Function Approximation is a popular engineering problems used in system identification or Equation
optimization. Due to the complex search space it requires, AI techniques has been used extensively to spot
the best curves that match the real behavior of the system. Genetic algorithm is known for their fast
convergence and their ability to find an optimal structure of the solution. We propose using a genetic
algorithm as a function approximator. Our attempt will focus on using the polynomial form of the
approximation. After implementing the algorithm, we are going to report our results and compare it with
the real function output.
A MODIFIED VORTEX SEARCH ALGORITHM FOR NUMERICAL FUNCTION OPTIMIZATIONijaia
The Vortex Search (VS) algorithm is one of the recently proposed metaheuristic algorithms which was
inspired from the vortical flow of the stirred fluids. Although the VS algorithm is shown to be a good
candidate for the solution of certain optimization problems, it also has some drawbacks. In the VS
algorithm, candidate solutions are generated around the current best solution by using a Gaussian
distribution at each iteration pass. This provides simplicity to the algorithm but it also leads to some
problems along. Especially, for the functions those have a number of local minimum points, to select a
single point to generate candidate solutions leads the algorithm to being trapped into a local minimum
point. Due to the adaptive step-size adjustment scheme used in the VS algorithm, the locality of the created
candidate solutions is increased at each iteration pass. Therefore, if the algorithm cannot escape a local
point as quickly as possible, it becomes much more difficult for the algorithm to escape from that point in
the latter iterations. In this study, a modified Vortex Search algorithm (MVS) is proposed to overcome
above mentioned drawback of the existing VS algorithm. In the MVS algorithm, the candidate solutions
are generated around a number of points at each iteration pass. Computational results showed that with
the help of this modification the global search ability of the existing VS algorithm is improved and the
MVS algorithm outperformed the existing VS algorithm, PSO2011 and ABC algorithms for the benchmark
numerical function set.
Modified Vortex Search Algorithm for Real Parameter Optimization csandit
The Vortex Search (VS) algorithm is one of the rece
ntly proposed metaheuristic algorithms
which was inspired from the vortical flow of the st
irred fluids. Although the VS algorithm is
shown to be a good candidate for the solution of ce
rtain optimization problems, it also has some
drawbacks. In the VS algorithm, candidate solutions
are generated around the current best
solution by using a Gaussian distribution at each i
teration pass. This provides simplicity to the
algorithm but it also leads to some problems along.
Especially, for the functions those have a
number of local minimum points, to select a single
point to generate candidate solutions leads
the algorithm to being trapped into a local minimum
point. Due to the adaptive step-size
adjustment scheme used in the VS algorithm, the loc
ality of the created candidate solutions is
increased at each iteration pass. Therefore, if the
algorithm cannot escape a local point as
quickly as possible, it becomes much more difficult
for the algorithm to escape from that point
in the latter iterations. In this study, a modified
Vortex Search algorithm (MVS) is proposed to
overcome above mentioned drawback of the existing V
S algorithm. In the MVS algorithm, the
candidate solutions are generated around a number o
f points at each iteration pass.
Computational results showed that with the help of
this modification the global search ability of
the existing VS algorithm is improved and the MVS a
lgorithm outperformed the existing VS
algorithm, PSO2011 and ABC algorithms for the bench
mark numerical function set
APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ...cscpconf
EM algorithm is popular in maximum likelihood estimation of parameters for state-space models. However, extant approaches for the realization of EM algorithm are still not able to fulfill the task of identification systems, which have external inputs and constrained parameters. In this paper, we propose new approaches for both initial guessing and MLE of the parameters of a constrained state-space model with an external input. Using weighted least square for the initial guess and the partial differentiation of the joint log-likelihood function for the EM algorithm, we estimate the parameters and compare the estimated values with the “actual” values, which are set to generate simulation data. Moreover, asymptotic variances of the estimated parameters are calculated when the sample size is large, while statistics of the estimated parameters are obtained through bootstrapping when the sample size issmall. The results demonstrate that the estimated values are close to the “actual” values.Consequently, our approaches are promising and can applied in future research.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
A MODIFIED VORTEX SEARCH ALGORITHM FOR NUMERICAL FUNCTION OPTIMIZATIONijaia
The Vortex Search (VS) algorithm is one of the recently proposed metaheuristic algorithms which was
inspired from the vortical flow of the stirred fluids. Although the VS algorithm is shown to be a good
candidate for the solution of certain optimization problems, it also has some drawbacks. In the VS
algorithm, candidate solutions are generated around the current best solution by using a Gaussian
distribution at each iteration pass. This provides simplicity to the algorithm but it also leads to some
problems along. Especially, for the functions those have a number of local minimum points, to select a
single point to generate candidate solutions leads the algorithm to being trapped into a local minimum
point. Due to the adaptive step-size adjustment scheme used in the VS algorithm, the locality of the created
candidate solutions is increased at each iteration pass. Therefore, if the algorithm cannot escape a local
point as quickly as possible, it becomes much more difficult for the algorithm to escape from that point in
the latter iterations. In this study, a modified Vortex Search algorithm (MVS) is proposed to overcome
above mentioned drawback of the existing VS algorithm. In the MVS algorithm, the candidate solutions
are generated around a number of points at each iteration pass. Computational results showed that with
the help of this modification the global search ability of the existing VS algorithm is improved and the
MVS algorithm outperformed the existing VS algorithm, PSO2011 and ABC algorithms for the benchmark
numerical function set.
