Knowledge Discovery in a Direct Marketing Case using Least Squares Support Vector Machines

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1 Knowledge Dscovery n a Drect Marketng Case usng Least Squares Support Vector Machnes S. Vaene, 1, * B. Baesens, 1 T. Van Gestel, 2 J. A. K. Suykens, 2 D. Van den Poel, 3 J. Vanthenen, 1 B. De Moor, 2 G. Dedene 1 1 K.U. Leuven, Department of Appled Economc Scences, Naamsestraat 69, B-3000 Leuven, Belgum 2 K.U. Leuven, Department of Electrcal Engneerng ESAT-SISTA, Kasteelpark Arenberg 10, B-3001 Leuven, Belgum 3 Ghent Unversty, Department of Marketng, Hovenersberg 24, B-9000 Ghent, Belgum We study the problem of repeat-purchase modelng n a drect marketng settng usng Belgan data. More specfcally, we nvestgate the detecton and qualfcaton of the most relevant explanatory varables for predctng purchase ncdence. The analyss s based on a wrapped form of nput selecton usng a senstvty based prunng heurstc to gude a greedy, stepwse, and backward traversal of the nput space. For ths purpose, we make use of a powerful and promsng least squares support vector machne Ž LS-SVM. classfer formulaton. Ths study extends beyond the standard recency frequency monetary Ž RFM. modelng semantcs n two ways: Ž 1. by ncludng alternatve operatonalzatons of the RFM varables, and Ž. 2 by addng several other Ž non-rfm. predctors. Results ndcate that elmnaton of redundant rrelevant nputs allows sgnfcant reducton of model complexty. The emprcal fndngs also hghlght the mportance of frequency and monetary varables, whle the recency varable category seems to be of somewhat lesser mportance to the case at hand. Results also pont to the added value of ncludng non-rfm varables for mprovng customer proflng. More specfcally, customer company nteracton, measured usng ndcators of nformaton requests and complants, and merchandse returns provde addtonal predctve power to purchase ncdence modelng for database marketng John Wley & Sons, Inc. * Author to whom correspondence should be addressed; e-mal: Stjn.Vaene@ econ.kuleuven.ac.be. Contract grant sponsor: Flemsh government ŽResearch Councl K.U. Leuven: GOA-Mefsto; FWO-Flanders: ICCoS and AN-MMM; IWT: STWW Eureka.. Contract grant sponsor: Belgum government. Contract grant number: IUAP-IV 02, IV-24. Contract grant sponsor: European Commsson. Contract grant number: TMR, ERNSI. Ž. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 16, John Wley & Sons, Inc.

2 1024 VIAENE ET AL. I. INTRODUCTION The man objectve of ths paper nvolves the detecton and qualfcaton of the most relevant varables for repeat-purchase modelng n a drect marketng settng. Ths knowledge s beleved to vastly enrch customer proflng and thus contrbute drectly to more targeted customer contact. The emprcal study focuses on the purchase ncdence,.e., the ssue whether or not a purchase s made from any product category offered by the drect malng company. Standard recency frequency monetary modelng seman- 1 tcs underle the dscussed purchase ncdence model. Ths bnary Žbuyer versus nonbuyer. classfcaton problem s beng tackled n ths paper by usng least squares support vector machne Ž LS-SVM. classfers. LS-SVMs have recently been ntroduced n the lterature 2 and excellent benchmark results have been reported. 3 Havng constructed an LS-SVM classfer wth all avalable predctors, we engage n an nput selecton experment. Input selecton has been an actve area of research n the datamnng feld for many years now. A compact, yet hghly accurate model may come n very handy n Ž on-lne. customer proflng systems. Furthermore, by reducng the number of nput features, both human understandng and computatonal performance can often be vastly enhanced. Secton II elaborates on some response modelng ssues ncludng a lterature revew and descrpton of the data set. In Secton III, we dscuss the basc underpnnngs of LS-SVMs for bnary classfcaton. The nput selecton experment and correspondng results are presented and dscussed n Secton IV. II. THE RESPONSE MODELING CASE FOR DIRECT MARKETING A. Response Modelng n Drect Marketng Cullnan s generally credted for dentfyng the three sets of varables most often used n response modelng: recency, frequency, and monetary Ž RFM.. 1,4,5 Snce then, the lterature has provded so many uses of these three varable categores, that there s overwhelmng evdence both from academcally revewed studes as well as from practtoners experence that the RFM varables are an mportant set of predctors for modelng mal-order repeat purchasng. However, the benefcal effect of ncludng other varables nto the response model has also been nvestgated. For mal-order response modelng, several alternatve problem formulatons have been proposed based on the choce of the dependent varable. The frst category s purchase ncdence modelng. 6 In ths problem formulaton, the man queston s whether a customer wll purchase durng the next malng perod,.e., one tres to predct the purchase ncdence wthn a fxed tme nterval Žtypcally half a year.. Other authors have nvestgated related problems dealng wth both the purchase ncdence and the amount of purchase n a jont model. 7,8 A thrd alternatve perspectve for response modelng s to model nterpurchase tme through survval analyss or Ž splt-. hazard rate models whch model whether a purchase takes place together wth the duraton of tme untl a purchase

