OPTIMIZING HIDDEN MA
RKOV MODELS USING
GENETIC ALGORITHMS A
ND ARTIFICIAL IMMU
NE
SYSTEMS
Mohamed Korayem, Amr Badr, Ibrahim Farag
Department of Computer Science
Faculty of Computers and Information
Cairo University
ABSTRACT
Hidden Markov Models are
widely used in speech
recognition and bioinformatics systems. Conventional
methods are usually used in the parameter estimation
process of Hidden Markov Models (HMM). These
methods are based on iterative procedure, like Baum

Welch method
, or
gradient bas
ed method
s
. However,
these methods can yield to local optimum parameter
values. In this work, we use artificial techniques such
as Artificial Immune Systems (AIS) and Genetic
Algorithms (GA) to estimate HMM parameters. These
techniques are global search op
timization techniques
inspired from biological systems.
Also,
t
he hybrid
between genetic algorithms and artificial immune
system was used to optimize HMM parameters.
Keywords:
Artificial
Immune System
s; Genetic
Algorithm; Clonal
Selection
Algorithm,
Hybri
d
Geneti
c Immune System ;Hidden Markov
Models(HMM); Baum

Welch(BW)
1.
INTRODUCTION
Hidden Markov Models (HMM) have many
applications in signal processing, pattern recognition,
and speech recognition
(
Rabiner
, 1993
)
.
HMM
is
considered
a
basic component i
n speech
recognition systems. The estimation of good model
parameters affects the performanc
e of the recognition
process so
the values of these
parameters
are
need
ed
to be
estimated such that the
recognition error
is
minimized
.
HMM parameters are determine
d during iterative
process called
"training p
rocess
"
. One of the
conventional methods that
are
applied in setting HMM
model parameters values is Baum Welch algorithm.
One drawback of this method is that it converges to a
local optimum.
Global search techn
iques can be used to optimize
HMM parameters.
In this paper
,
the performance of
two
global optimization techniques
is
compared with
B
aum Welch algorithm which is one of the traditional
techniques that
are
used to estimate HMM parameters
.
These te
chniques a
re Genetic Algorithms and
Clonal
Selection
Algorithm
which is
inspire
d from artificial
immune system. Also, a h
ybrid genetic immune
method
is proposed to optimize HMM parameters
and
then
compared with the above methods
.
The natural immune system uses a va
riety of
evolutionary and adaptive mechanisms to protect
organisms from foreign pathogens and misbehaving
cells in the body
(
Forrest
, 1997)
(
De Castro
, 2005
)
.
Artificial immune systems (AIS)
(
Somayaji,
1998)
(
Hofmeyr,
2000)
seek to capture some a
spects of the
natural immune system in a computational framework,
either for the purpose of modeling th
e natural immune
system
or for
solving engineering problems
(
Glickman
,
2005)
.
Clonal selection algorithm which is
a
n aspect from immune system
is
used
to optimize
HMM parameters. Clonal
selection
algorithm
(
De
Castro
2000)(
De Castro
2002)
is a special kind of
artificial immune systems algorithms that uses the
clonal expansion
principle
and the affinity maturation
as the main forces
of the evolutionary
process
(
De
Castro,2002
b
)
. Genetic Algorithm
is
another global
optimization technique
which is used to optimize
HMM parameters
.
The main force of the evolutionary
process for the GA which is crossover operator
and
mutation operator can be merged with cl
onal selection
principle to optimize HMM parameters. So, a
hybrid
genetic immume
technique
is
proposed
.
2. HIDDEN MARKOV MOD
ELS (HMM)
HMM
are probabilistic models useful for modeling
stochastic sequence with underlying finite state
structure. Stochastic
sequences in speech recognition
are called observation sequences
O
=
o
1
o
2
………
o
T
,
where
T
is the length of the sequence. HMM with
n
states (
S
1
,
S
2
….
S
n
) can be characterized by a set of
parameters
, where
is
the initial
distribution probability that describes the probability
distribution of the observation symbol in the initial
moment, and
and
>=0.
A
is the transition probability matrix {
a
ij

i
,
j
=1,2,3 …
n
},
a
ij
is the probability of transition from state
i
to
state
j
, and
and
>=0.
B
is the observation matrix
{
b
ik

