Research Article Feature Selection for Very Short …downloads.hindawi.com/journals/amete/2014/203545.pdfResearch Article Feature Selection for Very Short-Term Heavy Rainfall Prediction

Research ArticleFeature Selection for Very Short-Term Heavy Rainfall PredictionUsing Evolutionary Computation

Jae-Hyun Seo1 Yong Hee Lee2 and Yong-Hyuk Kim1

1 Department of Computer Science and Engineering Kwangwoon University 20 Kwangwoon-Ro Nowon-GuSeoul 139-701 Republic of Korea

2 Forecast Research Laboratory National Institute of Meteorological Research Korea Meteorological Administration45 Gisangcheong-gil Dongjak-gu Seoul 156-720 Republic of Korea

Correspondence should be addressed to Yong-Hyuk Kim yhdflykwackr

Received 16 August 2013 Revised 23 October 2013 Accepted 1 November 2013 Published 6 January 2014

Academic Editor Sven-Erik Gryning

Copyright copy 2014 Jae-Hyun Seo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We developed a method to predict heavy rainfall in South Korea with a lead time of one to six hours We modified the AWSdata for the recent four years to perform efficient prediction through normalizing them to numeric values between 0 and 1and undersampling them by adjusting the sampling sizes of no-heavy-rain to be equal to the size of heavy-rain Evolutionaryalgorithms were used to select important features Discriminant functions such as support vector machine (SVM) k-nearestneighbors algorithm (k-NN) and variant k-NN (k-VNN) were adopted in discriminant analysis We divided our modified AWSdata into three parts the training set ranging from 2007 to 2008 the validation set 2009 and the test set 2010 The validation setwas used to select an important subset from input features The main features selected were precipitation sensing and accumulatedprecipitation for 24 hours In comparative SVM tests using evolutionary algorithms the results showed that genetic algorithm wasconsiderably superior to differential evolutionThe equitable treatment score of SVMwith polynomial kernel was the highest amongour experiments on average k-VNN outperformed k-NN but it was dominated by SVM with polynomial kernel

1 Introduction

South Korea lies in the temperate zone In South Korea wehave clearly distinguished four seasons where spring and fallare short relatively to summer and winter It is geographicallylocated between the parallels 125∘0410158401015840E and 131∘5210158401015840E and themeridians 33∘0610158401015840N and 38∘ 2710158401015840N in the Northern Hemi-sphere on the east coast of the Eurasian Continent and alsoadjacent to the Western Pacific as shown in Figure 1 There-fore it has complex climate characteristics which show bothcontinental and oceanic features It has a wide interseasonaltemperature difference and much more precipitation thanthat of the Continent In addition it has obvious monsoonseason wind a rainy period from the East Asian Monsoonlocally called Changma [1] typhoons and frequently heavysnowfalls in winter The area belongs to a wet region becauseof more precipitation than that of the world average

The annual mean precipitation of South Korea as shownin Figure 2 is around 1500mm and 1300mm in the central

part Geoje-si of Gyeongsangnam-do has the largest amountof precipitation 20073mm and Baegryeong island ofIncheon has the lowest amount of precipitation 8256mm

When a stationary front lingers across the Korean Penin-sula for about a month in summer more than half of theannual precipitation falls during the Changma season Pre-cipitation for the winter is less than 10 of the total Changmais a part of the summer Asian monsoon system It brings fre-quent heavy rainfall and flash floods for 30 days on averageand serious natural disasters often occur

The heavy rainfall is one of the major severe weather phe-nomena in South KoreaThe weather phenomena can lead toserious damage and losses of both life and infrastructure andit is very important to forecast heavy rainfall However it isconsidered a difficult task because it takes place in very shorttime interval [2]

We need to predict this torrential downpour to preventthe losses of life and property [1 3] Heavy rainfall forecastingis very important to avoid or minimize natural disasters

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2014 Article ID 203545 15 pageshttpdxdoiorg1011552014203545

2 Advances in Meteorology

Figure 1 The location of South Korea in East Asia and the dispersion of automatic weather stations in South Korea

34

35

36

37

38

126 127 128 129125 130

Sokcho

Gangrung

Ulsan

Youngduk

Pohang

Cheju

HaenamGeojeYeosuGohung

KwangjuSunchen

GunsanDaejeon

Daeku

Seoul

SeosanChungju

Chelwon

Taebaek

Chunchen

Pusan

Ulrungdo

800

900

1000

1100

Und

er 7

00

1200

1300

1400

1500

1600

1700

1800

1900

Abov

e 200

0

(mm)

(a)

34

35

36

37

38

126 127 128 129125 130

(mm)

600

700

800

900

Und

er 5

00

Abov

e 100

0

Sokcho

Gangrung

Ulsan

Youngduk

Pohang

Cheju

HaenamGeojeYeosuGohung

KwangjuSunchen

GunsanDaejeon

Daeku

Seoul

SeosanChungju

Chelwon

Taebaek

Chunchen

Pusan

UlrungdoDokdo

(b)

Figure 2 Annual (a) and summer (b) mean precipitation in South Korea (mm) [4]

before the events occur We used real weather data collectedfrom 408 automatic weather stations [4] in South Korea forthe period from 2007 to 2010 We studied the prediction ofone hour to six hours of whether or not heavy rainfall willoccur in South Korea To the best knowledge of the authorsthis problem has not been handled by other researchers

There have been many studies on heavy rainfall usingvarious machine learning techniques In particular severalstudies focused on weather forecasting using an artificial

neural network (ANN) [5ndash11] In the studies of Ingsrisawanget al [11] and Hong [12] support vector machine was appliedto develop classification and prediction models for rainfallforecasts Our research is different from previous work onhow to process weather datasets

Kishtawal et al [13] studied the prediction of summerrainfall over India using genetic algorithm (GA) In theirstudy the genetic algorithm found the equations that bestdescribe the temporal variations of the seasonal rainfall over

Advances in Meteorology 3

India The geographical region of India has been dividedinto five homogeneous zones (excluding the North-WestHimalayan zone) They used the monthly mean rainfall dur-ing the months of June July and August The dataset consistof the training set ranging from 1871 to 1992 and the vali-dation set ranging from 1993 to 2003 The experiment of thefirst evolution process and the second evolution process wereconducted using the training set and the validation set inorder The performance of the algorithm for each case wasevaluated using the statistical criteria of standard error andfitness strength Chromosome was made up of five homo-geneous zones annual precipitation and four elementaryarithmetic operators The strongest individuals (equationswith best fitness) were then selected to exchange parts ofthe character strings between reproduction and crossoverwhile individuals less fitted to the data are discarded A smallpercentage of the equation stringsrsquomost basic elements singleoperators and variables are mutated at random The processwas repeated a large number of times (about 1000ndash10000) toimprove the fitness of the evolving population of equationsThe major advantage of using genetic algorithm versus othernonlinear forecasting techniques such as neural networksis that an explicit analytical expression for the dynamicevolution of the rainfall time series is obtained Howeverthey used quite simple or typical parameters of a geneticalgorithm If they conducted experiments by tuning variousparameters of their genetic algorithm they would report theexperimental results showing better performance

