCLEOTIDE SEQUENCES
In the classification of nucleotide sequences, we di-
vide a set of nucleotide sequences into positive and
negative examples. Then, in the phylogenetictree ker-
nels, we use two different phylogenetic trees recon-
structed from positive and negative examples, respec-
tively. Hence, the number of relabeled and trimmed
phylogenetic trees obtained from positive examples
is same as one from negative examples, which is the
length of nucleotide sequences. On the other hand,
the number of leaves in a relabeled phylogenetic tree
obtained from positive examples is different from one
from negative examples, which is the number of nu-
cleotide sequences.
4.1 Pandemic classification
In pandemic classification, we use 3670 nu-
cleotide sequences at 2008 and 2009 provided from
NCBI (Bao et al., 2008). The length of nucleotide se-
quences is 895, the number of nucleotide sequences
in non-pandemic viruses occurring at 2008 is 326 and
one in pandemic viruses occurring at 2009 is 3344.
Table 1 illustrates the F-value and the AUC
of 5-fold cross validation classifying nucleotide se-
quences in non-pandemic viruses from ones in pan-
demic viruses by using all the kernels through LIB-
SVM (Chang and Lin, 2013).
Table 1: The classification of nucleotide sequences in non-
pandemic viruses from ones in pandemic viruses.
K
1
K
2
K
×
K
∩
K
1
S
K
2
S
K
3
S
K
4
S
K
5
S
K
t
AM
K
t
LP
K
r
LP
F-value 1 1 0.999 0.999 1 1 1 1 1 0.911 0.915 1
AUC
1 1 0.999 0.999 1 1 1 1 1 0.951 0.866 1
In order to avoid the bias of the number of exam-
ples, Table 2 illustrates the F-value and the AUC of 5-
fold cross validation after randomly selecting 200 nu-
cleotide sequences from 2008 and 2009, respectively.
Table 2: The classification of randomly selected 400 nu-
cleotide sequences in non-pandemic viruses from ones in
pandemic viruses.
K
1
K
2
K
×
K
∩
K
1
S
K
2
S
K
3
S
K
4
S
K
5
S
K
t
AM
K
r
AM
K
t
LP
K
r
LP
F-value 1 1 0.995 0.997 1 1 1 1 1 0.975 0.975 1 1
AUC
1 1 0.998 0.995 1 1 1 1 1 0.992 0.998 1 1
Table 1 and 2 shows that, in the pandemic classi-
fication, all of the nucleotide sequence and the phylo-
genetic tree kernels succeed to classify well.
4.2 Regional Analysis
In regional analysis as an extension of the experimen-
tal result of (Hamada et al., 2013), we divide 3670
nucleotide sequences at 2008 and 2009 into seven re-
gions as Africa (AF), Asia (AS), Europe (EU), Mid-
dle East (ME), North America (NA), Oceania (OC)
and South America (SA). Table 3 illustrates the num-
ber of nucleotide sequences (#NS) and the number
ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods
344

of phylogenetic trees (#PT) obtained by removing the
positions with the same nucleotide in seven regions.
Table 3: The number of nucleotide sequences (#NS) and the
number of phylogenetic trees (#PT) in seven regions.
AF AS EU ME NA OC SA total
#NS 61 949 965 71 1403 47 174 3670
% 1.66 25.86 26.29 1.93 38.23 1.28 4.74
#PT 289 593 487 311 538 290 344 2852
% 10.13 20.79 17.08 10.90 18.86 10.17 12.06
Table 4 illustrates the F-value and the AUC of 5-
fold cross validation classifying nucleotide sequences
in one region given at the first line from nucleotide
sequences in the other regions by using all the kernels.
Table 4: The classification of nucleotide sequences in one
region given at the first line from ones in the other regions.
