a novel key influencing factors selection approach of p2p

Research ArticleA Novel Key Influencing Factors Selection Approach of P2PLending Investment Risk

Pingfan Xia 12 Zhiwei Ni 12 Xuhui Zhu 12 and Liping Ni 12

1School of Management Hefei University of Technology Hefei 230009 China2Key Laboratory of Process Optimization and Intelligent Decision-Making Ministry of Education Hefei 230009 China

Correspondence should be addressed to Zhiwei Ni zhiwein163com

Received 3 September 2019 Accepted 15 October 2019 Published 28 November 2019

Academic Editor Georgios Dounias

Copyright copy 2019 Pingfan Xia et al is 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

Recent frequent ldquothunderstorm incidentsrdquo of P2P lending industry have caused the panic of industry investors To predict theinvestment risk of P2P lending we should scientifically and rationally analyze the key influencing factors of P2P lending in-vestment risk Existing key influencing factors selection methods mainly involve traditional statistical approaches and artificialintelligence methods e traditional statistical approaches cannot deal with the high-dimensional nonlinear problems and itcannot find the exact key influencing factors of the P2P lending investment risk e artificial intelligence methods cannotrecognize and learn the application background and the selected attributes without active thinking and personal perception maynot be the key influencing factors of P2P lending investment risk To address the above issues a novel key influencing factorsselection approach of P2P lending investment risk is proposed by combining the proposed fireworks coevolution binaryglowworm swarm optimization (FCBGSO) multifractal dimension (MFD) probit regression and artificial prior knowledgeFirst multifractal dimension combined with the proposed FCBGSO is used to select the preliminary influencing factors of theinvestment risk second the nonsignificant relevant attributes in the preliminary influencing factors are removed using the probitregression and we add the influencing factors extracted from the original dataset of P2P lending using the artificial priorknowledge into the retaining influencing factors after removing one by one A small and reasonable number of influencing factorsubsets are achieved Finally we evaluate each influencing factors subset using extreme learning machine (ELM) and the subsetwith the best classification accuracy is efficiently achieved ie it is the key influencing factors of P2P lending investment riskExperimental results on the real P2P lending dataset from the Renrendai platform demonstrate that the proposed approachperforms better than other state-of-the-art methods and that it has validity and effectiveness It provides a new research idea forthe key influencing factors selection of P2P lending investment risk

1 Introduction

Peer-to-peer (P2P) lending is a new financial model thatintegrates Internet platforms and private lending Bothlenders and borrowers can directly complete the trans-actions through P2P lending platforms without goingthrough financial intermediaries [1 2] P2P lending is one ofthe most important modes of Internet finance On one handit can serve the real economy on the other hand the recentfrequent occurrences of P2P lending ldquothunderstorm in-cidentsrdquo have damaged the earnings of investors and hin-dered the healthy development of P2P lending industryAccording to preliminary statistics as of January 15 2019

there are 2746 transferred or closed platforms in ChinarsquosP2P lending industry and 2663 problematic platforms intotal Since June 2018 the risk incidents of P2P lendingplatforms have been continuously exposed e large-scaleldquothunderstorm incidentsrdquo in the P2P lending industry havecaused a strong impact on the healthy development of thisindustry Meanwhile it has attracted great attention of theChinese government In the 2018 report on the work of theChinese government it was definitely pointed out thatldquostrengthen the overall coordination of financial supervisionand improve the supervision of Internet financerdquo HenceInternet finance has been written into the report on the workof the government five times in a row From the initial

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 6086089 12 pageshttpsdoiorg10115520196086089

ldquopromoting developmentmdashstandardizing developmentmdashbeing vigilant of riskrdquo to the ldquoimproving Internet financialsupervisionrdquo in 2018 indicates that the standardizationcontrol of Internet financial investment risk is imperativeerefore it is urgent to explore the investment risk of P2Plending To research the investment risk we should analyzethe key influencing factors of P2P lending investment riskwhich can provide high-quality data for the prediction ofP2P lending investment risk

