Genetic Feature Construction: a parallel
implementation of a genetic programming tool for feature construction
Ioannis G. Tsoulos, Alexandros Tzallas, Dimitris Tsalikakis
Abstract—In this paper a parallel implementation of a recently introduced method for feature construction is described. This technique utilizes parallel genetic algorithms along with RBF neural networks to create new features from the original ones by discovering the hidden relations between patterns. The method is tested on series of classification problems from a variety of areas and the results are reported. The accompanied software is written entirely in ANSI C++ using the well established MPI library for parallelization.
Index Terms—Genetic algorithms, genetic programming, neu- ral networks, feature construction.
I. INTRODUCTION
T
HE problem of data classification has many practical application in areas such as chemistry[1], [2], [3], biology [4], [5], economics [6], [7], physics [8], [9] etc. Many methods have been proposed to tackle this problem such as neural networks [10], radial basis functions networks [11], support vector machines [12], etc. The proposed software utilizes a grammatical evolution approach [13] to create a subset of features from the original one using non-linear combinations from them. This method initially was described in [14] and it was been used with success on a series of problems such as Spam Identification [15], Fetal heart classification [16], epilep- tic oscillations in clinical intracranial electroencephalograms [17] etc. Nevertheless, the process of Grammatical Evolution can require a lot of execution time and hence parallelization is mandatory. Parallel genetic algorithms have been used in many applications such as aerodynamic optimization [18], steel structure optimization [19], brain images [20] etc. The used parallel genetic algorithm is based on Island model [21], [22], where computing nodes exchange information between them and one node acts as the server with important responsi- bilities such as collecting the best located values by the other clients. The proposed software implements a parallel genetic algorithm with some additions such as: an enhanced stopping rule[23] and a new local search procedure introduced here.The software has been written entirely in ANSI C++ using MPI libraries (Lam[24] or OpenMPI [25] ).
DOI: http://dx.doi.org/10.24018/ejers.2019.4.5.1272 Published on May 6, 2019
Ioannis G. Tsoulos is with the Department of Informatics and Telecommu- nications, University of Ioannina, Greece (e-mail: [email protected]).
Alexandros Tzallas is with the Department of Informatics and Telecommu- nications, University of Ioannina, Greece (e-mail: [email protected]).
Dimitris Tsalikais is with the Department of Engineering Informatics and Telecommunications, Greece (e-mail: [email protected]).
The rest of this article is organized as follows: in section II a detailed description of the method is given, in section III some experimental results in common classification problems are presented, in section IV typical usage of the software is provided and finally in section V some conclusions for the software are discussed.
II. METHOD DESCRIPTION
A. Server side algorithm
The program is executed in parallel on a series of machines.
One machine of them is considered as the server and each one from the others is considered as a client. The server periodi- cally collects information from the clients about the discovered train error and the corresponding generation number for every client. The algorithm that runs on server has as follows:
1) Set N the number of clients.
2) Set Nf the number of desired features.
3) If all clients have finished then
a) Report (x∗, y∗) as the pair of best chromosome and best train error.
b) Evaluation step
i) Create the Nf new features for chromosome x∗.
ii) Transform, using grammatical evolution the original train data. The new train data will be used to train a classification model such as an RBF network.
iii) Transform, using grammatical evolution the original test data.
iv) Apply the classification model trained before to the new test data and report the induced test error.
c) Terminate 4) EndIf
5) For i = 1 . . . N Do
a) Collect the information (xi, yi) from the client i b) If yi< y∗ Then (x∗, y∗) = (xi, yi)
6) EndFor 7) Goto 3
B. Client side algorithm
On each client a genetic algorithm with the termination rule described in [23] accompanied with an additional local search operator is applied. The steps of the algorithm are given below:
1) Initialization step
a) Set iter=0, where iter is the current number of generations
b) Set Nf the number of desired features.
c) Set Nc as the total chromosomes.
d) Initialize chromosomes Xi, i = 1 . . . NcThe chro- mosomes are initialized randomly as vectors of integers.
e) Set ITERMAX as the maximum number of al- lowed generations.
f) Set ps as the selection rate and pm the mutation rate. Both rates are in the range [0, 1]
g) Set fl= ∞, the best discovered fitness
h) Set LI the number of generations that should pass before the local search procedure is applied.
i) Set Lc the number of chromosomes that will participate in local search procedure.
2) Termination check. At every generation the variance σ(iter) of flis calculated. If there was no improvement of the genetic algorithm for a number of generations, then the algorithm should terminate. The stopping rule has as follows:
|fh− fl| ≤ e OR σ(iter)≤ σ(last)
2 OR iter>ITERMAX (1) Where last denotes the generation number where flwas produced initially. If equation 1 is true then Goto step 9.