Modified Vortex Search Algorithm for Real Parameter Optimization csandit
The Vortex Search (VS) algorithm is one of the rece
ntly proposed metaheuristic algorithms
which was inspired from the vortical flow of the st
irred fluids. Although the VS algorithm is
shown to be a good candidate for the solution of ce
rtain optimization problems, it also has some
drawbacks. In the VS algorithm, candidate solutions
are generated around the current best
solution by using a Gaussian distribution at each i
teration pass. This provides simplicity to the
algorithm but it also leads to some problems along.
Especially, for the functions those have a
number of local minimum points, to select a single
point to generate candidate solutions leads
the algorithm to being trapped into a local minimum
point. Due to the adaptive step-size
adjustment scheme used in the VS algorithm, the loc
ality of the created candidate solutions is
increased at each iteration pass. Therefore, if the
algorithm cannot escape a local point as
quickly as possible, it becomes much more difficult
for the algorithm to escape from that point
in the latter iterations. In this study, a modified
Vortex Search algorithm (MVS) is proposed to
overcome above mentioned drawback of the existing V
S algorithm. In the MVS algorithm, the
candidate solutions are generated around a number o
f points at each iteration pass.
Computational results showed that with the help of
this modification the global search ability of
the existing VS algorithm is improved and the MVS a
lgorithm outperformed the existing VS
algorithm, PSO2011 and ABC algorithms for the bench
mark numerical function set
APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ...cscpconf
EM algorithm is popular in maximum likelihood estimation of parameters for state-space models. However, extant approaches for the realization of EM algorithm are still not able to fulfill the task of identification systems, which have external inputs and constrained parameters. In this paper, we propose new approaches for both initial guessing and MLE of the parameters of a constrained state-space model with an external input. Using weighted least square for the initial guess and the partial differentiation of the joint log-likelihood function for the EM algorithm, we estimate the parameters and compare the estimated values with the “actual” values, which are set to generate simulation data. Moreover, asymptotic variances of the estimated parameters are calculated when the sample size is large, while statistics of the estimated parameters are obtained through bootstrapping when the sample size issmall. The results demonstrate that the estimated values are close to the “actual” values.Consequently, our approaches are promising and can applied in future research.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
This paper introduces a new comparison base stable sorting algorithm, named RA sort. The RA sort
involves only the comparison of pair of elements in an array which ultimately sorts the array and does not
involve the comparison of each element with every other element. It tries to build upon the relationship
established between the elements in each pass. Instead of going for a blind comparison we prefer a
selective comparison to get an efficient method. Sorting is a fundamental operation in computer science.
This algorithm is analysed both theoretically and empirically to get a robust average case result. We have
performed its Empirical analysis and compared its performance with the well-known quick sort for various
input types. Although the theoretical worst case complexity of RA sort is Yworst(n) = O(n√), the
experimental results suggest an empirical Oemp(nlgn)1.333 time complexity for typical input instances, where
the parameter n characterizes the input size. The theoretical complexity is given for comparison operation.
We emphasize that the theoretical complexity is operation specific whereas the empirical one represents the
overall algorithmic complexity.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Optimization is considered to be one of the pillars of statistical learning and also plays a major role in the design and development of intelligent systems such as search engines, recommender systems, and speech and image recognition software. Machine Learning is the study that gives the computers the ability to learn and also the ability to think without being explicitly programmed. A computer is said to learn from an experience with respect to a specified task and its performance related to that task. The machine learning algorithms are applied to the problems to reduce efforts. Machine learning algorithms are used for manipulating the data and predict the output for the new data with high precision and low uncertainty. The optimization algorithms are used to make rational decisions in an environment of uncertainty and imprecision. In this paper a methodology is presented to use the efficient optimization algorithm as an alternative for the gradient descent machine learning algorithm as an optimization algorithm.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
THE IMPLICATION OF STATISTICAL ANALYSIS AND FEATURE ENGINEERING FOR MODEL BUI...ijcseit
Scrutiny for presage is the era of advance statistics where accuracy matter the most. Commensurate
between algorithms with statistical implementation provides better consequence in terms of accurate
prediction by using data sets. Prolific usage of algorithms lead towards the simplification of mathematical
models, which provide less manual calculations. Presage is the essence of data science and machine
learning requisitions that impart control over situations. Implementation of any dogmas require proper
feature extraction which helps in the proper model building that assist in precision. This paper is
predominantly based on different statistical analysis which includes correlation significance and proper
categorical data distribution using feature engineering technique that unravel accuracy of different models
of machine learning algorithms.