Liu et al [14] proposed a filter method for feature selec-tion Genetic algorithm was used to select major features intheir study and the features were used for data mining basedon machine learning They proposed an improved NaiveBayes classifier (INBC) technique and explored the use ofgenetic algorithms (GAs) for selection of a subset of input fea-tures in classification problemsThey then carried out a com-parison with several other techniquesThis sets a comparisonof the following algorithms namely (i) genetic algorithmwith average classification or general classification (GA-ACGA-C) (ii) C45 with pruning and (iii) INBC with relativefrequency or initial probability density (INBC-RF INBC-IPD) on the real meteorological data in Hong Kong Intheir experiments the daily observations of meteorologicaldata were collected from the Observatory Headquarters andKingrsquos Park for training and test purposes for the periodfrom 1984 to 1992 (Hong Kong Observatory) During thisperiod they were only interested in extracting data fromMayto October (for the rainy season) each year INBC achievedabout a 90 accuracy rate on the rainno-rain (Rain) clas-sification problems This method also attained reasonableperformance on rainfall prediction with three-level depth(Depth 3) and five-level depth (Depth 5) which was around65ndash70 They used a filter method for feature selection Ingeneral it is known that a wrapper method performs betterthan a filter method In this study we try to apply a wrappermethod to feature selection

Nandargi and Mulye [15] analyzed the period of 1961ndash2005 to understand the relationship between the rain andrainy days mean daily intensity and seasonal rainfall over theKoyna catchment in India on monthly as well as seasonal

scale They compared a linear relationship with a logarithmicrelationship in the case of seasonal rainfall versus mean dailyintensity

Routray et al [16] studied a performance-based compar-ison of simulations carried out using nudging (NUD) tech-nique and three-dimensional variation (3DVAR) data assim-ilation system of a heavy rainfall event that occurred during25ndash28 June 2005 along the west coast of India In the exper-iment after observations using the 3DVAR data assimilationtechnique the model was able to simulate better structureof the convective organization as well as prominent synop-tic features associated with the mid-tropospheric cyclones(MTC) than the NUD experiment and well correlated withthe observations

Kouadio et al [17] investigated relationships betweensimultaneous occurrences of distinctive atmospheric easterlywave (EW) signatures that cross the south equatorial Atlanticintense mesoscale convective systems (lifespan gt 2 hours)that propagate westward over the western south equatorialAtlantic and subsequent strong rainfall episodes (anomaly gt10mmsdotdayminus1) that occur in eastern Northeast Brazil (ENEB)They forecasted rainfall events through real-time monitoringand the simulation of this ocean-atmosphere relationship

Afandi et al [2] investigated heavy rainfall events thatoccurred over Sinai Peninsula and caused flash flood usingthe Weather Research and Forecasting (WRF) model Thetest results showed that the WRF model was able to capturethe heavy rainfall events over different regions of Sinai andpredict rainfall in significant consistency with real measure-ments

Wang and Huang [18] studied on finding the evidence ofself-organized criticality (SOC) for rain datasets in China byemploying the theory and method of SOC For that reasonthey analyzed the long-term rain records of five meteorologi-cal stations inHenan a central province of ChinaThey foundthat the long-term rain processes in central China exhibit thefeature of self-organized criticality

Hou et al [19] studied the impact of three-dimensionalvariation data assimilation (3DVAR) on the prediction of twoheavy rainfall events over southern China in June and JulyThey used two heavy rainfall events one affecting severalprovinces in southern China with heavy rain and severeflooding the other is characterized by nonuniformity andextremely high rainfall rates in localized areas Their resultssuggested that the assimilation of all radar surface andradiosonde data had a more positive impact on the forecastskill than the assimilation of either type of data only for thetwo rainfall events

As a similar approach to ours Lee et al [20] studiedfeature selection using a genetic algorithm for heavy-rainprediction in South Korea They used ECMWF (EuropeanCentre for Medium-Range Weather Forecasts) weather datacollected from 1989 to 2009They selected five features among254 weather elements to examine the performance of theirmodel The five features selected were height humidity tem-perature U-wind and V-wind In their study a heavy-raincriterion is issued only when precipitation during six hoursis higher than 70mm They used a wrapper-based feature

4 Advances in Meteorology

Table 1 Modified weather elements [4 21]

Index Contents (original) Contents (modified)mdash Station number mdashmdash Day mdashmdash Latitude mdashmdash Longitude mdashmdash Height mdash1 mdash Month (1ndash12)2 Mean wind direction for 10 minutes (01 deg) Mean wind direction for 10 minutes (01 deg)3 Mean wind velocity for 10 minutes (01ms) Mean wind velocity for 10 minutes (01ms)4 Mean temperature for 1 minute (01 C) Mean temperature for 1 minute (01 C)5 Mean humidity for 1 minute (01) Mean humidity for 1 minute (01)6 Mean atmospheric pressure for 1 minute (01 hPa) Mean atmospheric pressure for 1 minute (01 hPa)mdash Mean sea level pressure for 1 minute (01 hPa) mdash7 Accumulated precipitation for 1 hour (01mm) Accumulated precipitation for 1 hour (01mm)8 Precipitation sensing (0 or 1) Precipitation sensing (0 or 1)9 mdash Accumulated precipitation for 3 hours (01mm)10 mdash Accumulated precipitation for 6 hours (01mm)11 mdash Accumulated precipitation for 9 hours (01mm)12 Accumulated precipitation for 24 hours (01mm) Accumulated precipitation for 24 hours (01mm)

selection method using a simple genetic algorithm and SVMwith RBF kernel as the fitness function They did not explainerrors and incorrectness for their weather data In this paperwe use theweather data collected from408 automaticweatherstations during the recent four years from 2007 to 2010 Ourheavy-rain criterion is exactly that of Korea MeteorologicalAdministration in South Korea as shown in Section 3We validate our algorithms with various machine learningtechniques including SVM with different kernels We alsoexplain and fixed errors and incorrectness for our weatherdata in Section 2

The remainder of this paper is organized as follows InSection 2 we propose data processing and methodology forvery short-term heavy rainfall prediction Section 3 describesthe environments of our experiments and analyzes the resultsThe paper ends with conclusions in Section 4