3) Calculate the fitness fi for every chromosome of the population:
a) Transform the original train data using grammat- ical evolution and create Nf features.
b) Train a classification model Ci obtaining the train error E
c) Assign the train error E to fitness value fi
4) Genetic Operators
a) Selection procedure: The chromosomes are sorted in descending order according to their fitness value.
The first (1 − ps) × Nc chromosomes are trans- ferred to the next generation. The rest of the chromosomes are substituted by offsprings created through one point crossover procedure.
b) Mutation procedure: For every element of each chromosome a random number r in range [0, 1]
is produced. If r ≤ pm then the corresponding element is randomly altered.
c) Replace the ps× Nc worst chromosomes in the population with the offsprings created by the ge- netic operators.
5) Set iter=iter+1 6) Local Search Step
a) If iters mod Li= 0 Then
i) Select randomly LC chromosomes from the genetic population and create the set LS from these chromosomes
ii) For every chromosome Xi in LS
A) Select randomly another chromosome Y from the population
B) Create an offspring of Xiand Y using one point crossover. Denote the offspring as Z C) Obtain the fitness f (Z) of chromosome Z.
If f (z) < fi then Xi= Z, fi= f (Z) b) Endif
7) Obtain the best value in the population, denoted as fl
for the corresponding chromosome xl
8) Send (xl, fl) to Server machine and Goto step 3 9) Send (xl, fl) to Server machine and Terminate
III. EXPERIMENTAL RESULTS
A. Datasets
The classification datasets were found in the Machine Learning Repository in the following URL: http://www.ics.
uci.edu/~mlearn/MLRepository.html The description of the classification datasets has as follows:
1) Ionosphere dataset: The ionosphere dataset (ION in the following tables) contains Radar data from the Johns Hopkins Ionosphere database. The dataset has 34 fea- tures.
2) Wine dataset: The wine recognition dataset (WINE) contains data from wine chemical analysis. The dataset has 13 features.
3) Parkinsons dataset: This dataset[27] is composed of a range of biomedical voice measurements from 31 people, 23 with Parkinson’s disease (PD). Each column in the table is a particular voice measure, and each row corresponds one of 195 voice recording from these individuals ("name" column). The main aim of the data is to discriminate healthy people from those with PD, according to "status" column which is set to 0 for healthy and 1 for PD. The dataset has 22 features.
4) Transfusion dataset[28]: Data taken from the Blood Transfusion Service Center in Hsin-Chu City in Taiwan.
The dataset has 4 features.
5) Wdbc dataset: The Wisconsin diagnostic breast cancer dataset (WDBC) contains data for breast tumors. The dataset has 30 features.
6) Hayes Roth dataset: This dataset[29] contains 5 numeric-valued attributes and 132 patterns.
7) EEG dataset. An EEG dataset, which is available online [30], [31] and includes recordings for both healthy and epileptic subjects, is used. The dataset includes five subsets (denoted as Z, O, N, F, and S) each containing 100 single-channel EEG segments, each one having 23.6-second duration. The dataset has 500 patterns and the number of features is 21.
8) Regions dataset. Regions Dataset is created from liver biopsy images of patients with hepatitis C [32]. The dataset has 18 features.
9) Gene dataset. Dataset that described primate splice- junction gene sequences (DNA) with associated imper- fect domain theory [36]. The dataset has 120 features.
B. Experiments
Firstly, a series of experiments was conducted using several classification methods from the relevant literature:
1) An RBF neural network
2) Minimum Redundancy Maximum Relevance Feature Selection method[33], [34]
3) A Principal Component Analysis (PCA) method ob- tained from Mlpack[35].
The results from the application of the classification methods to the above datasets are listed in Table I. The numbers in cells denote average classification error on the test set. The column RBF denotes average classification error for RBF with 10 hidden nodes, the column MRMR denotes average classification error for the MRMR feature selection method with two features selected and the column PCA denotes average classification error for the PCA method with two features created for every dataset.
For the case of the proposed method three sets of exper- iments were conducted with two, four and eight processors correspondingly. The parameters for the proposed algorithm are listed in Table V. Every experiment has been performed 30 times using different seed for the random generator each time. The parameter Nc was set to 500 for two processors, 250 for four processors and 125 for eight processors in order to have a fixed number of chromosomes (1000) in each case.
All the experiments were conducted on a cluster of 16 cpus running Ubuntu 16.04.
The results from the conducted experiments in two pro- cessors are listed in Table II. The results of the proposed method with four processors are listed in Table III and finally the results in eight processors are listed in Table IV. In all three tables the column TD1 denotes the average execution time for one constructed feature, the column ED1 denotes the average classification error for one constructed feature, the column TD2 denotes the average execution time for two constructed features and the column ED2 denotes the average classification error for the two constructed features. Also, the column TD4 denotes the average execution time for four constructed features and the column ED4 denotes the average classification error for the four constructed features and the column TD8 denotes the average execution time for eight constructed features and the column ED8 denotes the average classification error for the eight constructed features. From the results we can notice that the method maintains the good approximation abilities even if the number of chromosomes on each client is reduced. Additionally, the execution time seems to decreased as the the number of processors increases.