i
=1,2,3 ………….
n
,
k
=1,2……….
m
} where n is the number of the states
and m is the number of o
bservation symbols.
,
>=0
,
b
ik
is the probability of
observation symbol with index
k
emitted by the
current state
i
.
The main problems of HMM are:
evaluation
,
decoding
, and
Learning
problems.
Evaluation
problem
Given the HMM
and the observation
sequence
O
=
o
1
o
2
...
o
T
,
the probability that model
has generated sequence
O
is calculated
.
Often this problem is
solved by The Forward
Backward
Algorithm
(
Rabiner
,1
989) (
Rabiner
,1993)
.
Decoding problem
Given the HMM
and the observation
sequence
O
=
o
1
o
2
...
o
T
, calculate the most likely
sequence of hidden states
that produced this
observation sequence
O
.
Usually this problem i
s handled by Vit
erbi Algorithm
(
Rabiner
,1989) (
Rabiner
,1993)
.
Learning problem
Given some training observation sequences
O
=
o
1
o
2
...
o
T
and general structure of HMM (numbers of hidden
and visible states), determine HMM parameters
that best fit trai
ning data.
The most common solution for this problem is Baum

Welch algorithm
(
Rabiner
,1989) (
Rabiner
,1993)
which i
s considered the traditional method for training
HMM.
The third problem i
s solved by using three global
optimization techniques. T
he
results
from these
techniques a
re compared with the traditional technique
Figure 1 :Six state left

right HMM model
In this paper
,
a six state left

right HMM model
i
s used
as shown in figure
1
. Optimizing HMM parameters is
estimated
by using
the mentioned
thre
e global
optimization techniques and
the
traditional method .
The speech vectors are vectors quantized into a
codebook with a size of 32
.
The transition matrix
A
is
a 6 x 6 matrix and the observation matrix
B
is of size 6
x 32.
According to this configurat
ion (LR HMM
model) see figure 1, some transitions of the matrix are
constantly zero.
3

OPTIMIZING
HMM TRAINING
3.1Genetic Algorithm (GA)
The genetic algorithm is a robust general purpose
optimization technique
,
which evolv
es a population of
solutions
(
Goldberg
,1989)
.
GA
is
a search technique
that
has a representation of
the
problem states and
also has
a set of operations to
move through the search space. The states in the GA
are represented using a set of chromosomes. Each
chromosome represents a candi
date solution to the
problem. The set of candidate solutions forms a
population. In essence, the GA produces more
generations of this population ho
ping to reach a good
solution for
the problem. Members (candidate
solutions) of the population are improved a
cross
generation through a set of operations that GA
uses
during the search process.
GA has three basic
operations to expand a candidate solution into other
candidate solutions. These basic operations are:
Selection: In this operation, an objective
functio
n
(called fitness function) i
s used to
assess the quality of the solution. The fittest
sol
utions from each generation are
kept.
Crossover:
This operation generates
new
solutions given a set of selected members of
the current population.
Crossover
exchang
es
genetic material between two single
chromosome parents
This set of selected members is the outcome
of the selection operation.
Mutation: Biological organisms are often subject to a
sudden change in their chromosomes in an unexpected
manner. Such a sudd
en change is simulated in GA in
the mutation operation. This operation is a clever way
to escape from local optima trap in which state

space
search algorithms may fall into. In this operation
,
some values of a chromosome a
re changed by adding
random values
for the current values. This action
changes the member values and hence produces a
different solution.
Genetic Algorithm pseudo code:
1.
Generate initial random population of
chromosomes
2.
Compute the fitness for each chromosome
in the current population
3.
M
ake an intermediate population from the
current population using the reproduction
operator.
4.
Using the intermediate population,
generate a new population by applying the
crossover and mutation operators.
5.
If you get a member the population that
satisfies the
requirements stop, otherwise go
to step 2.
In this work, The GA
is
applied to estimate the HMM
model parameters. This
parameters estimation
problem i
s represented as shown in figure 2 as
follows:
Each member (chromosome) of the
generation represents the
A
matrix and the
B
matrix
jointly. Each row of the
A
matrix
i
s encoded into an
array, and all the arrays are concatenated to constitute
one array, where the first row
i
s followed by the
second row then the third row and so on. Then, the B
matrix
i
s encoded
row by row in the same way.
Figure
2:
Representation of Chromosome
The members from a given generation
a
re selected for
the reproduction phase. The fitness function which
is
used depend
s
on the average of all log likelihood for
all utterances for a wo
rd as described in section 4. The
arithmetic crossover
i
s applied on the population. The
arithmetic crossover generates two children of two
parents, and the values of a child
a
re set as the
averages of the values of the parents and the values of
the other
child
i
s set by using the equation (3*
p
1

