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IJCSIS Vol. 8, No. 9, December 2010 Edition
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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 9, December 2010 Constructing Models from Microarray Data with Swarm Algorithms. Mrs.Aruchamy Rajini Dr. (Mrs.)Vasantha kalayani David Lecturer in Computer Applications Associate Professor, Department of Computer Science Hindusthan College of Arts & Science, Coimbatore Avinashilingam Deemed University, Coimbatore aruchamy_rajini@yahoo.co.in vasanthadavid@yahoo.com Abstract been computed for better use of classification algorithm in Building a model plays an important role in DNA micro array gene expression data [3] [4]. microarray data. An essential feature of DNA microarray Variable selection refers to the problem of selecting input data sets is that the number of input variables (genes) is far variables that are most predictive for a given outcome. greater than the number of samples. As such, most classification schemes employ variable selection or feature Appropriate variable selection can greatly enhance the selection methods to pre-process DNA microarray data. In effectiveness and potential interpretability of an inference this paper Flexible Neural Tree (FNT) model for gene model. Variable selection problems are found in all expression profiles classification is done. Based on the pre- supervised and unsupervised machine learning tasks defined instruction/operator sets, a flexible neural tree including classification, regression, time-series prediction, model can be created and evolved. This framework allows and clustering [5]. input variables selection, over-layer connections and different activation functions for the various nodes involved. This paper develops a Flexible Neural Tree (FNT) [6] for The FNT structure is developed using the Ant Colony selecting the input variables. Based on the pre-defined Optimization (ACO) and the free parameters embedded in instruction/operator sets, a flexible neural tree model can the neural tree are optimized by Particle Swarm be created and evolved. FNT allows input variables Optimization (PSO) algorithm and its enhancement (EPSO). selection, over-layer connections and different activation The purpose of this research is to find the model which is functions for different nodes. The tuning of the an appropriate model for feature selection and tree-based parameters encoded in the structure is accomplished using ensemble models that are capable of delivering high performance classification models for microarray data. Particle Swarm Optimization (PSO) algorithm and its enhancement. Keywords --- DNA, FNT, ACO, PSO, EPSO The proposed method interleaves both optimizations. I. INTRODUCTION Starting with random structures and corresponding A DNA micro array (also commonly known as DNA chip parameters, it first tries to improve the structure and then or gene array) is a collection of microscopic DNA spots as soon as an improved structure is found, it then tunes its attached to a solid surface, such as glass, plastic or silicon parameters. It then goes back to improving the structure chip forming an array for the purpose of expression again and, then tunes the structure and rules' parameters. profiling, monitoring expression levels for thousands of This loop continues until a satisfactory solution is found genes simultaneously. Micro arrays provide a powerful or a time limit is reached. basis to monitor the expression of thousands of genes, in II. THE FLEXIBLE NEURAL TREE MODEL order to identify mechanisms that govern the activation of genes in an organism [1]. The function set F and terminal instruction set T used for generating a FNT model are described as S = F U T = Recent advances in DNA micro array technology allow {+2,+3, . . . ,+N}U{x1, . . . , xn}, where +i(i = 2, 3, . . .,N) scientists to measure expression levels of thousands of denote non-leaf nodes’ instructions and taking i genes simultaneously in a biological organism. Since the arguments. x1,x2,. . .,xn are leaf nodes instructions and cancer cells usually evolve from normal cells due to taking no other arguments. The output of a non-leaf node mutations in genomic DNA, comparison of the gene is calculated as a flexible neuron model (see Fig.1). From expression levels of cancerous and normal tissues or this point of view, the instruction +i is also called a different cancerous tissues may be useful to identify those flexible neuron operator with i inputs. genes that might anticipate the clinical behavior of cancers. In the creation process of neural tree, if a nonterminal instruction, i.e., +i(i =2, 3, 4, . . .,N) is selected, i real Micro array technology has made the modern biological values are randomly generated and used for representing research by permitting the simultaneous study of genes the connection strength between the node +i and its comprising a large part of genome [2]. In response to