3 KNOWLEDGE DISCOVERY IN DIRECT MARKETING 1025 occurs. 9,10 Table I provdes a summary of contrbutons wth regard to the three alternatve problem formulatons. We observe that the Ž frst. purchase ncdence formulaton s clearly the most popular n the exstng lterature. 11 Moreover, most studes nclude many predctors, even though only a mnorty ncludes all categores. Ths paper focuses on the frst type of problem,.e., purchase ncdence modelng. Ths choce s motvated by the fact that the majorty of prevous research n the drect marketng lterature focuses on the purchase ncdence problem. 12,13 Furthermore, ths s exactly the settng that mal-order companes are typcally confronted wth. They have to decde whether or not a specfc offerng wll be sent to a Ž potental. customer durng a certan malng perod. Gven a tendency of rsng malng costs and ncreasng competton, we can easly see an ncreasng mportance for response modelng. 14 Improvng the targetng of the offers may ndeed counter these two challenges by lowerng nonresponse. Moreover, from the perspectve of the recpent of the Ždrect mal. messages, mal-order companes do not want to overload consumers wth catalogs. The mportance of response modelng to the mal-order ndustry s further llustrated by the fact that the ssue of mprovng targetng was among the top three concerns wth 73.5% of the catalogers n the sample mentoned n Ref. 15. B. The Data Set From a major Belgan mal-order company, we obtaned data on past purchase behavor at the order-lne level,.e., we know when a customer purchased what quantty of a partcular product at whch prce as part of what order. Ths allowed us, n close cooperaton wth doman experts and guded by the extensve lterature, to derve all the necessary purchase behavor varables for a total sample sze of 5,000 customers, of whch 37.94% represent buyers. For each customer, these varables were measured for the perod between 1 July 1993 and 30 June The goal s to predct whether an exstng customer wll repurchase n the observaton perod between 1 July 1997 and 31 December 1997 usng the nformaton provded by the purchase behavor varables. Ths problem bols down to a bnary classfcaton problem: Wll a customer repurchase or not? Notce that the focus s on customer retenton and not on customer acquston. The recency, frequency, and monetary varables have then been modeled as descrbed n detal n Ref. 11. We used two tme horzons for all RFM varables. The Hst horzon refers to the fact that the varable s measured for the perod between 1 July 1993 and 30 June The Year horzon refers to the fact that the varable s measured over the last year. Includng both tme horzons allows us to check whether more recent data are more relevant than hstorcal data. All RFM varables are modeled both wth and wthout the occurrence of returned merchandse, ndcated by R and N n the varable name, respectvely. The former s operatonalzed by ncludng the counts of returned merchandse n the varable values, whereas n the latter case these counts are omtted. Takng