AN IMPROVED ITERATIVE METHOD FOR SOLVING GENERAL SYSTEM OF EQUATIONS VIA GENE...Zac Darcy
Various algorithms are known for solving linear system of equations. Iteration methods for solving the
large sparse linear systems are recommended. But in the case of general n× m matrices the classic
iterative algorithms are not applicable except for a few cases. The algorithm presented here is based on the
minimization of residual of solution and has some genetic characteristics which require using Genetic
Algorithms. Therefore, this algorithm is best applicable for construction of parallel algorithms. In this
paper, we describe a sequential version of proposed algorithm and present its theoretical analysis.
Moreover we show some numerical results of the sequential algorithm and supply an improved algorithm
and compare the two algorithms.
OCR-THE 3 LAYERED APPROACH FOR DECISION MAKING STATE AND IDENTIFICATION OF TE...ijaia
Optical Character recognition is the method of digitalization of hand and type written or printed text into
machine-encoded form and is superfluity of the various applications of envision of human’s life. In present
human life OCR has been successfully using in finance, legal, banking, health care and home need
appliances. India is a multi cultural, literature and traditional scripted country. Telugu is the southern
Indian language, it is a syllabic language, symbol script represents a complete syllable and formed with the
conjunct mixed consonants in their representation. Recognition of mixed conjunct consonants is critical
than the normal consonants, because of their variation in written strokes, conjunct maxing with pre and
post level of consonants. This paper proposes the layered approach methodology to recognize the
characters, conjunct consonants, mixed- conjunct consonants and expressed the efficient classification of
the hand written and printed conjunct consonants. This paper implements the Advanced Fuzzy Logic system
controller to take the text in the form of written or printed, collected the text images from the scanned file,
digital camera, Processing the Image with Examine the high intensity of images based on the quality
ration, Extract the image characters depends on the quality then check the character orientation and
alignment then to check the character thickness, base and print ration. The input image characters can
classify into the two ways, first way represents the normal consonants and the second way represents
conjunct consonants. Digitalized image text divided into three layers, the middle layer represents normal
consonants and the top and bottom layer represents mixed conjunct consonants. Here recognition process
starts from middle layer, and then it continues to check the top and bottom layers. The recognition process
treat as conjunct consonants when it can detect any symbolic characters in top and bottom layers of
present base character otherwise treats as normal consonants. The post processing technique applied to all
three layered characters. Post processing of the image: concentrated on the image text readability and
compatibility, if the readability is not process then repeat the process again. In this recognition process
includes slant correction, thinning, normalization, segmentation, feature extraction and classification. In
the process of development of the algorithm the pre-processing, segmentation, character recognition and
post-processing modules were discussed. The main objectives to the development of this paper are: To
develop the classification, identification of deference prototyping for written and printed consonants,
conjunct consonants and symbols based on 3 layered approaches with different measurable area by using
fuzzy logic and to determine suitable features for handwritten character recognition.
A FRAMEWORK FOR DETECTING FRAUDULENT ACTIVITIES IN EDO STATE TAX COLLECTION S...ijaia
Edo State Inland Revenue Services is overwhelmed with gigabyte of disk capacity containing data about tax
payers’ in the state. The data stored on the database increases in size at an alarming rate. This has resulted
in a data rich but information poor situation where there is a widening gap between the explosive growth
of data and its types, and the ability to analyze and interpret it effectively; hence the need for a new
generation of automated and intelligent tools and techniques known as investigative data mining, to look
for patterns in data. These patterns can lead to new insights, competitive advantages for business, and
tangible benefits for the State Revenue services. This research work focuses on designing effective fraud
detection and deterring architecture using investigative data mining technique. The proposed system
architecture is designed to reason using Artificial Neural Network and Machine learning algorithm in
order to detect and deter fraudulent activities. We recommend that the architectural framework be
developed using Object Oriented Programming and Agent Oriented Programming Languages.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
This paper introduces a new comparison base stable sorting algorithm, named RA sort. The RA sort
involves only the comparison of pair of elements in an array which ultimately sorts the array and does not
involve the comparison of each element with every other element. It tries to build upon the relationship
established between the elements in each pass. Instead of going for a blind comparison we prefer a
selective comparison to get an efficient method. Sorting is a fundamental operation in computer science.
This algorithm is analysed both theoretically and empirically to get a robust average case result. We have
performed its Empirical analysis and compared its performance with the well-known quick sort for various
input types. Although the theoretical worst case complexity of RA sort is Yworst(n) = O(n√), the
experimental results suggest an empirical Oemp(nlgn)1.333 time complexity for typical input instances, where
the parameter n characterizes the input size. The theoretical complexity is given for comparison operation.