the children. In addition, two adjustable parameters ai and bi development of DNA micro array technologies, are randomly created as flexible activation function classification methods and gene selection techniques are parameters and their value range are [0, 1]. For 237 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 9, December 2010 developing the forecasting model, the flexible activation on two specific SI algorithms well-known as Particle function f (ai, bi, x) = e− ((x−ai)/bi)2 is used. Swarm Optimization (PSO) and Ant Colony Optimization (ACO). The total excitation of +n is netn = ∑nj=1 wj * xj, PSO was originated from computer simulations of the coordinated motion in flocks of birds or schools of fish. where xj (j = 1, 2, . . ., n) are the inputs to node +n and wj As these animals wander through a three dimensional are generated randomly with their value range space, searching for food or evading predators, these are[0,1].The output of the node +n is then calculated by algorithms make use of particles moving at velocity outn = f(an, bn, netn) =e−( (netn−an)/bn)2 . The overall output of dynamically adjusted according to its historical behaviors flexible neural tree can be computed from left to right by and its companions in an n-dimensional space to search depth-first method, recursively [7]. for solutions for an n-variable function optimization problem. The Particle Swarm Optimization algorithm includes some tuning parameters that greatly influence the X1 algorithm performance, often stated as the exploration w1 exploitation trade off. Exploration is the ability to test various regions in the problem space in order to locate a f(a,b) w2 good optimum, hopefully the global one. Exploitation is X2 +n Y the ability to concentrate the search around a promising candidate solution in order to locate the optimum w3 precisely [8][9][10][11]. El-Desouky et al., in [10] proposed a more enhanced X3 particle swarm algorithm depending on exponential weight variation instead of varying it linearly which gives Output better results when applied on some benchmarks Layer +6 functions. In this paper three models are compared: 1) A Tree structure is created with ACO 2) A Tree structure is created with ACO and the parameters are optimized with PSO 3) A Tree Structure is created with ACO and the parameters are optimized with EPSO. Comparisons of the three models are shown in this paper to propose an efficient methodology. IV. ANT COLONY OPTIMIZATION (ACO) FOR Second hidden X1 X2 +2 X3 +3 +3 EVOLVING THE ARCHITECTURE OF FNT layer ACO is a new probabilistic technique for solving computational problems to find optimal path. It is a paradigm for designing metaheuristic algorithm for First combinatorial optimization problems. The main hidden +3 underlying idea, inspired by the behavior of real ants, is X1 X2 X3 layer +2 that of a parallel search over several constructive threads based on local problem data and on a dynamic memory structure containing information on the quality of previously obtained results. Input In this algorithm, each ant will build and modify the trees layer X1 X2 X3 X3 X2 X1 X2 X3 according to the quantity of pheromone at each node. Each node memorizes the rate of pheromone. First, a population of programs is generated randomly. Each node Fig. 1. A flexible neuron operator (left), and a typical representation of is initialized at 0.5, which means that the probability of the FNT with function instruction set F = {+2,+3,+4,+5,+6}, and terminal instruction set T = {x1, x2, x3} (right) choosing each terminal and function is equal initially. The higher the rate of pheromone, the higher the probability to III. SWARM INTELLIGENCE be chosen. Each ant is then evaluated using a predefined ALGORITHMS. objective function which is given by Mean Square Error (MSE)[7]. Swarm Intelligence (SI) has recently emerged as a family of nature inspired algorithms, especially known for their (1) ability to produce low cost, fast and reasonably accurate Fit (i) =1/p ∑p j=1 (At - Ex)2 solutions to complex search problems [1]. It gives an introduction to swarm intelligence with special emphasis 238 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 9, December 2010 Where p is the total number of samples, At and Ex are (i is the index of the particle) and a velocity represented actual and expected outputs of the j th sample. Fit(i) by a velocity-vector vi. Each particle remembers its own denotes the fitness value of the ith ant. best position so far in a vector x. The pheromone is updated by two mechanisms: Each particle keeps track of its own best position, which is associated with the best fitness it has achieved so far in – 1. Trail Evaporation: - Evaporation decreases the rate of a vector pi. The best position among all the particles pheromone for every instruction on every node, in order obtained so far in the population is kept track of as pg. to avoid unlimited accumulation of trails, according to following