4 1026 VIAENE ET AL. Table I. Lterature revew of response modelng papers. Independent Varable Dependent Varable Context of Applcaton Other Soco- Catalog or Behavoral Demographc Bnary & Bnary & Fund- Catalog Specalty Reference R F M Varables Varables Bnary Amount Tmng Rasng Ž general. Malng Berger and Maglozz Ž X X X X X X Btran and Mondschen Ž X X X X X Bult and Wttnk Ž X X X X X Bult Ž X X X X X Bult et al. Ž X X X X X X X Gonul and Sh Ž X X X X Kaslow Ž X X X X X X X Levn and Zahav Ž X X X X X X X X Maglozz and Berger Ž X X X X X Maglozz Ž X X X X X Thrasher Ž X X X X X X Van den Poel & Leuns Ž X X X X X X Ž. 11 Van den Poel 1999 X X X X X X X Van der Scheer Ž X X X X Zahav and Levn Ž X X X X X X

5 KNOWLEDGE DISCOVERY IN DIRECT MARKETING 1027 nto account both tme horzons Ž Year versus Hst. and ncluson versus excluson of returned tems Ž R versus N., we arrve at a 2 2 desgn n whch each RFM varable s operatonalzed n four ways. For the recency varable, many operatonalzatons have already been suggested. In ths paper, we defne the recency varable as the number of days snce the last purchase wthn a specfc tme wndow Ž Hst versus Year. and nor excludng returned merchandse Ž R versus N.. 4 Recency has been found to be nversely related to the probablty of the next purchase,.e., the longer the tme delay snce the last purchase the lower the probablty of a next purchase wthn the specfc perod. 1 In the context of drect mal, t has generally been observed that multbuyers Ž buyers who already purchased several tmes. are more lkely to repurchase than buyers who only purchased once. 4,26 Although no detaled results are reported because of the propretary nature of most studes, the frequency varable s generally consdered to be the most mportant of the RFM varables 12. Bauer suggests to operatonalze the frequency varable as the number of purchases dvded by the tme on the customer lst snce the frst purchase. 4 We choose to operatonalze the frequency varable as the number of purchases made n a certan tme perod Ž Hst versus Year. whle n- or excludng returned merchandse Ž R versus N.. In the drect marketng lterature, the general conventon s that the more money a person has spent wth a company, the hgher hs her lkelhood of purchasng the next offerng. 27 Nash suggests to operatonalze monetary value as the hghest transacton sale or as the average order sze. 12 Levn and Zahav propose to use the average amount of money per purchase. 27 We model the monetary varable as the total accumulated monetary amount of spendng by a customer durng a certan tme perod Ž Hst versus Year. whle n- or excludng returned merchandse Ž R versus N.. Addtonally, we nclude the natural logarthmc transformaton Ž ln. of all monetary varables as a means to reduce the skewness of the dstrbutons. Apart from the RFM varables, we also ncluded nne other customer proflng nputs. 11 The type and frequency of contact whch customers have wth the mal-order company may yeld mportant nformaton about ther future purchasng behavor. The GenInfo and GenCust are bnary customer company nteracton varables ndcatng whether the customer asked for general nformaton Ž respectvely, fled general complants.. Snce customer Ž ds. satsfacton may not only be revealed by general complants but also by returnng tems, we ncluded two extra varables. The RetMerch varable s a bnary varable ndcatng whether the customer has ever returned an tem that was prevously ordered from the mal-order company. The RetPerc varable measures the total monetary amount of returned orders dvded by the total amount of spendng. The Ndays varable models the length of the customer relatonshp n days. It s commonly beleved that consumers households wth a longer relatonshp wth the company have a hgher probablty of repurchase than households wth shorter relatonshps. IncrHst and IncrYear are operatonalzatons of a behavoral loyalty measure. We propose to perform a medan splt of the length of the