p
2
)/2,
where
p
1
is the first parent and
p
2
is the other parent.
When applying the arithmetic crossover, the resultant
values created from crossover must be in the range of
limited values for each parameter.
For the
mutation operation,
the following method
is
applied
:
According to the representation of chromosomes
which consist of real values, the creeping operator
i
s
used as the mutation operator which adds generated
random values (Gaussian values) to the original
values. The resultant values must be within the
defined limits.
3.2 Clonal
Selection
Algorithm
Artificial immune systems (AIS) are adaptive systems,
inspired by theoretical immunology and observed
immune functions, principles and models, which are
applie
d to problem solving
(
D
e Castro
,2002
c
)
.
The clonal selection algorithms
are a special kind of
Immune Algorithms using the clonal expansion and
the affinity maturation as the main forces of the
evolutionary process
.
The clonal selection algorithm is desc
ribed as follows:
1

Generate initial antibodies (each antibody
represents a solution that represents the
parameters of HMM in our case the
A
and
B
matrices).
2

Compute the fitness of each antibody. The
used fitness function computes the average
log probability
over training data.
3

Select antibodies from population which will
be used to generate new antibodies (the
selection can be random or according to the
fitness rank). The antibodies with highest
fitness
a
re selected such that they
a
re different
enough as des
cribed later.
4

For each antibody, generate clones and mutate
each clone according to fitness.
5

Delete antibodies with lower fitness form the
population, then add to the population the new
antibodies.
6

Repeat the steps from 2

5 until stop criterion
is met. T
he number of iterations can be used
as the stop criterion.
Antibodies represent the parameters of HMM. Each
antibody represents a candidate solution
.
Each
member (antibody) of the generation represents the
A
matrix and the
B
matrix jointly like a chromoso
me in
GA see figure (2).
The fitness value for each antibody
i
s computed
as follows:
F
=
,
(1)
where
L
i
is
log likelihood for utterance
,
n
is the
number of utterances for word.
Selection in clonal
Selection algorithm
depen
ds on the
fitness values for each antibody; the antibodies with
the highest fitness
a
re selected such that they
a
re
different enough
. The Euclidean distance between any
two antibodies is greater than a threshold
. The
Euclidean distance
i
s used to measure t
he difference
between the antibodies.
(2)
For all antibodies the fixed number
i
s used to generate
clones. In each cycle of the algorithm, some new
antibodies
a
re added to the population. The percentage
of these new antibodies i
s equal to 10% from the
population size. For mutation the value was added to
each value in the antibody this value
is
generated by
(
* Gaussian value) where
is computed according
to the following equation
=
,
(3)
where
F
is the fitness value for the antibody and
is
decaying factor.
3.3 Hybrid Genetic

Immune System Method
The
proposed
hybrid method
depend
s on genetic
algorithms and
immune system. The main forces of
the evolutionary process for the GA are crossover and
the mutation operators. For the Clonal
selection
algorithm the main force of the evolutionary process is
the idea of clone
selection
in
which new clones
are
generate
d.
T
hese new clones
are then mutated
and the
best of these clones
a
re added to the population plus
adding new generated members to the population. The
hybrid method take the main force of the evolutionary
process for the two systems.
The hybrid method is
described as follow:

1

Generate the initial population (candidate
solutions).
2

Select the (N) best items from the population.
3

For each selected item generate a number of
clones (N
c
) and mutate each item form (N
c
).
4

Select the best mutated item from each gro
up
(N
c
) and add it to the population.
5

Select from the population the items on which
the crossover will be applied. We select them
randomly in our system
but any selection
method can be used.
.
6

After selection make a crossover and add the
new items (items a
fter crossover) to the
population by replacing the low fitness items
with the new ones.
7

Add to the population a group of new
generated random items.
8

Repeat step 2

7 according to meeting the
stopping criterion.
The steps 2

5 were repeated for a nu
mber of times
before adding new group of generated random items
.
4. EXPERIMENTS
Dataset description
The used data i
s recorded for a speech recognition
task. The 30 samples for 9 words
a
re collected
. These
words
represent
th
e digits from 1 to 9
spoken in a
rabic
language. As a standard procedure in evaluating
machine learning techniques, the dataset
i
s split into a
training set and a test set. The training set
i
s composed
of 15
x
9 utterances, and the same size
i
s used for the
test set. HMM models
a
re trained using the above
three methods. Then, the performance of each model
i
s tested on the test dataset. Models
a
re compared
according to the average log likelihood over all
utterances for each word. Moreover, HMM model
i
s
trained by using one tradit
ional method (Baum