AF AS EU ME NA OC SA
K
1
F-value 0 0.029 0 0 0 0 0
AUC 0.622 0.690 0.657 0.636 0.662 0.743 0.645
K
2
F-value 0 0.012 0 0 0 0 0
AUC 0.628 0.689 0.650 0.559 0.662 0.745 0.646
K
×
F-value 0 0 0 0 0 0 0
AUC 0.437 0.501 0.541 0.437 0.544 0.549 0.470
K
∩
F-value 0 0.127 0.094 0 0.257 0 0
AUC 0.445 0.550 0.616 0.499 0.593 0.637 0.562
K
1
S
F-value 0 0 0 0 0 0 0
AUC 0.516 0.519 0.498 0.537 0.542 0.516 0.463
K
2
S
F-value 0 0.022 0 0 0.478 0 0
AUC 0.495 0.612 0.596 0.452 0.666 0.531 0.660
K
3
S
F-value 0 0.388 0.351 0 0.480 0 0.127
AUC 0.713 0.708 0.708 0.550 0.720 0.624 0.825
K
4
S
F-value 0.382 0.534 0.507 0 0.546 0.155 0.375
AUC 0.713 0.708 0.708 0.550 0.720 0.624 0.825
K
5
S
F-value 0.361 0.600 0.544 0.152 0.593 0.282 0.361
AUC 0.793 0.786 0.759 0.653 0.763 0.763 0.934
K
t
AM
F-value 0.911 0.766 0.929 0.031 0.830 0.300 0.753
AUC 0.947 0.898 0.978 0.814 0.955 0.933 0.919
K
t
LP
F-value 0.873 0.802 0.962 0.853 0.637 0.881 0.837
AUC 0,988 0.918 0.995 0.975 0.805 0.983 0.975
K
r
LP
F-value 1 1 1 0.998 1 1 1
AUC 1 1 1 0.996 1 1 1
Table 4 shows that, in regional analysis, while the
nucleotide sequence kernels fail to classify, the phy-
logenetic tree kernels succeed to classify well, except
K
t
AM
for the regions of ME and OC.
In particular, for the spectrum string kernel K
k
S
, the
larger value k tends to give the better performance ex-
cept the regions of AF and SA; in their regions, the
F-value of K
4
S
is larger than the F-value of K
5
S
. Then,
even if we give the value of k larger than 5, K
k
S
may
not give better performance in regional analysis.
Next, in order to avoid the bias of the number of
examples, we apply regional analysis for every pair of
regions. Table 5 illustrates the F-value and the AUC
of 5-fold cross validation classifying nucleotide se-
quences in one region as positive examples from nu-
cleotide sequences in another region as negative ex-
amples by using the phylogenetic tree kernels K
t
AM
,
K
t
LP
and K
r
LP
, respectively.
Table 5: The classification of nucleotide sequences in one
region from ones in another region.
AS EU ME NA OC SA
AF K
t
AM
F-value 0.967 1 0.940 0.989 0.949 0.994
AUC 0.991 1 0.940 0.989 0.949 0.994
K
t
LP
F-value 0.944 1 0.914 0.975 0.956 0.993
AUC 0.985 1 0.925 0.995 0.967 0.999
K
r
LP
F-value, AUC 1 1 1 1 1 1
AS K
t
AM
F-value 0.963 0.982 0.914 0.987 0.885
AUC 0.990 0.991 0.945 0.994 0.871
K
t
LP
F-value 0.996 0.975 0.865 0.984 0.910
AUC 0.999 0.984 0.921 0.994 0.936
K
r
LP
F-value, AUC 1 1 1 1 1
EU K
t
AM
F-value 0.998 0.944 0.998 0.989
AUC 1 0.971 1 0.999
K
t
LP
F-value 1 0.960 1 0.993
AUC 1 0.988 1 0.999
K
r
LP
F-value, AUC 1 1 1 1
ME K
t
AM
F-value 0.980 0.756 0.998
AUC 0.997 0.771 0.999
K
t
LP
F-value 0.977 0.920 0.998
AUC 0.991 0.934 0.999
K
r
LP
F-value, AUC 1 1 1
NA K
t
AM
F-value 0.996 0.937
AUC 0.999 0.969
K
t
LP
F-value 0.992 0.932
AUC 0.997 0.954
K
r
LP
F-value, AUC 1 1
OC K
t
AM
F-value 1
AUC 1
K
t
LP
F-value 0.998
AUC 1
K
r
LP
F-value, AUC 1
Note that Table 3 shows that the difference be-
tween the number of phylogenetic trees in AF and OC
is 1, one in OC and ME is 21, and one in ME and SA
is 33. Even such regions, K
t
AM
, K
t
LP
and K
r
LP
succeed
to classify except for K
t
AM
for the regions of ME and
OC. In particular, for K
t
AM
and K
t
LP
the F-value and
the AUC in Table 5 are larger than ones in Table 4.