6 1028 VIAENE ET AL. relatonshp Ž tme snce the household became a customer.. Ths enables us to compare the number of purchases Ž.e., frequency. between the frst and last half of the tme wndow. The followng formula s used: purchases second half purchases frst half purchases frst half Ž 1. When the above measure s postve, ths may gve us an ndcaton of ncreasng loyalty by that customer to the Ž mal-order. company, and pso facto satsfacton wth the current level of servce. Remember that the suffx Hst reflects that the whole purchase hstory s used, whereas n the case of the suffx Year, only transactons from the last year are ncluded. The ProdclaT respectvely ProdclaM varables represent the total Ž T. respectvely, mean Ž M. forward-lookng weghted product ndex. The weghtng procedure represents the forward-lookng nature of a product category purchase, derved from another sample of data. Table II gves an overvew of the varables dscussed above. Notce that all mssng values were handled by the mean mputaton procedure 28 and that all predctor varables were normalzed to zero mean and unt varance pror to ther ncluson n the model. 29 III. LEAST SQUARES SVM CLASSIFICATION A. LS-SVMs for Bnary Classfcaton Gven a tranng set x 4, y 1 N wth nput data x n and correspondng bnary class labels y 1, 1 4, the SVM classfer, accordng to Vapnk s orgnal formulaton, satsfes the followng condtons: w T Ž x. b 1 f y 1 Ž 2. w T Ž x. b 1 f y 1 Table II. A lstng of all nputs Ž both RFM and non-rfm. ncluded n the drect marketng case. Recency Frequency Monetary Other RecYearR FrYearR MonHstR ProdclaT RecYearN FrYearN MonHstN ProdclaM RecHstR FrHstR MonYearR GenCust RecHstN FrHstN MonYearN GenInfo lnž MonHstR. Ndays lnž MonHstN. IncrHst lnž MonYearR. lnž MonYearN. IncrYear RetMerch RetPerc

7 whch s equvalent to: KNOWLEDGE DISCOVERY IN DIRECT MARKETING 1029 Ž. Ž. T y w x b 1 1,...,N 3 Ž. n n The nonlnear functon : h maps the nput space to a hgh dmensonal Ž and possbly nfnte dmensonal. feature space. In prmal weght space the classfer then takes the form: T yž x. sgn w Ž x. b Ž 4. however, t s never evaluated n ths form. One defnes the optmzaton problem as: subject to: 1 T N Ý 1 mn T Ž w,. w w c Ž 5. 2 w, b, Ž. T y w x b 1 1,...,N 0 1,...,N The varables are slack varables whch are needed to allow msclassfcatons n the set of nequaltes Ž e.g., due to overlappng dstrbutons.. The postve real constant c should be consdered as a tunng parameter n the algorthm. For nonlnear SVMs, the QP-problem and the classfer are never solved and evaluated n ths form. Instead, a dual space formulaton and representaton are obtaned by applyng the Mercer condton Ž see Refs for detals.. Vapnk s SVM classfer formulaton was modfed by Suykens and Vandewalle 2 nto the followng LS-SVM formulaton: N T 2 Ý 1 Ž mn TŽ w, e. w w e Ž w, b, e subject to the equalty constrants: Ž. Ž. T y w x b 1 e, 1,...,N 8 Ths formulaton now conssts of equalty nstead of nequalty constrants and takes nto account a squared error wth a regularzaton term smlar to rdge regresson. The soluton s obtaned after constructng the Lagrangan: N T Ý 1 4 L Ž w, b, e;. TŽ w, e. y w Ž x. b 1 e Ž 9. where are the Lagrange multplers. After takng the condtons for optmal ty, one obtans the followng lnear system 2 : 0 Y T b 0 Ž Y I 1