A key influencing factors selection approach for P2Plending investment risk is essential to reduce irrelevant attri-butes with the investment risk in an original dataset of P2Plending and retain key influencing factors In fact there is a largeamount of noisy or irrelevant features with investment risk inthe real datasets of P2P lending Existing key influencing factorsselection approaches usually use traditional statistical methodsand attribute selection algorithms based on artificial intelligence[3 4] e statistical methods are commonly used in the se-lection of key influencing factors of P2P lending investmentrisk while there is no application of artificial intelligencemethods at least to our knowledge e traditional statisticalmethods are only limited to the discussion of the impact of asingle factor on the borrower for the order default risk but itignores the fusion and the crossover of multiple informationFor instance the credit rating of each loan has an importantimpact on investment risk which is presented by Guo et al [5]Larrimore et al examined the relationship between language useand investor decision-making [6] e soft information in loantitles has a significant influence on whether the loan is suc-cessful e results also suggest that investors do not investblindly based on returns [7] Xiao et al proposed a visualanalysis method which analyzes and detects risk in P2P lendingdeals [8] Perceived age of P2P lending orders shows a strongsignal of ability and experience and more mature perceived ageis more attractive to investors [9] Chen et al investigated theamount of punctuation used in loan descriptions can influencethe investment default risk using data from Renrendai (one ofthe largest P2P lending platforms in China) [10] To sumup thetraditional statistical methods such as regression analysis havesmall calculations and simple operations when they analyze theinfluencing factors of P2P lending investment risk

For feature selection based on artificial intelligence there aretwomain points one is the evaluation criterion selection and theother one is the search strategy With respect to evaluationcriterion various evaluation methods are used to evaluatefeature subsets Different evaluation methods have great re-lationship with the optimal subset For example informationtheory [11ndash13] distance analysis [4] rough sets [14ndash17] andfractal dimension [18ndash20] Fractal dimension is treated as anevaluation criterion which attracts many scholarsrsquo attentions Ithas two advantages [21] on one hand the number of an optimalfeature subset can be determined by calculating its fractal di-mension which can dramatically reduce computationalamount on the other hand the fractal dimension performs wellwhen it comes to solving high-dimensional datasets and non-linear problems Most existing feature selection approachesbased on fractal dimension use only a single fractal dimensionwhich may not precisely describe the original datasets [20]because of their complicated distribution In contrast

multifractal dimension (MFD) can describe the distribution ofdataset in different aspects [19] which is regarded as theevaluation criterion of feature subsets in this work In regard tosearching strategy finding an optimal feature subset of anoriginal dataset is a combinatorial optimization problem [17]erefore heuristic algorithms provide good searching strate-gies for the feature selection methods for example geneticalgorithm (GA) [22 23] ant colony optimization (ACO)[24ndash26] particle swarm optimization (PSO) [27 28] and ar-tificial fish swarm algorithm (AFSA) [29] However the com-plex coding process of GA is hard to be implemented [30 31]ACO has the disadvantages of the blindness search in the earlystage slow convergence speed and huge computing resourceconsumption PSO easily traps into local optimal solution[30 31] AFSAhas the weaknesses of lack of population diversityand slow convergence rate in the later stage In contrastglowworm swarm optimization (GSO) has the advantages ofsimplicity of implementation strong robustness and good andfast global convergence [32] which can be used as a searchingstrategy for solving a feature selection problem [33]We attemptto propose a fireworks coevolution binary glowworm swarmoptimization (FCBGSO) as the searching strategy in this work

Based on the above analysis first and foremost the tra-ditional statistical methods cannot solve the high-dimensionalnonlinear problem and the analysis is one-sided so it is dif-ficult to exactly analyze the key influencing factors of the P2Plending investment risk In addition the artificial intelligencemethods perform well when it comes to coping with high-dimensional and nonlinear datasets but it cannot recognizeand learn the application background lack of active thinkingand personal perception and the selected attributes may not bethe key influencing factors of P2P lending investment riskerefore we proposed a novel approach to find the keyinfluencing factors of P2P lending investment risk whichcombines MFD FCBGSO the probit regression and the ar-tificial prior knowledgeemission is attained in four steps inthe first step we take the proposed FCBGSO as a searchstrategy and treat MFD as an evaluation criterion for featuresubsets en the preliminary attribute subset extracted fromthe original dataset of P2P lending is attained using thecombination of FCBGSO and MFD In the second step thenonsignificant relevant attributes with the default risk areremoved from the preliminary subset using the probit re-gression In the third step a small and reasonable number ofattribute subsets are achieved by combining the retaining at-tributes after removing and the attributes obtained by theartificial prior knowledge In the final step considering theadvantages of extreme learning machine (ELM) such as goodgeneralization ability and the extremely fast learning speedELM is used to assess the classification accuracies of thesesubsets and the attribute subset with the best accuracy is thekey influencing factors of P2P lending investment risk