Furthermore, K
r
LP
succeeds to classify completely all
regions with the F-value and the AUC of 1.
ClassifyingNucleotideSequencesandtheirPositionsofInfluenzaAVirusesthroughSeveralKernels
345

5 CLASSIFICATION OF
POSITIONS IN NUCLEOTIDE
SEQUENCES
In the classification of positions in nucleotide se-
quences, we divide positions into positive positions
in target positions and negative positions not in tar-
get positions for a set of nucleotide sequences. Then,
in the phylogenetic tree kernels, we use two differ-
ent phylogenetic trees reconstructed from a set of nu-
cleotide sequences at positive positions and one at
negative positions, respectively. Hence, the number
of leaves in a relabeled phylogenetic tree obtained
from positive positions is same as one from nega-
tive positions, which is the number of nucleotide se-
quences. On the other hand, the number of relabeled
and trimmed phylogenetic trees obtained from posi-
tive positions is different from one from negative po-
sitions, which is the length of nucleotide sequences.
5.1 Packaging Signal
The negative-sense RNA genome of the influenza A
virus is composed of eight different segments, that is,
PB2, PB1, PA, HA, NP, NA, MP and NS. Since in-
fluenza virions do not typically package more than
eight segments, the virus has evolved a selective pack-
aging mechanism which ensures that virions incorpo-
rate one copy of each of the eight segments. A pack-
aging signal is a nucleotide to cause such a selective
packaging mechanism (Hutchinson et al., 2010).
Through reverse genetics, segment-specific pack-
aging signals have been found in unique regions adja-
cent to the panhandle of each segment. Table 6 repre-
sents the positions as packaging signals obtained by
reverse genetics summarized by (Hutchinson et al.,
2010) in Virology. Here, the column “NCBI” de-
notes the corresponding positions in nucleotide se-
quences of segments in influenza A (H3N2) viruses
provided from NCBI (Bao et al., 2008). Also the col-
umn (+) (resp., (− )) denotes the total number of pos-
itive (resp., negative) positions.
5.2 Packaging Signal Analysis
In packaging signal analysis, we use 1560 nucleotide
sequences of influenza A (H3N2) viruses. Then,
Table 7 illustrates the F-value and the AUC of 5-
fold cross validation classifying positive positions
from negative positions by using the nucleotide se-
quence and the phylogenetic tree kernels through
LIBSVM (Chang and Lin, 2013). Here, we can ob-
tain no value of K
t
AM
for the NS segment.
Table 6: The positions in packaging signals of RNA seg-
ments (Hutchinson et al., 2010).
RNA length NCBI (+) (−)
PB2 2341 35–114, 2209–2304 174 2167
PB1 2341 38–163, 2197–2299 227 2114
PA 2233 38–124, 691–731, 742–767, 220 2013
2094–2156, 2169–2176
HA 1778 38–125, 1659–1671 99 1679
NP 1565 46–165, 1482–1526 163 1402
NA 1413 35–185, 1211–1413 352 1061
MP 1027 ε – –
NS 890 36–56 20 870
Table 7: The classification of positive positions from nega-
tive positions.