8 1030 VIAENE ET AL. where Z Ž x. T y ;...; Ž x. T y, Y y ;...; y, 1 1;...;1, 1 1 N N 1 N T 2 ;...;, ZZ, and Mercer s condton s appled wthn the matrx: 1 N T j j Ž. Ž j. yy x x yykž x, x. j j For the kernel functon KŽ,. one typcally has the followng choces: KŽ x, x. x T x, Ž lnear kernel. Ž T d K x, x x x 1, polynomal kernel of degree d Ž. Ž. KŽ x, x. exp x x, Ž radal bass functon Ž RFB. kernel. Ž. KŽ x, x. tanh x T x, multlayer perceptron Ž MLP. kernel Ž 11. Ž. where d,,, and are constants. Notce that the Mercer condton holds for all and d values n the RBF and the polynomal cases, but not for all possble choces of and n the MLP case. The LS-SVM classfer s then constructed as follows: N Ý 1 yž x. sgn ykž x, x. b Ž 12. Note that the matrx n Ž 10. s of dmenson Ž N 1. Ž N 1.. For large values of N, ths matrx cannot easly be stored, such that an teratve soluton method for solvng t s needed. A Hestenes Stefel conjugate gradent algorthm s suggested n Ref. 34 to overcome ths problem. Bascally, the latter rests upon a Ž. 34 transformaton of the matrx n 10 to a postve defnte form. A straghtforward extenson of LS-SVMs to multclass problems has been proposed n Ref. 35, where addtonal outputs are taken to encode multclasses as s often done n classcal neural network methodology. 29 A drawback of LS-SVMs s that sparseness s lost due to the choce of a 2-norm. However, ths can be crcumvented n a second stage by a prunng procedure whch s based upon removng tranng ponts guded by the sorted support value spectrum. 36 B. Calbratng the RBF LS-SVM Classfer All classfers were traned usng RBF kernels. 3 Estmaton of the generalzaton ablty of the RBF LS-SVM classfer s then realzed by the followng expermental setup 3 : 3 1 Ž. 1 Set asde 4 of the data for the tranng set and the remanng 4 for testng, respectng the orgnal class dstrbuton. Ž. 2 Perform 10-fold cross valdaton on the tranng data for each Ž,. combnaton from the ntal canddate tunng sets and typcally chosen as follows: 0.5, 5, 10, 15, 25, 50, 100, 250, 5004 n , 0.5, 1, 10, 50, 100, 500, N '

9 KNOWLEDGE DISCOVERY IN DIRECT MARKETING 1031 The square root ' n of the number of nputs n s ntroduced, snce x x 2 2 n 1 the RBF kernel s proportonal to n and the factor N s ntroduced such that the msclassfcaton term Ý 1 N e 2 s normalzed wth the sze of the data set. Ž. 3 Choose optmal Ž,. from the ntal canddate tunng sets and by lookng at the best cross valdaton performance for each Ž,. combnaton. Ž. 4 Refne and teratvely by means of a grd search mechansm to further optmze the tunng parameters Ž,.. In our experments, we repeated ths step three tmes. Ž. 5 Construct the LS-SVM classfer usng the total tranng set for the optmal choce of the tuned hyperparameters Ž,.. Ž. 6 Assess the generalzaton ablty by means of the ndependent test set. Followng the procedure outlned above, one obtaned the results depcted 3 n Table III. The optmzed RBF LS-SVM classfer, traned on 4 of the data set, acheves a percentage correctly classfed on the tranng data of 77.54% wth and Performance on the ndependent test data amounts to 74.48% correctly classfed. We contrasted these results wth those obtaned usng a lnear kernel for the LS-SVM classfer. As can be observed from Table III, the percentage correctly classfed drops to 76.26% on the tranng set and to 73.76% on the ndependent test set. IV. THE INPUT SELECTION EXPERIMENT A. Input Selecton n a Nutshell Input selecton s a commonly adhered technque to reduce model complexty. The goal s to fnd a reduced coordnate system that allows one to project the data on a more compact representaton. The general assumpton underlyng ths operaton and justfyng t, s that the studed data approxmately le wthn the bounds of ths reduced space. As such, models wth fewer nputs are capable of mprovng both human understandng and computatonal performance. Moreover, elmnaton of redundant and or rrelevant nputs may also mprove the predctve power of an algorthm. 37 Selectng the best subset of a set of n predctors s a nontrval problem. Ths follows from the fact that the optmal nput subset can only be obtaned when the nput space s exhaustvely searched. When n nputs are present, ths would mply the need to evaluate 2 n 1 nput subsets. Unfortunately, as n grows, ths very quckly becomes computatonally nfeasble. For that reason, heurstc search procedures are often preferred. Input selecton can then ether be performed as a preprocessng step, ndepen- Table III. Classfcaton accuracy of the optmzed RFB LS-SVM classfer versus an LS-SVM optmzed usng a lnear kernel. LS-SVM LS-SVM Classfcaton Accuracy RBF Kernel Lnear Kernel Tranng Ž 3750 observatons % 76.26% Test Ž 1250 observatons % 73.76%