2 Data and Methodology

21 Dataset The weather data which are collected from 408automatic weather stations during the recent four years from2007 to 2010 had a considerable number of missing dataerroneous data and unrelated features We analyzed the dataand corrected the errors We preprocessed the original datagiven by KMA in accordance with Table 1 Some weatherelements of the original data had incorrect value and wereplaced the value with a very small one (minus107) We createdseveral elements such as month (1ndash12) and accumulatedprecipitation for 3 6 and 9 hours (01mm) from the originaldata [21] We removed or interpolated each day data of theoriginal data when important weather elements of the daydata had very small value Also we removed or interpolatednew elements such as accumulated precipitation for 3 6 and

f1 f2 middot middot middotmiddot middot middot f12 times6hours f9984001 f998400

2 f99840071 f998400

72

Figure 3 Representation with 72 features (accumulated weatherfactors for six hours)

9 hours which had incorrect value We undersampled theweather data that were adjusted for the proportion of heavy-rain against no-heavy-rain to be one in the training set asshown in Section 23

The new data were generated in two forms whetheror not we applied normalization The training set rangingfrom 2007 to 2008 was generated by undersampling Thevalidation set the data for 2009 was used to select animportant subset from input featuresThe selected importantfeatures were used for experiments with the test set the datafor 2010 Representation of our GA and DE was composed of72 features accumulated for the recent six hours as shown inFigure 3The symbols119891

1minus12shown in Figure 3meanmodified

weather elements in order by index number shown in Table 1The symbol ldquomdashrdquo in Table 1 means (NA not applicable)

22 Normalization The range of each weather element wassignificantly different (see Table 2) and the test results mightrely on the values of a few weather elements For that reasonwe preprocessed the weather data using a normalizationmethod We calculated the upper bound and lower bound ofeach weather factor from the original training set The valueof each upper bound and lower bound was converted to 1 and0 respectively Equation (1) shows the process for the usednormalization In (1) 119889 means each weather element Thevalidation set and the test set were normalized in accordance

Advances in Meteorology 5

Table 2 The upper and lower bound ranges of weather data

Weather elements Upper bound Lower boundLatitude 3853 3250Longitude 13188 3250Height 1673 15Mean wind direction for 10 minutes(01 deg) 3600 0

Mean wind velocity for 10 minutes(01ms) 424 0

Mean temperature for 1 minute(01∘C) 499 minus399

Mean humidity for 1 minute (01) 1000 0Mean atmospheric pressure for 1minute (01 hPa) 10908 0

Mean sea level pressure for 1 minute(01 hPa) 11164 0

Precipitation sensing (01) 1 0Accumulated precipitation for 1hour (01mm) 1085 0

Accumulated precipitation for 24hours (01mm) 8040 0

Table 3 Heavy rainfall rate

Year Heavy-rain (hours) No-heavy-rain (hours) Ratio ()2007 1018 874982 000122008 971 877429 000112009 1932 871668 000222010 1466 872135 00017

with the ranges in the original training set Precipitation sens-ing in Table 2 means whether or not it rains

119889max = max 119889 119889min = min 119889

119889119894=

119889119894minus 119889min

119889max minus 119889min

(1)

23 Sampling Let 119897 be the frequency of heavy rainfall occur-rence in the training set We randomly choose 119897 among thecases of no-heavy-rain in the training set Table 3 shows theproportion of heavy-rain to no-heavy-rain every year Onaccount of the results of Table 3 we preprocessed our datausing this method called undersampling We adjusted theproportion of heavy rainfall against the other to be one asshown in Figure 4 and Pseudocode 1

Table 4 shows ETS for prediction after 3 hours and theeffect of undersampling [22] and normalization for 3 ran-domly chosen stations The tests without undersamplingshowed a low equitable threat score (ETS) and required toolong a computation time In tests without undersampling thecomputation time took 3 721 minutes in k-NN and 3 940minutes in k-VNN (see Appendix B) the ldquoreachedmax num-ber of iterationsrdquo error was raised in SVM with polynomialkernel (see Appendix C) and 119886 and 119887 of ETS were zeroIn tests with undersampling the computation time tookaround 329 seconds in k-NN 349 seconds in k-VNN and506 seconds in SVM with polynomial kernel The test results

Heavy-rainNo-heavy-rain

Training set of one stationTraining set of one station

Undersampling

Figure 4 Example of our undersampling process

with normalization showed about 10 times higher than thosewithout normalization

24 Genetic-Algorithm-Based Feature Selection Pseudocode 2shows the pseudocode of a typical genetic algorithm [23] Inthis figure if we define that 119899 is the count of solutions inthe population set we create 119899 new solutions in a randomway The evolution starts from the population of completelyrandom individuals and the fitness of the whole populationis determined Each generation consists of several operationssuch as selection crossover mutation and replacementSome individuals in the current population are replaced withnew individuals to form a new population Finally this gen-erational process is repeated until a termination conditionhas been reached In a typical GA the whole number ofindividuals in a population and the number of reproducedindividuals are fixed at 119899 and 119896 respectively The percentageof individuals to copy to the new generation is defined as theratio of the number of new individuals to the size of the parentpopulation 119896119899 which we called ldquogeneration gaprdquo [24] If thegap is close to 1119899 the GA is called a steady-state GA

We selected important features using the wrapper meth-ods that used the inductive algorithm to estimate the valueof a given subset The selected feature subset is the bestindividual among results of the experiment with the vali-dation set The experimental results in the test set with theselected features showed better performance than those usingall features

The steps of the GA used are described in Box 1 Allsteps will be iterated until the stop condition (the number ofgenerations) is satisfied Figure 5 shows the flow diagram ofour steady-state GA

25 Differential-Evolution-Based Feature Selection Khush-aba et al [25 26] proposed a differential-evolution-basedfeature selection (DEFS) technique which is shown schemat-ically in Figure 6The first step in the algorithm is to generatenew population vectors from the original population A newmutant vector is formedby first selecting two randomvectorsthen performing a weighted difference and adding the resultto a third random (base) vector The mutant vector is thencrossed with the original vector that occupies that position inthe originalmatrixThe result of this operation is called a trialvectorThe corresponding position in the newpopulationwillcontain either the trial vector (or its corrected version) orthe original target vector depending on which one of thoseachieved a higher fitness (classification accuracy) Due to the