e contributions of the proposed approach are pre-sented as follows

(1) A novel approach for key influencing factors selec-tion of P2P lending investment risk is proposedusing the combination of FCBGSO MFD the probitregression and the artificial prior knowledge

2 Mathematical Problems in Engineering

(2) e proposed FCBGSO works well with respect tosearching for the optimal solution in a binary space

(3) Experiments on the real dataset of P2P lending fromRenrendai platform demonstrate that the proposedmethod significantly performs better than traditionalstatistical approaches and artificial intelligencemethods and that it has validity and effectiveness

(4) It provides a novel research idea for the key influ-encing factors selection of P2P lending investmentrisk

e rest of this paper is organized as follows In the nextsection we briefly review the basic concept of a GSO andthen FCBGSO is proposed e key influencing factorsselection method of P2P lending investment risk and how touse it are presented in Section 3 Experimental results areshown in Section 4 In Section 5 the conclusions and thefuture work are presented

2 Fireworks Coevolution Binary GlowwormSwarm Optimization (FCBGSO)

Swarm intelligence algorithms combined with MFD can beapplied in attribute selection Swarm intelligence algorithmsare used as searching strategies GSO has some advantagessuch as simplicity of implementation strong robustness andgood global convergence So it can be used as a searchingstrategy but there are still drawbacks eg insufficient di-versity low convergence precision and searching efficiencyTo address the above drawbacks FCBGSO is proposedwhich significantly improves its convergence speed andprecision e preliminary influencing factors can be effi-ciently achieved e outline of FCBGSO is presented asfollows

21 Glowworm Swarm Optimization (GSO) GSO is a rela-tively novel swarm intelligence algorithm proposed byKrishnanand and Ghose [34ndash36] which is a bionic swarmintelligent algorithm by imitating the luminous behavior inthe process of foraging and courtship of glowworms innature [37] In GSO each glowworm represents a solutionand it is randomly distributed in a solution spacee higherbrightness the glowworm individual has the more attractionit gains [38] e glowworms move forward to theirneighbors with higher luciferin and these individuals can beupdated us the global optimal solution is attained ebasic steps of GSO are listed as follows

(1) Updating luciferin of the glowworm Xi(t) at the tthiteration is given by equation (1) e luciferin re-newal depends on the objective function valueJ(Xi(t)) of the glowworm

li(t) (1 minus ρ)li(t minus 1) + cJ Xi(t)( 1113857 (1)

where li(t) is the luciferin level of Xi(t) at the tthiteration ρ represents the luciferin decay constant

(0lt ρlt 1) and c indicates the luciferin enhance-ment constant

(2) e glowworms in the dynamic decision domain ofXi(t) whose luciferin is greater than Xi(t) can beused to make up its set of neighbors Ni(t) and it isexpressed as equation (2) e probability Pij(t) ofXi(t) moving to neighbor Xj(t) in a set of neighborsis described as equation (3)

Ni(t) j Xj(t) minus Xi(t)

lt rid(t) li(t)lt lj(t)1113882 1113883

(2)

Pij(t) lj(t) minus li(t)

1113936kisinNi(t)lk(t) minus li(t)

(3)

where rid(t) is the dynamic radial range 0lt ri

d lt rs

and rs is the radial range of the luciferin sensor(3) Each glowworm selects a objective glowworm Xj(t)

with a higher luciferin at a probability Pij(t) enthe position of Xi(t) can be updated as the followingequation

Xi(t + 1) Xi(t) + s timesXj(t) minus Xi(t)

Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (4)

where s is a moving step set by the user(4) After updating the positions of all the glowworms

the dynamic radial range of local-decision domain isnoticed using the rule given as the followingequation

rid(t + 1) min rs max 0 r

id(t) + β nt minus Ni(t)

111386811138681113868111386811138681113868111386811138681113872 11138731113966 11139671113966 1113967

(5)

where β is a constant parameter and nt is a parameterto control the number of neighbors

22 Position Updating Modification Based on DynamicInertia Weight Dynamic inertia weight strategies arecategorized into four classes linear decreasing inertiaweight nonlinear decreasing inertia weight adaptiveinertia weight and stochastic inertia weight [39ndash41]Consider that the stochastic inertia weight (SIW) in theposition updating equation can balance the relationshipbetween the local and the global search It can obtainstable optimization results and quickly jump out of thelocal optima erefore we use SIW to solve the drawbackof slow convergence speed of basic GSO e SIW isdefined as follows

w rmin + rmax minus rmin( 1113857 times normrnd( ) + σ times randn( )

(6)

where rmin denotes the lower limit value of SIW rmax in-dicates the upper limit value of SIW randn( ) shows a

Mathematical Problems in Engineering 3

random number which follows the normal distributionnormrnd( ) expresses a random number of uniform dis-tribution and σ represents the deviation between inertiaweights and their mean value

e SIW is mainly used to update the positions ofglowworms and it is updated as follows

Xi(t + 1) w times Xi(t) + s timesXj(t) minus Xi(t)

Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (7)

To solve a binary combinational optimization problemthe positions of glowworms are mapped into 0 or 1 using asigmoid function e mapping process is presented asequations (8) and (9)

xik 1 if randle S xik( 1113857

0 else

⎧⎪⎨

⎪⎩(8)

S xi( 1113857 1

1 + exp minus xi( 1113857 (9)

where Xi(t) (xi1 xi2 xik xis) (1le kle s) s is thedimension of the solution space of the problem and S(xi) isa sigmoid function

23 Coevolution Mechanism To overcome the weakness ofslow convergence speed in GSO a coevolutionmechanism isintroduced into GSO which can promote the process ofevolution To avoid invalid crossover caused by the excessivesimilarities between glowworms the initial population isdivided into three equal subpopulations by the proportion 1 1 1 according to their fitness values ey are elite sub-population PE excellent subpopulation PA and commonsubpopulation PB respectively Each subpopulation evolvesindependently and synchronously and keeps dynamicupdating during the search process e most excellentglowworm individual is selected from the elite sub-population and it performs a crossover with the optimalindividual of PA and PB respectively en four new off-spring are generated which keeps the diversity of thepopulation

We introduce a competitive factor μ1 into this work ecoevolution mechanism can be denoted as follows

If randlt μ1 then

XEAprime (t) round

12

(1 + r) times XA(t) +(1 minus r) times XE(t)( 11138571113874 1113875

XEAPrime

(t) round12

(1 minus r) times XA(t) +(1 + r) times XE(t)( 11138571113874 1113875

XEBprime (t) round

12

(1 + r) times XB(t) +(1 minus r) times XE(t)( 11138571113874 1113875

XEBPrime

(t) round12

(1 minus r) times XB(t) +(1 + r) times XE(t)( 11138571113874 1113875

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)

where rand r are randomly generated variables boundedbetween 0 and 1 XA(t) XB(t) andXE are different glow-worms in PA PB and PE respectively XEA

prime (t) XEAPrime

(t)XEBprime (t) and XEB

Prime(t) are the four new offspring XE will be

replaced by the best glowworm selected from XEAprime (t)

XEAPrime

(t) XEBprime (t) and XEB

Prime(t) if the best individual performs

better than XE e architecture of the coevolution mech-anism is presented in Figure 1

24 Fireworks Evolution Strategy To effectively avoid thedefects of the premature convergence and the insufficientdiversity of population in GSO a fireworks explosion op-eration [42] is introduced e current glowworm Xi pro-duces multiple offspring by explosion with a certainprobability e best individual extracted from the multipleoffspring can be retained to the next generation We in-troduce a probability factor μ2 and the scale of the individualglowworms produced around Xi is formulized as follows