10 1032 VIAENE ET AL. dent of the nducton algorthm, or explctly make use of t. The former approach s termed flter, the latter wrapper. 38 Flter methods operate ndependently of the learnng algorthm. Undesrable nputs are fltered out of the data before nducton commences. Focus 39 and Relef 40 are well-known flter methods. Wrapper methods make use of the actual target learnng algorthm to evaluate the usefulness of nputs. Typcally, the nput evaluaton heurstc that s used s based upon nspecton of the traned parameters and or comparson of predctve performance under dfferent nput subset confguratons. Input selecton s then often performed n a sequental fashon, e.g., guded by a best-frst nput selecton strategy. The backward selecton scheme starts from a full nput set and stepwse prunes nput varables that are undesrable. The forward selecton scheme starts from the empty nput set and stepwse adds nput varables that are desrable. Hybrds of the above also exst. B. Wrappng the Optmzed LS-SVM Classfer Input selecton effectvely starts at the moment the LS-SVM classfer has been constructed on the full set of n avalable predctors. The nput selecton procedure s based upon a Ž greedy. best-frst heurstc, gudng a backward search mechansm through the nput space. 38 The mechancs of the mplemented heurstc for assessng the senstvty of the classfer to a certan nput are qute straghtforward. We apply a strategy of constant substtuton n whch an nput s perturbed to ts mean whle all other nputs keep ther values and compute the mpact of ths operaton on the performance of the obtaned LS-SVM classfer wthout reestmaton of the LS-SVM parameters and b. Ths assessment s done usng the separate prunng set to obtan an unbased estmate of the change n classfcaton accuracy of the constructed classfer. The prunng set conssts of 1250 observatons that were randomly selected from the tranng set of 3750 observatons. Fgure 1 provdes a concse overvew of the dfferent steps of the expermental procedure. Fgure 1.

11 KNOWLEDGE DISCOVERY IN DIRECT MARKETING 1033 Startng wth a full nput set F 1, all n nputs are pruned sequentally,.e., one by one. The frst nput fp to be removed, s determned at the end of Step 1 task Ž. 4. After havng removed ths nput from F 1, the reduced nput set F F f p s used for subsequent nput removal. At ths moment, an teraton of dentcal Steps s started, n whch, n a frst phase, the LS-SVM parameters and b are re-estmated on the tranng set task Ž. 1 of Step, however, wthout recalbraton for and, and the generalzaton ablty of the classfer s quantfed on the ndependent test set task Ž. 2 of Step. Notce that the orgnally optmzed and values obtaned n task Ž. 1 of Step 1 reman unchanged durng the entre nput selecton phase. Agan, nput senstvtes of the resultng classfcaton model Ž wthout re-estmaton of and b. are assessed on the prunng set to dentfy the nput to whch the classfer s least senstve when perturbed to ts mean task Ž. 3 of Step. Ths nput s then pruned from the remanng nput subset and dsregarded for further analyss. The prunng procedure s thereupon resumed wth a reduced nput set, untl all nputs are eventually removed. Once all nputs have been pruned, the preferred reduced model s then determned by means of the hghest prunng set performance. Table IV summarzes the emprcal fndngs of the prunng procedure for the RFM case. Observe how the suggested nput selecton method allows sgnfcant reducton of model complexty Ž from 25 to 9 nputs. wthout any sgnfcant degradaton of the generalzaton behavor on the ndependent test set. The test set performance amounts to 73.92% for the full model and 73.52% for the reduced model. The order of nput removal as depcted n Table V, provdes further nsght nto the relatve mportance of the predctor categores Ž cf. Table II.. The reduced model conssts of the nne nputs that are underlned n Table V. Ths reduced set of predctors conssts of frequency, monetary, and other Ž non-rfm. varables. It s especally mportant to note that the reduced model ncludes nformaton on returned merchandse. Furthermore, notce the absence of the recency component n the reduced nput set. Inspecton of the order of removal of nputs, whle further prunng ths reduced nput set, hghlghts the relatve mportance of the frequency varables. More specfcally, the last two varables to be removed belong to ths predctor category. Note that an nput set consstng of only these two nputs, stll yelds a percentage correctly classfed at 72.00% on the test set. Results also pont to the benefcal effect of ncludng the Table IV. Emprcal assessment of the RBF LS-SVM classfers for the full and reduced models. Classfcaton Accuracy Full Model Reduced Model Tranng Ž 2500 observatons % 76.04% Prunng Ž 1250 observatons % 77.20% Test Ž 1250 observatons % 73.52% Number of Inputs 25 9