6 Advances in Meteorology

Weather factors

Stopcondition

Populationcreation

Tournamentselection

Multipointcrossover

RandommutationReplacement

Clas

sifier

s

GA process

Selected features

This step requires a classifier process

Figure 5 Flow diagram of the proposed steady-state GA

Originalpopulation

Populationvector

Base

vec

tor

Computeweighteddifference

+

+

+

Mutantspopulation

Cros

sove

r tar

get w

ith m

utan

t

Sele

ct tr

ial o

r tar

get

Trial vector

Newpopulation

Mutant vector

Target vector

minus

Pxg

Pg

XN

Pminus1

g

XN

Pminus2

g

X4g

X3g

X2

g

X1

g

X0

g

F X

VN

Pminus1

g

VN

Pminus2

g

V4g

V3g

V2

g

V1

g

V0

g

Uog

Chec

k fo

r red

unda

ncy

in fe

atur

es an

dus

e rou

lette

whe

el to

corr

ect t

he su

bset

sif

redu

ndan

cy ex

ist

Pxg+1

XNPminus2g+1

XNPminus2g+1

middot middot middot

X4g+1

X3g+1

X2g+1

X1g+1

X0g+1

113

27214153

1924

425

2853021616

317

1829922

1710

2311 32 20 12 26 8

Figure 6 The DEFS algorithm [25 26]

fact that a real number optimizer is being used nothing willprevent two dimensions from settling at the same featurecoordinates In order to overcome such a problem theyproposed to employ feature distribution factors to replaceduplicated features A roulette wheel weighting scheme isutilized In this scheme a cost weighting is implemented inwhich the probabilities of individual features are calculatedfrom the distribution factors associated with each featureThe distribution factor of feature 119891

119894is given by the following

equation

FD119894= 1198861lowast (

PD119894

PD119894+ND

119894

)

+ 1198862lowast (1 minus

119875119863119894+ND

119894

isin +max (PD119894+ND

119894))

(2)

where 1198861 1198862are constants and isin is a small factor to avoid

division by zero PD119894is the positive distribution factor that

is computed from the subsets that achieved an accuracy thatis higher than the average accuracy of the whole subsetsND119894is the negative distribution factor that is computed from

the subsets that achieved an accuracy that is lower thanthe average accuracy of the whole subsets This is shownschematically in Figure 7 with the light gray region beingthe region of elements achieving less error than the averageerror values and the dark gray being the region with elementsachieving higher error rates than the average The rationalebehind (2) is to replace the replicated parts of the trial vectorsaccording to two factorsThePD

119894(PD119894+ND119894) factor indicates

the degree to which 119891119894contributes to forming good subsets

On the other hand the second term in (2) aims at favoringexploration where this term will be close to 1 if the overallusage of a specific feature is very low

Advances in Meteorology 7

Table 4 Effect of undersampling (sampled 3 stations prediction after 3 hours)

wo undersampling wundersampling119896-NN (min) 119896-VNN (min) SVM (min) 119896-NN (sec) 119896-VNN (sec) SVM (sec)

wo normalization 0000 (3323) 0000 (3760) NA (gt10000000) 0003 (301) 0014 (329) 0024 (285)wnormalization 0000 (3721) 0000 (3940) NA (gt10000000) 0032 (329) 0094 (349) 0267 (506)

119860 set of heavy-rain cases in training set 119861 set of no-heavy-rain cases in training set 119877 set of no-heavy-rain cases sampled from B that is 119877 sube 119861 119879 undersampled training set

119897 larr the number of heavy-rain cases that is |A|initialize 119877 to be emptywhile (l gt 0)

randomly choose one value from Bif the value is not in 119877 then

add the value to 119877119897 larr 119897 minus 1

end ifend whileTlarr the union of A and 119877Return T

Pseudocode 1 A pseudocode of our undersampling process

Create an initial population of size 119899repeat

for 119894 = 1 to 119896choose 119901

1

and 1199012

from the populationoffspring

119894

= crossover(1199011

1199012

)offspring

119894

= mutation(offspring119894

)end forreplace(population [offspring

1

offspring2

offspring119896

])until (stopping condition)return the best solution

Pseudocode 2 The pseudocode of a genetic algorithm

3 Experimental Results

We preprocessed the original weather data Several weatherelements are added or removed as shown in Table 1 Weundersampled and normalized the modified weather dataEach hourly record of the data consists of twelve weatherelements and representation was made up of the latest sixhourly records 72 features as shown in Figure 3We extracteda feature subset using the validation set and used the featuresubset to do experiments with the test set

The observation area has 408 automatic weather stationsin the southern part of the Korean peninsula The predictiontime is from one hour to six hours We adopted GA and DEamong the evolutionary algorithms SVM k-VNN and k-NNare used as discriminant functions Table 5 shows the parame-ters of a steady-state GA andDE respectively LibSVM [27] is

adopted as a library of SVM and we set SVM type one of theSVM parameters as C SVC that regularizes support vectorclassification and the kernel functions used are polynomiallinear and precomputed We set 119896 to be 3 in our experiments

In South Korea a heavy-rain advisory is issued whenprecipitation during six hours is higher than 70mm or pre-cipitation during 12 hours is higher than 110mm A heavy-rain warning is issued when precipitation during 6 hours ishigher than 110mm or precipitation during 12 hours is higherthan 180mm We preprocessed the weather data using thiscriterion To select the main features we adopted a wrappermethod which uses classifier itself in feature evaluationdifferently from a filter method

An automatic weather station (AWS) [28] is an auto-mated version of the traditional weather station either tosave human labor or to enable measurements from remote

8 Advances in Meteorology

(1) Population Initialization generatem random solutions(2) Selection a number Tour of individuals is chosen randomly from the population and the best individualfrom this group is selected as parent(3) Crossover create an offspring by the genetic recombination of Parent1 and Parent2(4) Mutation change each gene of the offspring at the rate of 5 percent(5) Replacement if the offspring is superior to the worst individual of population replace the worst one withthe offspring

Box 1 Steps of the used GA

1 1 0 1 0 1 01 0 0 0 0 0 01 0 1 1 1 1 11 0 1 0 1 1 00 0 0 1 1 1 00 1 0 0 0 0 11 1 1 0 0 1 10 0 0 0 0 1 10 1 1 0 1 1 01 0 1 0 0 1 1

3214

1017169

1413

4 1 2 2 2 3 1PD =

Positive distribution (PD)

2 3 3 1 2 5 4ND =

Negative distribution (ND)