If randlt μ2 then

Si H timesymax minus f xi( 1113857 + ε

1113936Ni1 ymax minus f xi( 1113857( 1113857 + ε

(11)

where Si is the number of newly generated glowworms ymaxshows the maximal fitness value of glowworms at the currentiteration H denotes a constant to adjust the amount ofglowworm offspring and ε is a small constant which canavoid zero division error

e rth dimension in Xi is randomly selected to performGaussian mutation operation namely it is changed from 0to 1 or 1 to 0

r ri

d times e

2

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (12)

where e sim N(1 1) and N(1 1) indicates the Gaussian dis-tribution with a mean value of 1 and a variance value of 1

e glowworm offspring are produced by the fireworksevolution strategy and their fitness values can be achieved Ifthe optimal glowworm in the generated offspring performsbetter than Xi then Xi is replaced by it

3 Key Influencing Factors Selection Method

31 Multifractal Dimension (MFD) Mandelbrot first pro-posed the concept of fractal in 1983 [43] which is used todescribe the irregular geometry of the nature ere are twoproperties with respect to the fractal object one is the self-similarity and the other one is the scale invariability namelythere is a similar appearance when the fractal object isviewed in indifferent scales Fractal theory is used in a widevariety of fields

ere are often two kinds of dimensions on datasets iethe embedding dimension and the intrinsic dimension eembedding dimension indicates the number of the originaldatasetrsquos features the intrinsic dimension represents thenumber of irrelevant features Generally speaking the in-trinsic dimension is less than the embedding dimension Ifall features are irrelevant with each other the intrinsic


dimension is equal to the embedding dimension e fractaldimension can represent the intrinsic dimension and theupper bound of the fractal dimension is the number of keyfeatures required to characterize the original dataset Trainaet al [44] showed that most of the datasets have fractalcharacteristic and the fractal dimension can be regarded asan evaluation criterion for feature selection

Fractal feature selection approaches were first proposedby Traina et al [44] e fractal dimension is taken as anevaluation criterion which can measure the importance offeatures e advantage of fractal feature selection algo-rithms is that the number of the selected features can bedetermined but the fractal dimension needs to be recal-culated after removing some features To improve compu-tational efficiency GA [22 23] ACO [24ndash26] PSO [27 28]AFSA [29] and so on are employed as searching strategies toenhance efficiency of the fractal feature selection methods

However most existing fractal feature selection methodsonly take a single fractal dimension such as informationdimension or correlation dimension A single fractal di-mension may not precisely describe a dataset [45] Incontrast MFD can describe the datasetrsquos distribution indifferent aspects which can be calculated as the followingequation

Dq

limr⟶0

1q minus 1

timeslog1113936 p

qi

log r qne 1

limr⟶0

logpi 1113936 pi

log r q 1

r isin r1 r21113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

where pi stands for the probability of a data point droppedinto the ith grid r indicates the grid size [r1 r2] denotes thescale-free interval of a dataset and q is an integer

When qlt 0 Dq shows the void distribution of a fractaldataset when qgt 0 Dq indicates the aggregation degree of afractal dataset Fractal dimension (FD) can just describe thedistribution of a dataset in a single aspect In contrast theMFD can describe the distribution in many aspects HenceMFD is regarded as an evaluation criterion of feature subsetsin this work

32 Construct the Objective Function By comparison with asingle fractal dimension MFD can accurately describe

datasets So the objective function can be expressed as thefollowing equation

f

1113944q

fracq minus Dq1113872 11138732

1113971

(14)

where fracq represents the qth-order fractal dimension of afeature subset and Dq illustrates the qth-order fractal di-mension of the original dataset

We regard the difference between the MFD of a featuresubset and the original dataset as the objective functionAccording to the definition of the objective function we cansee that the smaller the value of the objective function is thebetter the solution is Dq is specified with five fractal di-mensions D2 D3 D4 D5 andD6 respectively [19]