At it can be deduced from the experiments the proposed method is able to construct a more efficient set of artificial features and in the majority of the experiments it can outper- form other classification methods. As it can shown from the experimental results, the method is stable concerning execution time and classification error making use of 4 constructed features and even though 8. It seems that there is no significant change in error and average execution time in the majority of datasets.
IV. USAGE OF THE SOFTWARE
The software can be downloaded from the relevant github directory https://github.com/itsoulos/FeatureConstruction and the installation procedure is provided in the associated wiki page. For the reader’s convenience we demonstrate the use of the proposed method using two computing nodes (node1, node2) and the wdbc dataset, which is located under example sub - directory.
A. Installation
The program can be easily installed in any operating system with ANSI C++ installed and the required MPI library. The steps are the following:
1) Download a zip file named FeatureConstruction- master.zip from https://github.com/itsoulos/
FeatureConstruction
2) unzip FeatureConstruction-master.zip
3) Inspect Makefile.inc in order to change if required the parameters of the compilation.
4) Issue the command make.
B. Command line options
The outcome of the compilation is the executable fc under bin subdirectory, with many command line options such as:
1) -d dimension. The integer parameter dimension specifies the required number of features to be created by the genetic algorithm process. The default value for this parameter is 1.
2) -o dir. The string parameter dir determines the output directory for the produced train and test files by the algorithm. These file will have the same format as the input train and test files and the dimension will be the same as defined in parameter -d. This parameter has not default value and the user should determine it.
3) -p file. The string parameter file determines the train file that will be used by the proposed technique. This parameter has not default value and the user must specify it. The format of the file is specified in Figure 1.
The integer number D denotes the number of features (dimensionality) of the dataset and M determines stands for the number of points (patterns). In every subsequent line of the file should be the input pattern and the final column is the real output (category) for the correspond- ing pattern.
4) -t file. The string parameter file specifies the test file used by the algorithm. This parameter has not default value and the user should specifie it. The file should have the same format as in parameter -p.
5) -w num. The integer parameter num determines the num- ber of weights (computing units) of the Rbf network.
The default value for this parameter is 1.
C. A typical run
We create a file with the name of the above nodes with the name hostfile. The contents of hostfile will be:
node1
node2
For the LAM MPI case we initiate the MPI environment using the command
lamboot -v -d /home/user/hostfile
With user we denote the current user of the UNIX pc. Now we can run the example with the command
mpirun -np 3 /home/user/FeatureConstruction/bin/fc -p examples/wdbc.train
-t examples/wdbc.test -d 2 -w 5
The output of the above command is outlined in Figure 2. The program prints
1) The average number of generations required 2) The best discovered fitness value
3) The constructed program, which is the two artificial features created by the program. In our case from the 30 original features of WDBC problem the program created two artificial ones: f1(x) = 997.3−x22
1.868
, f2(x) = x23 4) The test error produced by RBF neural network using
1 to 20 processing nodes. Every run of RBF were conducted 30 times and different seed for the random generators was used each time and averages are reported.
V. CONCLUSIONS AND FUTURE RESEARCH
The software is written in ANSI C++ using the com- mon MPI library for parallelization. The proposed algorithm utilized an enhanced stopping rule and a new local search procedure. The proposed method was used to improve the efficiency of classification problems by constructing artificial features from the existing ones and the results from the conducted experiments were very promising. Furthermore, future versions of the software may include
• A graphical user interface for the software in some portable library such as Qt or Gtk.
• A technique to identify the optimal grammar for every dataset.
• Additional stopping rules for the termination of the genetic algorithm, such as stopping rules on the server side.
• Ability for the software to read datasets from various format available
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Fig. 1. Data file description.
D M
x11 x12 . . . x1D y1
x21 x22 . . . x2D y2
... ... ... ... ... xM 1 xM 2 . . . xM D yM
TABLE I
EXPERIMENTAL RESULTS FROM OTHER METHODS.
DATASET RBF MRMR PCA
WINE 30.73% 30.39% 38.69%
IONOSPHERE 12.93% 21.22% 17.16%
PARKINSONS 17.16% 17.96% 17.39%
TRANSFUSION 27.22% 26.21% 22.90%
REGIONS 21.11% 25.45% 28.14%
WDBC 12.91% 10.28% 17.64%
EEG 43.04% 56.45% 44.88%
HAYES ROTH 61.21% 61.13% 60.64%
GENE 37.12% 40.68% 51.44%
Fig. 2. Terminal output for the example run.