Fit (error) Population

0 0 0 1 1 1 00 1 0 0 0 0 11 1 1 0 0 1 10 0 0 0 0 1 10 1 1 0 1 1 01 0 1 0 0 1 1

1017169

1413

1 1 0 1 0 1 01 0 0 0 0 0 01 0 1 1 1 1 11 0 1 0 1 1 0

3214

( ) p

Figure 7 The feature distribution factors [25 26]

areas An automatic weather station will typically consistof a weather-proof enclosure containing the data loggerrechargeable battery telemetry (optional) and the meteoro-logical sensors with an attached solar panel or wind turbineand mounted upon a mast The specific configuration mayvary due to the purpose of the system In Table 6 Fc and Obsare abbreviations for forecast and observed respectively Thefollowing is a measure for evaluating precipitation forecastskill

ETS (equitable threat score)

=(119886 minus 119886

119903)

(119886 + 119887 + 119888 minus 119886119903) 119886119903=(119886 + 119887) (119886 + 119888)

119899

FBI (frequency bias index) = (119886 + 119887) (119886 + 119888)

PC (proportion correct) = (119886 + 119889)119899

POD (probability of detection) = 119886

(119886 + 119888)

PAG (post-agreement) = 119886

(119886 + 119887)

(3)

These experiments were conducted using LibSVM [27]on an Intel Core2 duo quad core 30GHz PC Each run ofGA took about 201 seconds in SVM test with normalizationand about 202 seconds without normalization it took about126 seconds in k-NN test with normalization and about 171seconds without normalization it took about 135 secondsin k-VNN test with normalization and about 185 secondswithout normalization

Each run of DE took about 6 seconds in SVM test withnormalization and about 5 seconds without normalization

Table 5 Parameters in GADE

GA parameters

Fitness function119896-NN (119896 = 3) 119896-VNN (119896 = 3) SVM (type

C SVC kernel function polynomial linear andprecomputed) [27]

Encoding Binary (72 dimensions)No of populations 20No of generations 100Selection Tournament selectionCrossover Multipoint crossover (3 points)Mutation Genewise mutation (119875 = 0005)

ReplacementIf an offspring is superior to the worst

individual in the population we replace it withthe worst one

DE parameters

Fitness function 119896-NN (119896 = 3) 119896-VNN (119896 = 3) SVM (typeC SVC kernel function polynomial)

Encoding Real number (23 dimensions)No of populations 20No of generations 100Crossover rate 003FVal 005

Replacement If an offspring is superior to the parent in thepopulation we replace it with the parent

it took about 5 seconds in k-NN test with normalizationand about 4 seconds without normalization it took about5 seconds in k-VNN test with normalization and about 4seconds without normalization

The heavy-rain events which meet the criterion of heavyrainfall consist of a consecutive time interval which hasa beginning time and an end time The coming event is todiscern whether or not it is a heavy rain on the beginningtime For each hour from the beginning time to the end timediscerning whether or not it is a heavy rain means the wholeprocess We defined CE and WP to be forecasting the comingevent and the whole process of heavy rainfall respectively

Table 7 shows the experimental results for GA and DEOverall GA was about 142 and 149 times better than DEin CE and WP predictions respectively In DE experimentsSVM and k-VNN were about 211 and 110 times better thank-NN in CE prediction respectively SVM and k-VNN wereabout 248 and 108 times better than k-NN inWP prediction

Advances in Meteorology 9

Table 6 Contingency table

ForecastEvent

Event observedYes No Marginal total

Yes Hit (119886) False alarm (119887) Fc Yes (119886 + 119887)No Miss (119888) Correct nonevent (119889) Fc No (119888 + 119889)Marginal total Obs Yes (119886 + 119888) Obs No (119887 + 119889) Sum total (119886 + 119887 + 119888 + 119889 = 119899)

Table 7 Experimental results (1ndash6 hours) by ETS

Prediction typePrediction hour

1 2 3 4 5 6CE WP CE WP CE WP CE WP CE WP CE WP

DE119896-NN 0096 0183 0062 0127 0043 0093 0026 0059 0020 0049 0014 0035119896-VNN 0098 0187 0073 0147 0049 0104 0030 0069 0021 0048 0015 0037SVM (polynomial) 0192 0383 0139 0320 0140 0329 0090 0238 0027 0105 0005 0019

GA119896-NN 0070 0265 0068 0212 0056 0160 0035 0105 0025 0078 0009 0044119896-VNN 0179 0314 0152 0279 0113 0230 0084 0184 0047 0117 0029 0078SVM

Polynomial 0276 0516 0239 0481 0160 0373 0102 0271 0040 0148 0008 0046Linear 0043 0095 0096 0196 0127 0200 0083 0150 0152 0240 0102 0173Precomputed 0048 0102 0055 0126 0040 0086 0079 0157 0048 0090 0040 0074

CE forecasting the coming event of heavy rainfall WP forecasting the whole process of heavy rainfall

respectively In GA experiments SVM with polynomialkernel showed better performance than that with linear orprecomputed kernel on average SVMwith polynomial kerneland k-VNN were about 262 and 239 times better than k-NN in CE prediction respectively SVM with polynomialkernel and k-VNN were about 201 and 149 times betterthan k-NN in WP prediction respectively As the predictiontime is longer ETS shows a steady downward curve SVMwith polynomial kernel shows the best ETS among GA testresults Figure 8 visually compares CE and WP results in GAexperiments

Consequently SVM showed the highest performanceamong our experiments k-VNN showed that the degree ofgenesrsquo correlation had significantly effects on the test resultsin comparisonwith k-NN Tables 8 9 10 and 11 showdetailedSVM (with polynomial kernel) test results for GA and DE

We selected the important features using the wrappermethods using the inductive algorithm to estimate the valueof a given set All features consist of accumulated weatherfactors for six hours as shown in Figure 3The selected featuresubset is the best individual among the experimental resultsusing the validation set Figure 9 shows the frequency for theselected features after one hour to six hours The test resultsusing the selected features were higher than those using allfeatures We define a feature as 119891 The derived features fromthe statistical analysis which has a 95 percent confidenceinterval were the numbers 119891

3 1198917 1198918 11989110 11989112 11989119 11989120 11989121

11989122 11989123 11989124 11989131 11989132 11989136 11989143 11989144 11989146 11989148 11989155 11989156 and

11989168 The main seven features selected were the numbers 119891

8

11989112 11989120 11989124 11989132 11989144 and 119891

56and were evenly used by each

prediction hourThese features were precipitation sensing andaccumulated precipitation for 24 hours