33 Extreme Learning Machine (ELM) ELM was first pro-posed by Huang et al [45] which was developed for singlehidden layer feedforward networks (SLFNs) By comparingwith traditional neural networks it requires great efforts inthe adjustment of hyperparameter [46] ELM can providegood generalization ability and extremely fast learningspeed ELM contains input hidden layers and output nodesand only hidden layer nodes required to be set in ELM Forgiven M different samples (xi yi) the model of ELM can beexpressed as follows

1113944

L

i1bigi xj1113872 1113873 1113944

L

i1big ωiji + bi( 1113857 yi (15)

where xi [xi1 xi2 xin]T isin Rn yi [yi1 yi2 yim]T

isin Rm L denotes hidden nodes g(x) indicates a hidden layeractivation function ωi illustrates the weight vector con-necting the ith hidden node and input nodes and bi is thethreshold of ith hidden nodes For all M samples equation(15) can be written as

Hβ Y (16)

where H

g(ω1x1 + b1) middot middot middot g(ωLx1 + bL)

⋮ ⋱ ⋮g(ω1xN + b1) middot middot middot g(ωLxN + bL)

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

NtimesL

Y

yT1⋮yT

N

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ntimesm

and β

βT1⋮βT

L

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ltimesm

H shows the hidden layer

output matrix e ELM theory states that the hidden node

PA PBPE

Initial population layerPartitioned population layer

Crossover

Subpopulation layer

Competitive

mechanism

P (t) P (t + 1)

Population

segmentation

Crossover

Figure 1 e architecture of the coevolution mechanism


learning parameters ω and b can be randomly assignedregardless of input data

erefore the system equation (15) becomes a linearmodel By finding the least squares solution of the linearsystem (15) the output weights can be analytically de-termined as follows

β HdaggerT (17)

where Hdagger indicates the MoorendashPenrose generalized inverseof the hidden layer output matrix H [47]

34 Key Influencing Factors Selection Model Constructione effective integration of FCBGSO MFD probit re-gression and artificial prior knowledge is applied to the keyinfluencing factors selection of P2P lending investmentrisk Firstly the MFD is treated as an evaluation criterionfor a feature subset and FCBGSO is used as a searchstrategy e combination of FCBGSO and MFD(FCBGSO+MFD) is used for reducing the redundancyattributes in the original dataset and the preliminary subsetis attained Secondly we analyze the correlation betweenthe selected attributes and the default risk of P2P lendinginvestment using the probit regression and those attributesthat are nonsignificantly correlated with the investmentrisk will be removed Finally the attributes that have asignificant impact on the investment risk are selected fromthe original dataset using the artificial prior knowledgewhich are added into the retaining attributes one by oneen a small and reasonable number of attribute subsetsare achieved and we assess their classification accuraciesusing ELM e attribute subset with the highest classifi-cation accuracy is the key influencing factors of P2Plending investment risk

e pseudocode of Algorithm 1 is presented as followse main steps of the model construction are as follows

Step 1 calculate the MFD of the original dataset of P2Plending and obtain the number of attributes in the pre-liminary subset mprime(mprime D D max(Dq)) the objec-

tive function f 1113936q(fracq minus Dq)2

1113969 q 2 3 4 5 6

Step 2 search the preliminary attribute subset B1 of P2Plending orders with the minimal objective functionvalue using FCBGSOStep 3 eliminate attributes that are nonsignificantlyrelated to default risk in B1 using the probit regressionand get the attribute subset B2

Step 4 select the attributes extracted from the originaldataset that have a significant influence on the in-vestment risk and do not belong to B2 using the ar-tificial prior knowledge and form the attribute subset A

Step 5 add the attributes in A into B2 one by one andget a small and reasonable number of attribute subsetsB1prime B2prime Bn

prime

Step 6 calculate the classification accuracy of eachattribute subset in B1prime B2prime Bn

prime using ELM and thenobtain their classification accuracies p1 p2 pn

Step 7 assume pi(i 1 2 n) is the highest classi-fication accuracy in p1 p2 pn and then the attri-bute subset Bi

prime is the key influencing factors of P2Plending investment risk

4 Experimental Results

In this section to assess the performance of the proposedapproach the experiments are implemented in MATLAB2017a e algorithm is tested on a computer running 64-bitWindows 10 with 281GHz processor and 8GB memoryExperimental parameters are set as follows the populationsize N 30 the maximum number of iterations tmax 20luciferin volatile factor ρ 04 luciferin renewal ratec 06 dynamic decision domain update rate β 008neighborhood threshold nt 5 and the remaining param-eters are analyzed in Section 44