We emphasize that the theoretical complexity is operation specific whereas the empirical one represents the
overall algorithmic complexity.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Optimization is considered to be one of the pillars of statistical learning and also plays a major role in the design and development of intelligent systems such as search engines, recommender systems, and speech and image recognition software. Machine Learning is the study that gives the computers the ability to learn and also the ability to think without being explicitly programmed. A computer is said to learn from an experience with respect to a specified task and its performance related to that task. The machine learning algorithms are applied to the problems to reduce efforts. Machine learning algorithms are used for manipulating the data and predict the output for the new data with high precision and low uncertainty. The optimization algorithms are used to make rational decisions in an environment of uncertainty and imprecision. In this paper a methodology is presented to use the efficient optimization algorithm as an alternative for the gradient descent machine learning algorithm as an optimization algorithm.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
THE IMPLICATION OF STATISTICAL ANALYSIS AND FEATURE ENGINEERING FOR MODEL BUI...ijcseit
Scrutiny for presage is the era of advance statistics where accuracy matter the most. Commensurate
between algorithms with statistical implementation provides better consequence in terms of accurate
prediction by using data sets. Prolific usage of algorithms lead towards the simplification of mathematical
models, which provide less manual calculations. Presage is the essence of data science and machine
learning requisitions that impart control over situations. Implementation of any dogmas require proper
feature extraction which helps in the proper model building that assist in precision. This paper is
predominantly based on different statistical analysis which includes correlation significance and proper
categorical data distribution using feature engineering technique that unravel accuracy of different models
of machine learning algorithms.
AN IMPROVED ITERATIVE METHOD FOR SOLVING GENERAL SYSTEM OF EQUATIONS VIA GENE...Zac Darcy
Various algorithms are known for solving linear system of equations. Iteration methods for solving the
large sparse linear systems are recommended. But in the case of general n× m matrices the classic
iterative algorithms are not applicable except for a few cases. The algorithm presented here is based on the
minimization of residual of solution and has some genetic characteristics which require using Genetic
Algorithms. Therefore, this algorithm is best applicable for construction of parallel algorithms. In this
paper, we describe a sequential version of proposed algorithm and present its theoretical analysis.
Moreover we show some numerical results of the sequential algorithm and supply an improved algorithm
and compare the two algorithms.
OCR-THE 3 LAYERED APPROACH FOR DECISION MAKING STATE AND IDENTIFICATION OF TE...ijaia
Optical Character recognition is the method of digitalization of hand and type written or printed text into
machine-encoded form and is superfluity of the various applications of envision of human’s life. In present
human life OCR has been successfully using in finance, legal, banking, health care and home need
appliances. India is a multi cultural, literature and traditional scripted country. Telugu is the southern
Indian language, it is a syllabic language, symbol script represents a complete syllable and formed with the
conjunct mixed consonants in their representation. Recognition of mixed conjunct consonants is critical
than the normal consonants, because of their variation in written strokes, conjunct maxing with pre and
post level of consonants. This paper proposes the layered approach methodology to recognize the
characters, conjunct consonants, mixed- conjunct consonants and expressed the efficient classification of
the hand written and printed conjunct consonants. This paper implements the Advanced Fuzzy Logic system
controller to take the text in the form of written or printed, collected the text images from the scanned file,
digital camera, Processing the Image with Examine the high intensity of images based on the quality
ration, Extract the image characters depends on the quality then check the character orientation and
alignment then to check the character thickness, base and print ration. The input image characters can
classify into the two ways, first way represents the normal consonants and the second way represents
conjunct consonants. Digitalized image text divided into three layers, the middle layer represents normal
consonants and the top and bottom layer represents mixed conjunct consonants. Here recognition process
starts from middle layer, and then it continues to check the top and bottom layers. The recognition process
treat as conjunct consonants when it can detect any symbolic characters in top and bottom layers of
present base character otherwise treats as normal consonants. The post processing technique applied to all
three layered characters. Post processing of the image: concentrated on the image text readability and
compatibility, if the readability is not process then repeat the process again. In this recognition process
includes slant correction, thinning, normalization, segmentation, feature extraction and classification. In
the process of development of the algorithm the pre-processing, segmentation, character recognition and
post-processing modules were discussed. The main objectives to the development of this paper are: To
develop the classification, identification of deference prototyping for written and printed consonants,
conjunct consonants and symbols based on 3 layered approaches with different measurable area by using
fuzzy logic and to determine suitable features for handwritten character recognition.