We compared the heavy rainfall prediction test resultsof GA and DE as shown in Table 7 The results showedthat GA was significantly better than DE Figure 10 showsprecipitation maps for GA SVM test results with normaliza-tion and undersampling from one to six hours The higherETS is depicted in the map in the darker blue color Thenumbers of automatic weather stations by prediction hoursare 105 205 231 245 223 and 182 in order from one to sixhours respectively The reasons for the differential numbersof automatic weather stations by prediction hours are asfollows First we undersampled the weather data by adjustingthe sampling sizes of no-heavy-rain to be equal to the sizeof heavy-rain in the training set as shown in Section 23Second we excluded the AWS number in which the recordnumber of the training set is lower than three Third weexcluded the AWS in which hit and false alarm are 0 fromthe validation experimental results Finally we excluded theAWS in which hit false alarm and miss are 0 from the testexperimental results

The weather data collected from automatic weather sta-tions during the recent four years had a lot of missing dataand erroneous data Furthermore our test required morethan three valid records in the training set For that reasonthe number of usable automatic weather stations was the

10 Advances in Meteorology

0

01

02

03

04

05

06

1 2 3 4 5 6

k-NNk-VNNSVM

ETS

(hour)

(a) Comparison among classifiers (ETS for CE)

0

01

02

03

04

05

06

1 2 3 4 5 6

k-NNk-VNNSVM

ETS

(hour)

(b) Comparison among classifiers (ETS for WP)

Figure 8 Experimental results for GA from 1 to 6 hours

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(a) Prediction after 1 hour

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(b) Prediction after 2 hours

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(c) Prediction after 3 hours

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(d) Prediction after 4 hours

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(e) Prediction after 5 hours

050

100150200250300350

1 11 21 31 41 51 61 71

Freq

uenc

y

Feature number

(f) Prediction after 6 hours

Figure 9 Frequency for selected features after from 1 to 6 hours

Advances in Meteorology 11

Table 8 Results of DE with SVM from 1 to 6 hours (CE)

Hour ETS FBI PC POD PAG Hit False alarm Miss Correct nonevent No of AWSs1 0192 4116 0994 0627 0340 11619 41305 7067 8160305 1052 0139 5108 0994 0531 0332 8737 45332 7902 8139571 2053 0140 5615 0994 0512 0301 8238 41710 8338 8102411 2314 0090 9517 0990 0486 0264 7878 69261 9008 8048094 2455 0027 30133 0977 0419 0116 5707 183378 8053 7942960 2236 0005 79798 0901 0589 0041 5484 817126 3874 7315505 182

Table 9 Results of DE with SVM from 1 to 6 hours (WP)

Hour ETS FBI PC POD PAG Hit False alarm Miss Correct nonevent No of AWSs1 0383 2558 0994 0813 0535 30295 41305 7067 8160305 1052 0320 3055 0994 0766 0538 25356 45332 7902 8139571 2053 0329 3308 0994 0756 0512 24814 41710 8338 8102411 2314 0238 5252 0990 0744 0475 24820 69261 9008 8048094 2455 0105 13148 0977 0741 0312 23156 183378 8053 7942960 2236 0019 31885 0901 0846 0144 23341 817126 3874 7315505 182

Table 10 Results of GA with SVM from 1 to 6 hours (CE)

Hour ETS FBI PC POD PAG Hit False alarm Miss Correct nonevent No of AWSs1 0276 2168 0997 0589 0403 10581 19524 8105 8182086 1052 0239 2398 0997 0529 0383 8771 19824 7868 8165078 2053 0160 3613 0995 0463 0316 8000 32918 8576 8111203 2314 0102 6421 0992 0417 0291 7747 57514 9139 8059841 2455 0040 20543 0984 0397 0117 5695 122857 8126 8007287 2236 0008 66609 0944 0420 0025 4192 437291 5984 7546929 182

Table 11 Results of GA with SVM from 1 to 6 hours (WP)

Hour ETS FBI PC POD PAG Hit False alarm Miss Correct nonevent No of AWSs1 0516 1577 0997 0797 0622 29686 19524 8105 8182086 1052 0481 1671 0997 0766 0610 25805 19824 7868 8165078 2053 0373 2274 0995 0735 0561 24970 32918 8576 8111203 2314 0271 3685 0992 0713 0540 25069 57514 9139 8059841 2455 0148 10285 0984 0733 0341 23363 122857 8126 8007287 2236 0046 27701 0944 0786 0165 23154 437291 5984 7546929 182

lowest in the prediction after one hour and increased as theprediction time became longer

4 Conclusion

In this paper we realized the difficulty necessity and signifi-cance of very short-term heavy rainfall forecasting We usedvarious machine learning techniques such as SVM k-NNand k-VNN based on GA and DE to forecast heavy rainfallafter from one hour to six hours The results of GA weresignificantly better than those of DE SVM with polynomialkernel among various classifiers in our GA experimentsshowed the best results on average A validation set was used

to select the important features and the selected featureswere used to predict very short-term heavy rainfall Wederived 20 features from the statistical analysis which hasa 95 percent confidence interval The main features selectedwere precipitation sensing and accumulated precipitation for24 hours

In future work we will preprocess the weather databy various methods such as representation learning cyclicloess contrast and quantile normalization algorithms Alsowe will apply other machine learning techniques such asstatistical relational learning multilinear subspace learningand association rule learning As more appropriate param-eters are applied to the evolutionary algorithm or machine

12 Advances in Meteorology

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(a) Prediction after 1 hour (105)

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(b) Prediction after 2 hours (205)

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(c) Prediction after 3 hours (231)

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(d) Prediction after 4 hours (245)

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(e) Prediction after 5 hours (223)

ETS40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10090807060504030201

(f) Prediction after 6 hours (182)

Figure 10 Individual maps with AWS in blue dots for GA heavy rainfall prediction after from 1 to 6 hours (ETS)

learning techniques we expect to get better results We havevalidated our algorithms with AWS data however it wouldbe interesting to examine the performance with for examplesatellite data as another future work

Appendices

A Spatial and Temporal Distribution ofHeavy Rainfall over South Korea

We calculated the rainfall duration whichmeets the criterionof heavy rainfall from each automatic weather station for theperiod from 2007 to 2010 We divided the rainfall durationby 100 and let the result be depicted in the map Figure 11shows the distribution of heavy rainfall for the whole seasonsFigure 12 shows the distribution of heavy rainfall by seasonsMost heavy rainfalls have been concentrated in summer andthey have a wide precipitation range regionally Also theirfrequencies are quite different from region to region

B k-Nearest Neighbors Classifier

In pattern recognition the k-nearest neighbors algorithm (k-NN) [29] is a method for classifying objects based on the

closest training examples in the feature space k-NN is atype of instance-based learning or lazy learning where thefunction is only approximated locally and all computation isdeferred until classification The k-NN algorithm is amongstthe simplest of all machine learning algorithms an object isclassified by a majority vote of its neighbors with the objectbeing assigned to the class most common amongst its k-nearest neighbors (119896 is a positive integer typically small)Thek-NN classifier is commonly based on the Euclidean distancebetween a testing sample and the specified training samples