formula: Each particle i maintains the following information: xi the current position of the particle, vi the current Pg = (1 − α) Pg−1 (2) velocity of the particle must be defined by parameters vmin and vmax. At each time step t, by using individual best where Pg denotes the pheromone value at the generation position pi, and all the global best position, pg(t), a new g, α is a constant (α = 0.15). velocity for particle i is updated by[1] – 2.Daemon actions: - For each tree, the components of the tree will be reinforced according to the Fitness of the Vi (t+1) = wvi(t)+c1φ1(pi(t) – xi(t))+ tree. The formula is c2φ2 (pg(t) – Xi(t)) (4) Where w is the inertia weight whose range is [0.4, 0.9], c1 Pi,si = Pi,si + α (3) and c2 are positive constant and are the learning factors called, respectively, cognitive parameter and social F it(s) parameter. The proper fine-tuning may result in faster convergence and alleviation of local minima. The default values, usually, c1=c2=2 are used. Even by using where s is a solution (tree), Fit(s) its Fitness, si the c1=c2=1.49 gives better results. φ1and φ2 are uniformly function or the terminal set at node i in this individual, á distributed random number in range of [0, 1]. is a constant (á = 0.1), Pi,si is the value of the pheromone for the instruction si in the node i[7]. During the iteration time t, the update of the velocity from the previous velocity to the new velocity is determined. A brief description of AP algorithm is as follows:(1) The new position is then determined by the sum of the every component of the pheromone tree is set to an previous and the new velocity, according to the formula: average value; (2) random generation of tree based on the pheromone; (3) evaluation of ants (4) update of the Xi (t+1) = xi(t) + vi(t+1) (5) pheromone; (5) go to step (1) unless some criteria is satisfied[7] Various methods are used to identify particle to influence the individual. Two basic approaches to PSO exist V. PARAMETER OPTIMIZATION WITH PSO. based on the interpretation of the neighborhood of particles. They are (1) global best (gbest) version of PSO [12] is in principle such a multi-agent parallel search PSO where the neighborhood of each particle is the technique. It does not require any gradient information of entire swarm. The social component then causes the function to be optimized, uses only primitive particles to be drown toward the best particle in the mathematical operators. Particles are conceptual entities swarm.(2) local best (lbest) PSO model, particles have which fly through the multi-dimensional search space. information only of their own and their nearest array neighbors best(lbest) rather than that of entire group. The PSO was inspired by the social behavior of a bird gbest model converges quickly but has weakness of being flock or fish school.PSO[13] conducts searches using a trapped in local optima. The gbest is recommended population of particles which correspond to individuals. strongly for unimodal objective function [1]. In the PSO algorithm, the birds in a flock are symbolically represented as particles. These particles The PSO is executed with repeated application of can be considered as simple agents flying” through a equation (4), (5) until a specified number of problem space. A particle’s location represents a potential iterations has been exceeded or when the velocity solution for the problem in the multi-dimensional problem updates are close to zero over a number of iterations. space. A different problem solution is generated, when a particle moves to a new location. The PSO algorithm work as follows: PSO model consists of a swarm of particles, which are 1) Initial population is generated randomly. The learning initialized with a population of random positions. They parameters c1, c2 are assigned in advance.2) The objective move iteratively through the d-dimension problem space function value for each particle is calculated.3) Search to search the new solutions, where the fitness, f, (Eqn. (1)) point is modified. The current search point of each can be calculated as the certain qualities measure. Each particle is changed using Equations (4) and (5).4) If particle has a position represented by a position-vector xi 239 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 9, December 2010 maximum number of iterations is reached, then stop; flexible activation function parameters) encoded in the otherwise go to step (2). best tree formulate a particle. 