A FRAMEWORK FOR DETECTING FRAUDULENT ACTIVITIES IN EDO STATE TAX COLLECTION S...ijaia
Edo State Inland Revenue Services is overwhelmed with gigabyte of disk capacity containing data about tax
payers’ in the state. The data stored on the database increases in size at an alarming rate. This has resulted
in a data rich but information poor situation where there is a widening gap between the explosive growth
of data and its types, and the ability to analyze and interpret it effectively; hence the need for a new
generation of automated and intelligent tools and techniques known as investigative data mining, to look
for patterns in data. These patterns can lead to new insights, competitive advantages for business, and
tangible benefits for the State Revenue services. This research work focuses on designing effective fraud
detection and deterring architecture using investigative data mining technique. The proposed system
architecture is designed to reason using Artificial Neural Network and Machine learning algorithm in
order to detect and deter fraudulent activities. We recommend that the architectural framework be
developed using Object Oriented Programming and Agent Oriented Programming Languages.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
Suitability of naïve bayesian methods for paragraph level text classification...ijaia
The amount of data present online is growing very rapidly, hence a need for organizing and categorizing
data has become an obvious need. The Information Retrieval (IR) techniques act as an aid in assisting
users in obtaining relevant information. IR in the Indian context is very relevant as there are several blogs,
news publications in Indian languages present online. This work looks at the suitability of Naïve Bayesian
methods for paragraph level text classification in the Kannada language. The Naïve Bayesian methods are
the most primitive algorithms for Text Categorization tasks. We apply dimensionality reduction technique
using Minimum term frequency, stop word identification and elimination methods for achieving the task. It
is evident that Naïve Bayesian Multinomial model outperforms simple Naïve Bayesian approach in
paragraph classification tasks.
The economic growth is a consensus in any country. To grow economically, it is necessary to channel the
revenues for investment. One way of raising is the capital market and the stock exchanges. In this context,
predicting the behavior of shares in the stock exchange is not a simple task, as itinvolves
variables not always known and can undergo various influences, from the collective emotion to
high-profile news. Such volatility can represent considerable financial losses for investors. In
order to anticipate such changes in the market, it has been proposed various mechanisms trying
to predict the behavior of an asset in the stock market, based on previously existing information.
Such mechanisms include statistical data only, without considering the collective feeling. This
paper is going to use natural language processing algorithms (LPN) to determine the
collective mood on assets and later with the help of the SVM algorithm to extract patterns in an
attempt to predict the active behaviour.
CROSS DATASET EVALUATION OF FEATURE EXTRACTION TECHNIQUES FOR LEAF CLASSIFICA...ijaia
In this work feature extraction techniques for leaf classification are evaluated in a cross dataset scenario.
First, a leaf identification system consisting of six feature classes is described and tested on five established
publicly available datasets by using standard evaluation procedures within the datasets. Afterwards, the
performance of the developed system is evaluated in the much more challenging scenario of cross dataset
evaluation. Finally, a new dataset is introduced as well as a web service, which allows to identify leaves
both photographed on paper and when still attached to the tree. While the results obtained during
classification within a dataset come close to the state of the art, the classification accuracy in cross dataset
evaluation is significantly worse. However, by adjusting the system and taking the top five predictions into
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A Survey of Techniques for Maximizing LLM Performance.pptx
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATION
1. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
DOI: 10.5121/ijaia.2016.7301 1
GENETIC ALGORITHM FOR FUNCTION
APPROXIMATION: AN EXPERIMENTAL
INVESTIGATION
Abdulrahman Baqais1
1
Department of Information and Computer Science, KFUPM, Dhahran, Saudi Arabia
ABSTRACT
Function Approximation is a popular engineering problems used in system identification or Equation
optimization. Due to the complex search space it requires, AI techniques has been used extensively to spot
the best curves that match the real behavior of the system. Genetic algorithm is known for their fast
convergence and their ability to find an optimal structure of the solution. We propose using a genetic
algorithm as a function approximator. Our attempt will focus on using the polynomial form of the
approximation. After implementing the algorithm, we are going to report our results and compare it with
the real function output.
KEYWORDS
Genetic Algorithm, Function Approximation, Experimentation
1. INTRODUCTION
Function approximation is used in science and engineering field in order to find the relationship
between two or more variables: the independent variable (x) and the dependent variable (y) [1-3].
In such situation, input-output pairs of any engineering or scientific problems are collected using
a suitable experiment or instrument. However, a direct relation in the form of equation can’t be
inferred between these pairs due to the absence of strong correlations.
To address this issue, Artificial Intelligence (AI) algorithms have been utilized to produce an
equation between input-output pairs with higher accuracy. Genetic algorithms have been
implemented in various articles with promising results as in [4-6].
2. LITERATURE REVIEW
Genetic algorithm is a metaheuristic algorithm that is designed by Holland in 1975 [7]. The
algorithm starts by providing a random population of points of the search space. At each
iteration, the algorithm applies some operators such as: crossover and mutation on the current
population and evaluate them using an objective (fitness) function. In Function approximation,
the objective function of each problem is to come up with an equation with higher accuracy
between input-output pairs. That is, the objective function is to reduce the errors of the equation.