Golub et al [30] developed a procedure that uses a fixedsubset of informative genes and makes a prediction basedon the expression level of these genes in a new sample Eachinformative gene casts a weighted vote for one of the classeswith themagnitude of each vote dependent on the expressionlevel in the new sample and the degree of that genersquoscorrelation with the class distinction in their class predictorWe made a variant k-nearest neighbors algorithm (k-VNN)that the degree (1205881015840) of genesrsquo correlation was applied to amajority vote of its neighbors Box 2 shows the equationcalculating correlation between feature and class In Box 2119892 means a feature (ie a weather element) and 119862 means aclass (ie heavy-rain or no-heavy-rain) The test results of k-VNN were better than those of k-NN We set 119896 to be 3 in our

Advances in Meteorology 13

1205831

(119892)larr average of 119892 for the samples in 11205830

(119892)larr average of 119892 for the samples in 01205901

(119892)larr standard deviation of 119892 for the samples in 11205900

(119892)larr standard deviation of 119892 for the samples in 01205881015840

(119892 119862) larr (1205831

(119892) minus 1205830

(119892))(1205901

(119892) + 1205900

(119892))

Box 2 Correlation 1205881015840 between feature 119892 and class 119862 (0 or 1) [30 31]

CNT100

40∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10

09

08

07

06

05

04

03

02

01

Figure 11 The distribution of heavy rainfall for the whole seasons(2007ndash2010)

experiments because it is expected that the classifier will showlow performance if 119896 is just 1 and it will take a long computingtime when 119896 is 5 or more

C Support Vector Machine

Support vector machines (SVM) [32] are a set of relatedsupervised learning methods that analyze data and recognizepatterns and are used for classification and regression analy-sis The standard SVM takes a set of input data and predictsfor each given input which of two possible classes the input isamember of whichmakes the SVManonprobabilistic binarylinear classifier Since an SVM is a classifier it is then givena set of training examples each marked as belonging to oneof two categories and an SVM training algorithm builds amodel that assigns new examples into one category or theother Intuitively an SVM model is a representation of theexamples as points in space mapped so that the examples ofthe separate categories are divided by a clear gap that is aswide as possible New examples are then mapped into thatsame space and predicted to belong to a category based onwhich side of the gap they fall on

D Evolutionary Computation

A genetic algorithm (GA) is a search heuristic that mimicsthe process of natural evolution and this heuristic is routinelyused to generate useful solutions to optimization and searchproblems [33] In the process of a typical genetic algorithmthe evolution starts from the population of completely ran-dom individuals and the fitness of the whole population isdetermined Each generation consists of several operationssuch as selection crossover mutation and replacementSome individuals in the current population are replaced withnew individuals to form a new population Finally this gener-ational process is repeated until a termination condition hasbeen reached

Differential evolution (DE) is an evolutionary (direct-search) algorithm which has been mainly used to solve opti-mization problems DE shares similarities with traditionalevolutionary algorithms However it does not use binaryencoding as a simple genetic algorithm and it does not usea probability density function to self-adapt its parameters asan evolution strategy Instead DE performs mutation basedon the distribution of the solutions in the current populationIn this way search directions and possible step sizes dependon the location of the individuals selected to calculate themutation values [34]

E Differences between Adopted Methods

In applied mathematics and theoretical computer sciencecombinatorial optimization is a topic that consists of findingan optimal object from a finite set of objects In many suchproblems exhaustive search is not feasible It operates on thedomain of those optimization problems in which the set offeasible solutions is discrete or can be reduced to discrete andin which the goal is to find the best solution [33]

Feature selection is a problem to get a subset amongall features and it is a kind of combinatorial optimizationGenetic algorithms (GAs) and differential evolutions (DEs)use a random element within an algorithm for optimizationor combinatorial optimization and they are typically usedto solve the problems of combinatorial optimization such asfeature selection as in this paper

Machine learning techniques include a number of sta-tistical methods for handling classification and regressionMachine learning mainly focuses on prediction based onknown properties learned from the training data [33] It isnot easy to use general machine learning techniques forfeature selection In this paper machine learning techniques

14 Advances in Meteorology

CNT10040∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10

09

08

07

06

05

04

03

02

01

(a) Spring

CNT10040∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10

09

08

07

06

05

04

03

02

01

(b) Summer

CNT10040∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10

09

08

07

06

05

04

03

02

01

(c) Fall

CNT10040∘N

38∘N

36∘N

34∘N

32∘N124∘E 126∘E 128∘E 130∘E

10

09

08

07

06

05

04

03

02

01

(d) Winter

Figure 12 The distribution of heavy rainfall by seasons (2007ndash2010)

were used for classification GA and DE could be used forregression but they have a weakness in handling regressionbecause these algorithms will take longer computing timethan other regression algorithms

F Detailed Statistics of Experimental Results

Tables 8ndash11 show SVM (with polynomial kernel) test resultsfor GA and DE As shown in the contingency Table 6 the testresults show ETS and other scores We defined CE and WPto be forecasting the coming event and the whole process ofheavy rainfall respectively The test results include the num-ber of used automatic weather stations by each predictionhour and the number of those is equally set in the sameprediction hour of each experiment As a result GA wasconsiderably superior to DE

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

A preliminary version of this paper appeared in the Pro-ceedings of the International Conference on Convergenceand Hybrid Information Technology pp 312ndash322 2012 Theauthors would like to thank Mr Seung-Hyun Moon for hisvaluable suggestions in improving this paper The presentresearch has been conducted by the Research Grant ofKwangwoon University in 2014 This work was supported bythe Advanced Research on Meteorological Sciences throughthe National Institute ofMeteorological Research of Korea in2013 (NIMR-2012-B-1)

Advances in Meteorology 15

References

[1] J Bushey ldquoThe Changmardquo httpwwwtheweatherpredictioncomweatherpapers007

[2] G E Afandi M Mostafa and F E Hussieny ldquoHeavy rainfallsimulation over sinai peninsula using the weather researchand forecasting modelrdquo International Journal of AtmosphericSciences vol 2013 Article ID 241050 11 pages 2013

[3] J H Seo andYHKim ldquoA survey on rainfall forecast algorithmsbased onmachine learning techniquerdquo inProceedings of theKIISFall Conference vol 21 no 2 pp 218ndash221 2011 (Korean)

[4] Korea Meteorological Administration httpwwwkmagokr[5] M N French W F Krajewski and R R Cuykendall ldquoRainfall

forecasting in space and time using a neural networkrdquo Journal ofHydrology vol 137 no 1ndash4 pp 1ndash31 1992