PB2 PB1 PA HA NP NA NS
K
1
, K
2
, K
×
, F-value 1 1 1 1 1 1 1
K
∩
, K
k
S
, K
r
LP
AUC 1 1 1 1 1 1 1
K
t
AM
F-value 0.925 0.559 0.797 0.308 0.942 0.867 –
AUC 0.999 0.913 0.989 0.781 1 0.967 –
K
t
LP
F-value 1 0.649 0.921 0.414 1 0.951 1
AUC 1 0.923 0.966 0.859 1 0.988 1
Next, in order to avoid the bias of the number of
positions and the positions with the same nucleotide,
for every RNA segment, we remove the positions in
positive and negative positions where nucleotide is
same. As a result, the number of positive positions
of PB2 decreases from 174 to 150; PB1 from 227 to
113; PA from 220 to 87; HA from 99 to 77; NP from
163 to 64; NA from 352 to 205; NS from 20 to 11.
Table 8 illustrates the F-value and the AUC of 5-
fold cross validation classifying positive positions af-
ter the removal of positions from randomly selected
negative positions with the same number of positive
positions by using the nucleotide sequence kernels ex-
cept K
k
S
and the phylogenetic tree kernels.
Hence, Table 7 and 8 show that K
1
, K
2
, K
×
, K
∩
and K
r
LP
succeed to classify the positions in packaging
signals from ones not in packaging signals. In partic-
ular, the F-value of K
r
LP
for the NS segment is smaller
than the F-values for other segments. On the other
hand, K
t
AM
and K
t
LP
do not classify well segments PA
and NA and segments PA, HA and NS, respectively.
6 CONCLUSION
In this paper, we have classified nucleotide sequences
ICPRAM2015-InternationalConferenceonPatternRecognitionApplicationsandMethods
346

Table 8: The classification of positive positions from ran-
domly selected negative positions.
PB2 PB1 PA HA NP NA NS
K
1
F-value 0.999 1 1 1 1 0.999 1
AUC 1 1 1 1 1 1 1
K
2
F-value 0.999 1 1 1 1 0.999 1
AUC 1 1 1 1 1 1 1
K
×
F-value 1 1 0.999 1 0.998 1 0.994
AUC 1 1 1 1 0.999 1 0.995
K
∩
F-value 1 1 0.999 1 0.997 1 0.995
AUC 1 1 1 1 0.999 1 0.996
K
t
AM
F-value 0.909 0.935 0.721 0.959 0.916 0.825 –
AUC 0.981 0.961 0.745 0.984 0.988 0.918 –
K
t
LP
F-value 0.966 0.912 0.818 0.603 0.984 0.944 0.521
AUC 0.986 0.933 0.856 0.585 0.999 0.952 0.330
K
r
LP
F-value 1 1 1 1 1 1 0.916
AUC 1 1 1 1 1 1 0.966
and positions in them of influenza A viruses by using
the phylogenetic tree and the nucleotide sequence ker-
nels. Then, we have observed that both the nucleotide
sequence kernels and the phylogenetictree kernels are
effective to the pandemic classification. Also the nu-
cleotide sequence kernels and the leaf-path kernel are
effective to the packaging signal analysis. Further-
more, the phylogenetic tree kernels and none of nu-
cleotide sequence kernels are effective to the regional
analysis.
In the case that the phylogenetic tree kernels suc-
ceed to classify, two different phylogenetic trees re-
constructed from positive and negative examples or
positions work well as background knowledge in our
classification. This is typical for regional analysis
which the nucleotide sequence kernels fail to classify.
It is a future work to apply the regional analysis
to influenza A (H3N2) viruses and the analysis of po-
sitions in packaging signals to influenza A (H1N1)
viruses. It is also an important future work to compare
the correlated mutations (Shimada et al., 2012) with
our results and to analyze our results from the view-
points of Virology. Furthermore, it is a future work
to analyze, classify and evaluate another nucleotide
sequences by using the phylogenetic tree kernels and
the nucleotide sequence kernels.
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