Different error measurement can be used such as: Least Absolute Error (LAE), Mean Squared
Error (MSE) or residual sum of squares (RSS).
There are many studies that use different AI algorithms including GA to finding the function
approximation as in [4, 6].
2. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
2
In [8], a variant of neural network named Wavelet Neural Network was used to approximate the
function of pollution at Texas in USA. In [9, 10], the authors were able to provide an equation of
higher accuracy with few coefficients of real-world data problem concerning the seawater
density. The equation was generated using GA. Fuzzy Systems were used in [11] to approximate
nonlinear relations.
3. RESEARCH METHODOLOGY
In this paper, we are proposing using genetic algorithms for approximation of polynomial
functions. Genetic algorithms are known for their fast search for solution in a large complex
space. Basically, Genetic algorithms can effectively find an optimal approximated curve to any
mathematical equations with high accuracy. It should be noted that genetic algorithms requires a
deep understanding of the problem and a crafted design of the chromosome. The fitness function
must be chosen carefully to reflect the most contributable feature to the final solution. By
maximization of the fitness function in each generation, genetic algorithm will exhibit a schema
that converges to an optimal robust solution.
In the next section, we are going to explain the details of our program and experiment. The
rationale behind each decision in our experiment is explained in details with sound justifications.
Each step in setting up our experimental framework is written clearly with supporting figures. It
must be understood that the objective of this project is to design a specific genetic algorithm for
approximating polynomial function. Since this is an Artificial Intelligence course, our aim is to
give a deep analysis of the behavior of genetic algorithm and its parameters.
We used Matlab Toolbox to give us a quick access to various parameters of the genetic algorithm
such as selection, number of generation and for plotting purposes. However, the design of the
chromosome and the fitness function is coded to be adjusted to our problem.
In function approximation, the most feature of the solution is to have a high accuracy of the
obtained curve to the original equation. This implies very low errors in approximating each
point in relative to the actual point. So our fitness function will be minimization rather than
maximization. To ensure, that our fitness function is coded correctly, the errors must be
decreasing through the generations until a convergence or an optimal solution is found. Mean
squared error (MSE) was used as a fitness function and it’s defined:
MSE =
The population of our solutions is represented as binary bits. This gives us the flexibility we
need to manipulate the chromosome in a variety of ways as we are going to explain shortly.
Each chromosome (or individual) contains many terms where each term is composed of two
parts:
Coefficient
Power of the variable.
Each term is composed 15 bits, where 10 bits is allocated to coefficient and the remaining bits
are allocated to represent the power.
Now, for simplicity we will assume that all terms are polynomial functions since polynomial
functions are known to be a universal function approximator.
3. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
3
Another contribution of this paper lies in the range the power of each terms may have. In normal
regression approximation, the researcher is constrained to use only integer values in the power
part. However, using a resolution concept, we are allowing both the coefficient and the power to
have real values. The range of values that the coefficient and the power may take is depicted in
the Table 1.
Table 1: Range of Coefficient and Power Variables
Variable Resolution
Coefficient (Coefficient /10) – 50.4
Power (Power *0.25) - 4
le. Another aspect that needs to be considered is the probability of crossover and mutation and
the range of bits they are applied to. Crossover and mutation can be implemented in various
ways: either on the term boundary, on the part unit boundary or within the individual bits. Each
method has its merits and drawbacks based on the targeted problem. In this specific chromosome
design, we opt to play with the crossover and mutation within the bits themselves. This is done
for twofold: one all of our terms are in polynomial shape and hence targeting with the term
boundary will not help much in converging the solution. If our chromosome design exhibits other
function types such as trigonometric function, then targeting terms boundary may have better
results. The second reason is that manipulating individual bits increase the chances of finding
better solution. Even though, It may increases the complexity of the problem and the search
space to explore in general large problems, the simplicity of our problem that allocates only 15
bits to the term mitigate these issues and the extra time added will be negligible or of little
significance as we are going to show in the experiment sections.
We opt to represent our population of individuals as binary strings. That gives us the flexibility
to specify the range of the values of the coefficient and the powers. The following figure shows
the basic design of the chromosome:
The Fitness Function: where y refers to the real output and is the
approximated output.
The Final form of the polynomial equation will be on the form of:
A(x) = coefficent * X1
power
+ coefficient * X2
power
… + coefficent * Xn
power
4. EXPERIMENTAL SETUP:
In the literature review, we explored different functions proposed by many authors as the target
equation. Some choose normal polynomial; others opt for Rastrigin functions due to its
suitability since it poses many local minimum points and some may prefer to run their
experiments approximating real equations from engineering domains. In this paper, we opt to
target polynomial functions of the form:
F(x) = x2
Where x ranges between 0.1 - 10.00 with an increasing step of 0.1.