Welch
algorithm)
. The results are reported in table 1.
The objective of these experiments is to determine
which of four methods yields better model in terms of
the maximum likelihood estimation (MLE) of training
and testing data.
5.
RESULTS
Table1 :
Average Log
Likelihood
for
Genetic Algorithms , Clonal
Selection
, Hybrid Method vs. Baum Welch
Table1 shows the average likelihood for each w
ord
resulting from applying the GA, clonal
selection
,
Hybrid genetic immune, and Baum Welch algorithms.
The figures
3 and 4 present comparison of the four
techniques.
GA, Clonal
Selection
, Hybrid Method Vs.
Baum

Welch
It's clear from table 1
that GA, Cl
onal
Selection
Algorithm, and The Hybrid Method optimize HMM
Experiment
Genetic Algorithms
Clonal
Selection
Hybrid Genetic Immune
Baum Welch
Training
Data
Testing Data
Training Data
Testing Data
Training
Data
Testing Data
Training
Data
Testing Data
Word 1

87.678826

120.456613

87.571879

122.846582

79.952704

112.972627

100.256415

132.043827
Word 2

112.853853

129.668485

109.478160

124.280939

99.285726

116.882284

126.857669

144.2
17638
Word 3

120.233247

136.341848

117.629193

135.939801

110.821281

127.068196

127.729650

144.002114
Word 4

99.422550

106.937365

97.869824

105.532062

90.419239

98.660715

100.071147

109.651458
Word 5

114.924569

135.706757

107.990526

1
27.026957

100.729004

120.318206

119.703586

139.742821
Word 6

111.930453

128.168076

105.539754

123.945254

97.301037

114.680868

118.338618

135.820565
Word 7

103.412966

113.111271

100.211900

109.174607

94.428044

106.360118

112.493737

120
.044928
Word 8

91.442692

121.272038

91.163196

122.357082

80.717414

111.834818

92.313749

123.730211
Word 9

87.677962

112.124334

82.390500

105.931426

76.158748

98.281587

95.080516

117.038164
parameters better than Baum Welch Algorithm for all
Words, they maximize likeli
hood better over training
data (
see figure3) and testing data (see figure 4)
We note that for experiment eight the B
aum

Welch ,
GA, Clonal
Selection
Algorithm almost yield to the
same results but the Hybrid Method gives better
results. .
GA Vs Clone
Selection
Algorithm
The immune clone
selection
gives
better results than
GA for all words .We also we note that for t
he
experiment one, four, and eight the two algorithms
almost yield the same result.
Figure 5 a , b
shows that the fitness function in clonal
selection
is better than genetic algorithm which yields
to better results for optimizing HMM parameters. The
figu
re also show that the clonal
selection
fitness
function increase faster than genetic algorithms
especially in the beginning iterations.
Hybrid Method Vs GA and Clonal
Selection
Algorithm
We note from the results above The Hybrid Method is
give better r
esults than GA and Clonal
Selection
Algorithm for all experiments over the training data
and the testing da
ta, and it's clear from figure 5 a, b
and
c
that the fitness function for The Hybrid Method
is better at any moment in the graph than Genetic
Algorit
hm and Clonal
Selection
Algorithm.
Figure 3 : Log Likelihood for Training Data
Figure 4 : Log Likelihood for Testing Data
a
b
c
Figure 5
a, b and c
:
Fitness function of clonal
selection
algorithm, genetic algorithms and hyb
rid m
ethod
word 9 .
C
ONCLUSION
In this paper, we presented the results of using the
Genetic Algorithm and the clonal
selection
algorithm
to optimize the HMM parameters. We also proposed a
hybrid
immune genetic
algorithm
for optimizing
HMM parameters
.
it t
akes into account the main
immune aspects: selection and cloning of the most
stimulated cells, death of non

stimulated cells, affinity
maturation and reselection of the clones with higher
affinity, generation and maintenance of diversity
.
It
also takes int
o account the main force
s
of the
evolutionary process for the GA which
are
crossover
operator and mutation operator.
T
he results show that
the used global optimization techniques produce better
results than the traditional Baum Welch algorithm.
Moreover, t
he proposed hybrid algorithm produced
the best resu
lts over all tested techniques.
The
global
search algorithms
generated better results because it
doesn't fall in local minima like the Baum Welch
algorithm.
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