5) If the maximum number of local search is reached, or VI. EXPONENTIAL PARTICLE SWARM no better parameter vector is found for a significantly OPTIMIZATION (EPSO) long time then go to step 6); otherwise go to step 4); 6) If satisfactory solution is found, its corresponding In linear PSO, the particles tend to fly towards the gbest informative genes are extracted, then the algorithm is position found so far for all particles. This social stopped; otherwise go to step 2). cooperation helps them to discover fairly good solutions rapidly. However, it is exactly this instant social VII. RESULTS collaboration that makes particles stagnate on local optima and fails to converge at global optimum. Once a As a Preliminary study, the Wisconsin Prognostic breast new gbest is found, it spreads over particles immediately cancer (WPBC)[18] data set has 34 attributes (32 real- and so all particles are attracted to this position in the valued) and 198 instances. The methodology adopted for subsequent iterations until another better solution is breast cancer data set was applied. Half of the observation found. Therefore, the stagnation of PSO is caused by the was selected for training and the remaining samples for overall speed diffusion of newly found gbest [10]. testing the performance of different models. All the models were trained and tested with same set of data. The An improvement to original PSO is constituted by the fact instruction set used to create an optimal FNT classifier S that w is not kept constant during execution; rather, = FUT = {+2,……… ,+N} U {x0.x1,…..,x31}Where xi starting from maximal value, it is linearly decremented as (i=0,1,….31) denotes the 32 input features. To get an the number of iterations increases down to a minimal optimal tree structure an ACO algorithm is applied. In this value [4], initially set to 0.9, decreasing to 0.4 over the experiment the input is the number of ant and the number first 1500 iterations if the iterations are above 1500, and of iterations. Each ant is made to run for a specified remaining 0.4 over the remainder of the run according to number of iterations. Each ant constructs a neural tree with its objective function which is calculated as MSE. The ant which gives the low MSE is taken to be the best W = (w – 0.4) (MAXITER - ITERATION) tree for which the parameters are optimized with PSO and + 0.4 EPSO. The tree which produces the low error is the MAXITER (6) optimized neural tree and this extracts the informative genes. MAXITER is the maximum number of iterations, and As with breast cancer data set, it was well proven that the ITERATION represents the number of iterations. tree structure with ACO and parameter optimization done with EPSO can achieve better accuracy compared with EPSO has a great impact on global and local exploration the other models. The main purpose is to compare the it is supposed to bring out the search behavior quickly and models quality, where the quality is measured according intelligently as it avoid the particles from stagnation of to the error rate, mean absolute percentage error and local optima by varying this inertia weight exponentially, accuracy. The ACO-EPSO model has the smallest error as given rate when compared with the other models. All the three models are made to run for the same number of iterations W = (w – 0.4) e( MAXITER - ITERATION )-1 / MAXITER + 0.4 and the results shows that ACO-EPSO success to reach (7) optimal minimum in all runs. This method gives the best minimum points better than the other models. This is By using the Equation (7) the movement of particles will depicted in the following figures. be faster and distant from each other. In Figure 1 and 2 the error rate and mean absolute A. General learning Procedure: percentage error of the model ACO-EPSO is low when compared with ACO and ACO–PSO. The general learning procedure for constructing the FNT model can be described as follows. 1) Create an initial population randomly (Set FNT trees and its corresponding parameters); 2) Structure optimization is achieved by the Ant Colony Optimization Algorithm. 3) If a better structure is found, then go to step 4), otherwise go to step 2); 4) Parameter optimization is achieved by the EPSO algorithm. In this stage, the architecture of FNT model is fixed, and it is the best tree developed during the end of run of the structure search. The parameters (weights and 240 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 9, December 2010 Fig1: Comparison of models in terms of error rate Fig3: Comparison of models in terms of accuracy VIII.CONCLUSION A new forecasting model based on neural tree representation by ACO and its parameters optimization by EPSO was proposed in this paper. A combined approach of ACO and EPSO was encoded in the neural tree was developed. It should be noted that there are other tree- structure based evolutionary algorithms and parameter optimization algorithms that could be employed to accomplish same task but this proposed model yields feasibility and effectiveness .This proposed new model helps to find optimal solutions at a faster convergence. EPSO convergence is slower to low error, while other methods convergence faster to large error. The Proposed Fig2: Comparison of models in terms of mean absolute method increases the possibility to find the optimal percentage error solutions as it decreases with the error rate. 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