12 1034 VIAENE ET AL. Table V. Order of nput removal. Each nput s qualfed by ts category wth r, f, m and o respectvely standng for recency, frequency, monetary and other Ž cf. Table II.. Prunng Steps RetPerc o ProdclaM o RecHstN r FrYearN f MonYearR m lnž MonHstN. m MonHstR m IncrHst o lnž MonHstR. m MonYearN m RecHstR r IncrYear o RecYearR r MonHstN m GenInfo o Ndays o lnž MonYearR. m RecYearN r GenCust o FrHstR f ProdclaT o lnž MonYearN. m FrHstN f RetMerch o FrYearR f non-rfm customer proflng varables GenInfo and GenCust for mprovng predctve accuracy. They underlne that customer company nteracton varables, here measured by ndcators of nformaton requests and complants, provde addtonal predctve power to purchase ncdence modelng for database marketng. V. CONCLUSION In ths paper, we appled an LS-SVM based nput selecton wrapper to a real-lfe drect marketng case nvolvng the modelng of repeat-purchase behavor. Based on a thorough revew of the lterature, we extended the well-known recency, frequency, monetary Ž RFM. framework Ž 1. by usng alternatve operatonalzatons of the orgnal varables, and Ž. 2 by ncludng several addtonal behavoral varables. The senstvty based, stepwse nput selecton method, constructed as a wrapper around the LS-SVM classfer, allows sgnfcant reducton of model complexty wthout degradng predctve performance. The emprcal fndngs hghlght the role of frequency and monetary varables n the reduced model, whle the recency varable category seems to be of somewhat lesser mportance wthn the response model. Results also pont to the benefcal effect of ncludng non-rfm customer proflng varables for mprovng predctve accuracy. More specfcally, customer company nteracton, measured by ndcators of nformaton requests and complants, and merchandse returns provde addtonal predctve power to purchase ncdence modelng for database marketng. Ths work was partly carred out at the Leuven Insttute for Research on Informaton Systems Ž LIRIS. of the Department of Appled Economc Scences of the K.U. Leuven n the framework of the KBC Insurance Research Char. Ths work was partly carred out at the ESAT laboratory and the Interdscplnary Center of Neural Networks ICNN of the K.U. Leuven. S. Vaene, holder of the KBC Insurance Research Char, and B. Baesens are both Research Assstants of LIRIS. T. Van Gestel s a research assstant wth the Fund for Scentfc Research Flanders Ž FWO-Flanders., J. Suykens s a postdoctoral researcher wth the Fund for Scentfc Research Flanders Ž FWO-Flanders., B. De Moor s a senor research assocate wth the Fund for Scentfc Research Flanders Ž FWO-Flanders.. D. Van den Poel s an assstant professor at the Department of

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