Choosing the number of samples is very critical to be able to approximate any function. If the
number of samples is too small, then approximated function may miss some critical points and
thus the curve may not be correctly approximated. If the number is too large, then we will have
4. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
4
the issue of the over fitting, not to mention the added penalty in time and performance. So, in
regarding to that, we might apply some sampling theorem that is applied extensively in statistics.
Instead, we prefer to include only 100 of points. It’s important to understand the features of the
problem to be able to provide an efficient solution. Since we know from basic mathematics that a
squared function usually takes a shape of a parabola, then it will be enough to take all the points
on one side of the parabola and be able to approximate it, since the parabola is symmetric around
their axis. Arbitrarily, we decided to take all the points in the positive side of the parabola,
which has no more advantage or any increasing in contribution than the negative side. It’s just a
matter of an arbitrary decision.
A sharp observer may notice that the starting point of our samples is 0.1 not 0 and he or she
might wonder what is the rationale behind this decision. Selecting 0 as a sample point will do
more harm than good. Multiplying 0*0 in the actual calculation and then trying to approximate it
will result in a returning value of INF in Matlab. Matlab toolbox is set to tolerate a predefined
value of approximation to any actual number. By attempting to approximate (0^2
), the
approximator will be largely deviated and the error values between actual and approximated is
reaching a very large value that consequently leads to the returning value of infinity by Matlab.
5. RESULTS
After presenting to the reader the design of our solution and all the rationale behind our
experiments setup, we are ready now to run our experiment and record all the values.
To provide a good framework on how our experiment is designed to improve the solution, we
must decide on what parameters affect the obtained results. Next, we can validate our solution
accuracy by varying these parameters. In this problem, we have three parameters they may affect
the accuracy which are:
• Number of terms in the chromosome.
• The population of individuals.
• The number of generations.
Since our objective in this paper is to come up with an approximated curve of high accuracy, the
number of terms is not of much significance. If our problem is targeting reducing the number of
terms, then that parameter should be incorporated in the experiment. Hence, we fix the number
of terms in any chromosome to be 135 bits. That is, any chromosome will have 9 terms. The
population and the number of generations however will change and the obtained fitness function
will be recorded in each run. Table 2 gives the variation of our experiments.
Table 2: Experiments parameters
Experiment Case No No of terms Population Size No of Generation
1 9 1000 1000
2 9 1000 300
3 9 1000 50
4 9 200 1000
5 9 50 1000
Case 1: ( Best Case)
5. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
5
Population Size: 1000
Generations : 1000
Fitness : 0.252990008807331
In this run instance, we set the population size and generation size to 1000, As you can see from
the figure (1) , we reached the best value of all of our running experiments by obtaining a fitness
value of 0.25299. Since the fitness Value represents the error, it implies that the approximated
function returned by this instance of genetic algorithm will have an error as low as 0.25299. To
have a clearer picture of the behavior of our fitness function, figure (2) shows the same figure but
at log scale. Here, we can see that our fitness function is minimized from one generation to
another until it reaches convergence by not evolving in hundreds of generations.
It is clear that Log Figure shows the minimization from one generation to another better than the
linear figure. Thus, in the following experiments, we will show the Log figures only.
0 100 200 300 400 500 600 700 800 900 1000
0
2
4
6
8
10
12
14
x 10
4
Generation
Fitnessvalue
Best: 0.25299 Mean: 2121.1762
Best fitness
Mean fitness
Figure 1: Case 1 Fitness value Linear Scale
0 100 200 300 400 500 600 700 800 900 1000
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Generation
Fitnessvalue
Best: 0.25299 Mean: 2121.1762
Best fitness
Mean fitness
Figure 2: Case 1 Fitness Value Log Scale
Case 2:
Population Size: 1000
Generations : 300
Fitness : 0.57708
In this experiment, we reduced the number of generations to be maximum 300. Hence, the
fitness value is still small relatively, but is not as optimal as the previous case. It assists in
6. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
6
implying that the number of generation’s parameter has a small impact on the final result. The
following figure (3) using Log scale shows the behavior of fitness function in finding the
schema.
0 50 100 150 200 250 300
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Generation
Fitnessvalue
Best: 0.57708 Mean: 450.024
Best fitness
Mean fitness
Figure 3: Case 2 Fitness Value Log Scale
Case 3:
Population Size: 1000
Generations : 50
Fitness : 0.84211
This experiment supports our claim about the small effect generation’s parameter has on the final
result. By reducing the number of generations to a very small number such as 50, the fitness
value is higher than all of the previous two cases. It’s clear from this figure, that if we extend the
number of generation a little bit more, then a finer fitness value will be obtained.