Average number of Generations 25.50 Minimum fitness value 11.44180 Constructed program:
f1(x)=(997.3/((-x22)/1.868)) f2(x)=x23
Rbf error
TRAIN[ 1]= 57.34 CLASS[ 1]= 31.34%
TRAIN[ 2]= 18.88 CLASS[ 2]= 10.66%
TRAIN[ 3]= 16.47 CLASS[ 3]= 10.06%
TRAIN[ 4]= 13.82 CLASS[ 4]= 7.547%
TRAIN[ 5]= 12.9 CLASS[ 5]= 7.371%
TRAIN[ 6]= 12.53 CLASS[ 6]= 7.418%
TRAIN[ 7]= 11.73 CLASS[ 7]= 7.488%
TRAIN[ 8]= 11.28 CLASS[ 8]= 7.617%
TRAIN[ 9]= 11.15 CLASS[ 9]= 7.582%
TRAIN[10]= 11.04 CLASS[10]= 7.43%
TRAIN[11]= 10.92 CLASS[11]= 7.324%
TRAIN[12]= 10.7 CLASS[12]= 7.183%
TRAIN[13]= 10.5 CLASS[13]= 7.101%
TRAIN[14]= 10.3 CLASS[14]= 7.101%
TRAIN[15]= 10.12 CLASS[15]= 7.16%
TRAIN[16]= 9.971 CLASS[16]= 7.277%
TRAIN[17]= 9.828 CLASS[17]= 7.218%
TRAIN[18]= 9.754 CLASS[18]= 7.289%
TRAIN[19]= 9.7 CLASS[19]= 7.289%
TRAIN[20]= 9.708 CLASS[20]= 7.171%
TABLE II
EXPERIMENTAL RESULTS FOR TWO PROCESSORS(TIME AND CLASSIFICATION ERROR).
DATASETTD1ED1TD2ED2TD4ED4TD8ED8 WINE37.107.35%40.696.24%42.024.69%50.264.41% IONOSPHERE71.709.12%37.439.46%70.3111.43%105.788.91% PARKINSONS59.1311.63%41.798.68%60.118.40%76.288.61% TRANSFUSION107.7023.32%168.2224.27%366.1423.45%323.9123.09% REGIONS204.2916.82%154.7116.34%176.2314.28%269.0214.56% WDBC111.785.08%173.664.84%169.914.62%195.124.82% EEG75.7836.49%116.7931.29%216.2031.50%331.9731.66% HAYESROTH43.3433.56%18.1333.97%42.9534.05%63.5536.03% GENE114.6650.38%394.2040.37%820.0231.63%735.6322.64%
TABLE III
EXPERIMENTAL RESULTS FOR FOUR PROCESSORS(TIME AND CLASSIFICATION ERROR).
DATASETTD1ED1TD2ED2TD4ED4TD8ED8 WINE17.9413.49%18.297.53%31.146.41%59.675.55% IONOSPHERE37.249.41%17.0012.11%81.1910.22%120.4510.85% PARKINSONS38.6416.26%45.2210.55%61.649.43%85.1610.63% TRANSFUSION139.4024.92%138.1622.17%200.9622.86%244.6623.31% REGIONS101.0417.92%85.9617.30%115.7416.46%136.9214.83% WDBC117.194.96%169.254.97%176.455.61%198.634.85% EEG80.3540.88%72.1936.14%166.9734.39%279.2936.12% HAYESROTH11.6235.21%13.4037.59%23.6036.82%32.9535.56% GENE149.3946.43%412.6241.86%579.2831.88%483.7026.17%
TABLE IV
EXPERIMENTAL RESULTS FOR EIGHT PROCESSORS(TIME AND CLASSIFICATION ERROR).
DATASETTD1ED1TD2ED2TD4ED4TD8ED8 WINE13.928.55%13.915.96%19.305.78%22.025.67% IONOSPHERE34.3110.79%24.7510.78%36.1710.63%47.1110.55% PARKINSONS24.7712.02%24.728.67%26.3310.72%33.789.30% TRANSFUSION84.7924.39%82.5423.01%81.0422.72%87.1723.19% REGIONS92.6917.43%85.7615.51%68.9415.07%86.8115.02% WDBC80.724.86%82.413.67%77.494.54%95.925.16% EEG79.3741.27%62.8135.39%58.5035.34%83.8036.86% HAYESROTH10.8730.10%13.5736.76%10.0933.03%13.3231.19% GENE134.7746.18%231.6938.79%309.8129.07%458.0923.49%
TABLE V
PARAMETERS FOR THE PROPOSED METHOD.
PARAMETER VALUE
ITERMAX 200
pc 0.1
pm 0.05
Li 50
Ls 20
Weights of RBF 10