[6] E Toth A Brath and A Montanari ldquoComparison of short-term rainfall predictionmodels for real-time flood forecastingrdquoJournal of Hydrology vol 239 no 1ndash4 pp 132ndash147 2000

[7] S J Burian S R Durrans S J Nix and R E Pitt ldquoTraining arti-ficial neural networks to perform rainfall disaggregationrdquo Jour-nal of Hydrologic Engineering vol 6 no 1 pp 43ndash51 2001

[8] M C Valverde Ramırez H F de Campos Velho and N JFerreira ldquoArtificial neural network technique for rainfall fore-casting applied to the Sao Paulo regionrdquo Journal of Hydrologyvol 301 no 1ndash4 pp 146ndash162 2005

[9] N Q Hung M S Babel S Weesakul and N K Tripathi ldquoAnartificial neural network model for rainfall forecasting inBangkok Thailandrdquo Hydrology and Earth System Sciences vol13 no 8 pp 1413ndash1425 2009

[10] V M Krasnopolsky and Y Lin ldquoA neural network nonlinearmultimodel ensemble to improve precipitation forecasts overcontinental USrdquo Advances in Meteorology vol 2012 Article ID649450 11 pages 2012

[11] L Ingsrisawang S Ingsriswang S Somchit P Aungsuratanaand W Khantiyanan ldquoMachine learning techniques for short-term rain forecasting system in the northeastern part of Thai-landrdquo in Proceedings of the World Academy of Science Engineer-ing and Technology vol 31 pp 248ndash253 2008

[12] W-C Hong ldquoRainfall forecasting by technological machinelearning modelsrdquo Applied Mathematics and Computation vol200 no 1 pp 41ndash57 2008

[13] C M Kishtawal S Basu F Patadia and P K Thapliyal ldquoFore-casting summer rainfall over India using genetic algorithmrdquoGeophysical Research Letters vol 30 no 23 pp 1ndash9 2003

[14] J N K Liu B N L Li and T S Dillon ldquoAn improved NaıveBayesian classifier technique coupled with a novel input solu-tion methodrdquo IEEE Transactions on Systems Man and Cyber-netics C vol 31 no 2 pp 249ndash256 2001

[15] S Nandargi and S S Mulye ldquoRelationships between rainy daysmean daily intensity and seasonal rainfall over the koyna catch-ment during 1961ndash2005rdquoThe Scientific World Journal vol 2012Article ID 894313 10 pages 2012

[16] A Routray K K Osuri and M A Kulkarni ldquoA comparativestudy on performance of analysis nudging and 3DVAR in sim-ulation of a heavy rainfall event using WRF modeling systemrdquoISRN Meteorology vol 2012 no 21 Article ID 523942 2012

[17] Y K Kouadio J Servain L A TMachado andC A D LentinildquoHeavy rainfall episodes in the eastern northeast Brazil linkedto large-scale ocean-atmosphere conditions in the tropicalAtlanticrdquo Advances in Meteorology vol 2012 Article ID 36956716 pages 2012

[18] Z Wang and C Huang ldquoSelf-organized criticality of rainfall incentral Chinardquo Advances in Meteorology vol 2012 Article ID203682 8 pages 2012

[19] T Hou F Kong X Chen and H Lei ldquoImpact of 3DVAR dataassimilation on the prediction of heavy rainfall over southernChinardquo Advances in Meteorology vol 2013 Article ID 12964217 pages 2013

[20] H D Lee S W Lee J K Kim and J H Lee ldquoFeature selectionfor heavy rain prediction using genetic algorithmsrdquo in Proceed-ings of the Joint 6th International Conference on Soft Computingand Intelligent Systems and 13th International Symposium onAdvanced Intelligent Systems (SCIS-ISIS rsquo12) pp 830ndash833 2012

[21] J H Seo and Y H Kim ldquoGenetic feature selection for veryshort-termheavy rainfall predictionrdquo inProceedings of the Inter-national Conference on Convergence and Hybrid InformationTechnology vol 7425 of Lecture Notes in Computer Science pp312ndash322 2012

[22] N V Chawla ldquoData mining for imbalanced datasets an over-viewrdquo Data Mining and Knowledge Discovery Handbook vol 5pp 853ndash867 2006

[23] Y-S Choi and B-R Moon ldquoFeature selection in genetic fuzzydiscretization for the pattern classification problemsrdquo IEICETransactions on Information and Systems vol 90 no 7 pp 1047ndash1054 2007

[24] K A de Jong An analysis of the behavior of a class of geneticadaptive systems [PhD thesis] University of Michigan AnnArbor Mich USA 1975

[25] RNKhushaba AAl-Ani andAAl-Jumaily ldquoDifferential evo-lution based feature subset selectionrdquo in Proceedings of the 19thInternational Conference on Pattern Recognition (ICPR rsquo08) pp1ndash4 December 2008

[26] R N Khushaba A Al-Ani and A Al-Jumaily ldquoFeature subsetselection using differential evolution and a statistical repairmechanismrdquo Expert Systems with Applications vol 38 no 9 pp11515ndash11526 2011

[27] C-C Chang and C-J Lin ldquoLIBSVM a library for supportvector machinesrdquo ACM Transactions on Intelligent Systems andTechnology vol 2 no 3 article 27 2011

[28] AutomaticWeather Stations httpwwwautomaticweathersta-tioncom

[29] R Chang Z Pei and C Zhang ldquoA modified editing k-nearestneighbor rulerdquo Journal of Computers vol 6 no 7 pp 1493ndash15002011

[30] T R Golub D K Slonim P Tamayo et al ldquoMolecularclassification of cancer class discovery and class prediction bygene expressionmonitoringrdquo Science vol 286 no 5439 pp 531ndash527 1999

[31] Y H Kim S Y Lee and B R Moon ldquoA genetic approach forgene selection on microarray expression datardquo in Genetic andEvolutionary ComputationmdashGECCO 2004 K Deb Ed vol3102 of Lecture Notes in Computer Science pp 346ndash355 2004

[32] Y YinDHan andZCai ldquoExplore data classification algorithmbased on SVM and PSO for education decisionrdquo Journal ofConvergence Information Technology vol 6 no 10 pp 122ndash1282011

[33] Wikipedia httpenwikipediaorg[34] EMezura-Montes J Velazquez-Reyes andC A Coello Coello

ldquoA comparative study of differential evolution variants for globaloptimizationrdquo in Proceedings of the 8th Annual Genetic andEvolutionary Computation Conference pp 485ndash492 July 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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