0 5 10 15 20 25 30 35 40 45 50
10
-2
10
0
10
2
10
4
10
6
Generation
Fitnessvalue
Best: 0.84211 Mean: 2831.0001
Best fitness
Mean fitness
Figure 4: Case 3 Fitness Value Log Scale
Case 4:
Population Size: 200
Generations : 1000
Fitness : 2.0594
Case 4 & 5 targets the impact of the population size parameter on the solution. By having the
population size reduced from 1000 to 200, the error reaches a higher value and a convergence
point reaches quickly. This case and the following case prove the significant impact of
Population size on the final result.
7. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
7
0 100 200 300 400 500 600 700 800 900 1000
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Generation
Fitnessvalue
Best: 2.0594 Mean: 282.6528
Best fitness
Mean fitness
Figure 5: Case 4 Fitness Value Log Scale
Case 5:
Population Size: 50
Generations : 1000
Fitness : 4.5354
The population size is reduced significantly to only 50 random individuals. Even though the
number of generations is high (1000), the algorithm reaches convergence very early at 800. That
implies it has no improvement for 500 consecutive generations and as such it was stopped
abruptly by the toolbox. The error is the highest than all of the previous cases. It’s evident from
the graph, that genetic algorithms can’t gain much improvement when the population size is very
small. Since the population size is very small, genetic algorithm is very restricted in finding an
optimal solution and no matter how many generations are set or how other parameters behaves;
the base population size contributes little to the final result.
0 100 200 300 400 500 600 700 800 900 1000
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Generation
Fitnessvalue
Best: 4.5354 Mean: 3266.1098
Best fitness
Mean fitness
Figure 6: Case 5 Fitness Value Log Scale
Validation of the result can be done by comparing the results of the approximated function to the
actual function. This type of validation is error prone and time consuming. Instead, the figures
above show that the fitness function is decreasing across all the generation and this pattern is
consistent in all experiments. Thus, in all the experiments above, our fitness function is trying to
reach the global minimum before it reaches convergence. Hence, we can conclude that our
program is running correctly and our results are valid and optimized given the parameters
supplied. A summary of the result of the best case is given below where the initial population is
given in Appendix A. An interesting researcher who would like to replicate the experiment
8. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
8
would definitely obtain the same results provided that he or she supplemented the exact same
parameters values that we set.
Table 3: Results Summary
Number of Terms 9
Population Size 1000
No of Generations 1000
Fitness Values 0.2599
Individual populations : Appendix A
Output Population
(Binary):
1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0,
0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0,
0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0,
0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,1,1,1,0,
1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,1,1,1,1,0,0,1,0,
1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,1
Output approximated
function:
3.8 X 3.25
- 5.4 X 0.5
- 39.9 X-3.25
+ 25.2 X 2.25
+
45.4X -0.5
- 3.3 X -0.5
+ 13.2 X -0.75
-44.2 X -1.25
+ 13.5
X -2.75
6. CONCLUSION AND FUTURE WORK
Our attempt here of providing a robust yet fast method of finding an approximating function
works correctly. Genetic algorithm and its stochastic search of optimal solution in a large
complex space can save the effort and time to predict the approximated curve of any unknown
engineering system by supplying the input -output pairs only.
The design of chromosome and building parts plays a significant factor in reaching an optimal
solution quickly. The number of bits allocated to each building part and the decision of range
values must be crafted carefully to direct the genetic algorithm to the right region where optimal
solution may lay. Genetic algorithms even perceived as a successful implementation of random
search, a guided direction at the initial stage of the algorithm will ensure a better results and
that’s can be proven in our results above. We tested our algorithm on one function only which is
a squared function. Even though this might be considered as a drawback, it’s very important to
notice that our objective of this project not to design a universal function approximator using
genetic algorithm. Instead, our main objective is to show how genetic algorithm can play a vital
role in finding an optimal solution quickly and how adjusting the parameters is contributing to
the results significantly. Testing the algorithm on many different polynomial and non-polynomial
functions is set to be a future work plan and requires a deep understanding of mathematics to
craft an excellent chromosome that absorbs all the contributable features of all mathematical
equations.
7. THREATS TO VALIDITY
There are two main threats that may have impact on the results of this study. The first threat is
that we used the data of one system, however, we plan to use the data of more systems in future
studies.
Another threat is in data collection process. The process of collecting and analysing the data was
semi-automated. This may impact the results as human error may occur.
9. International Journal of Artificial Intelligence and Applications (IJAIA), Vol. 7, No. 3, May 2016
9
ACKNOWLEDGEMENTS
The authors would like to thank KFUPM for all support.
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Authors
Abdulrahman Baqais is a PhD candidate at Computer Science & Engineering
College, King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia. He
has obtained his Bachelor (Hons) in Software Engineering from Multimedia
University, Malaysia in 2007 and his MSc from Staffordshire University, UK in
2010. His research interests including: software engineering, metaheuristics and
search-based techniques and has published several articles in referred journal and
conferences in these areas. He served as the session chair in IAENG conference in
UK, 2013.