41 Data Preprocessing and Indicator System ConstructionRenrendai platform is one of the earliest P2P lending in-formation intermediary service platforms in China whichhas been steadily operating since its establishment It hasbeen ranked in the top 100 Internet companies in Chinatwice Hence we used the P2P lending datasets of Renrendaias the empirical data in this work We obtained more than400000 P2P lending transaction orders from the Renrendaiplatform and 396 993 of them are valid en the outlierorders and 295 589 orders of unsuccessful fundraising areremoved Finally 99 469 orders are available for the keyinfluencing factors selection of P2P lending investment riskAfter the above procedure the retaining dataset is an im-balanced dataset and then the balanced dataset of P2Plending investment risk is achieved using the undersamplingand the stratified sampling methods On the basis of therelevant knowledge of the Internet finance and the researchresults on the key influencing factors of P2P lending in-vestment risk [5 6] its index system is shown in Figure 2We take the default risk of the borrowers as the decisionattributes in this work

42 Experimental Results e proposed key influencingfactors selection method using the combination of FCBGSOand MFD (FCBGSO+MFD) selects the preliminary attri-bute subset from the original dataset of P2P lending orderse four attributes are retained after selection ie they areH1 (interest rate) H4 (number of investors) H7 (age) andH15 (occupation) e FCBGSO+MFD greatly reduces theredundant attributes in the original dataset While there is aquestion to discuss that is whether the retained four at-tributes are significantly related to the default risk We usethe probit regression model to assess the significance be-tween the four attributes and the default risk

We take the default state as the explained variable andregard interest rate number of investors age and occu-pation as the explanatory variables e probit regressionmodel is established as follows

P(default 1) f λSi + ρLi( 1113857 (18)


Inputs the initial parameters the initial data of P2P lending and MFD computing systemOutputs the key influencing factors of P2P lending Bi

prime(1) Initialize the parameters(2) N glowworms are generated randomly and compute their MFD f using equation (14)(3) Xopt⟵maxfitness(X1 X2 XN) fopt⟵max f1 f2 fN1113864 1113865(4) t⟵ 1(5) while tle tmax do(6) for i⟵ 1 to N do(7) Select the objective glowworm Xj in the radial range local-decision domain ri

d of the glowworm Xi(8) Move a step to Xj using equations (6)ndash(9)(9) Update the luciferin li and the radial range local-decision domain ri

d(10) if randlt r1 do(11) N glowworms are divided into three subpopulations according to their MFD(12) Perform the coevolution mechanism to create offspring glowworms and update their parent glowworms(13) end if(14) if randlt r2 do(15) Perform the fireworks evolution strategy to create new glowworms and update the current glowworm(16) end if(17) end for(18) Xopt⟵maxfitness(X1 X2 XN) fopt⟵max f1 f2 fN1113864 1113865(19) end while(20) Obtain the preliminary attribute subset B1 which corresponds to Xopt(21) Get the attribute subset B2 by eliminating those attributes that are not significantly related to the default risk in B1 using the probit

regression(22) Form an attribute subset A extracted from the original dataset of P2P lending using the artificial prior knowledge(23) Generate a small and reasonable number of attribute subsets B1prime B2prime Bn

prime by adding the attributes in A into B2(24) Get the classification accuracies by evaluating each subset in B1prime B2prime Bn

prime using ELM(25) Achieve the key influencing factors of P2P lending Bi

prime with the highest classification accuracy(26) return Bi

prime

ALGORITHM 1 e key factors selection approach

Index system of P2P lending investmentrisk key influencing factors selection

Order information

Borrower information

Interest rate H1

Loan amounts H2

Repayment period H3

Number of investors H4

Payment method H5

Credit rating H6

Age H7

Education background H8

Marriage H9

Income level H10

Historical borrowings H11

Numbers of historical overdue H12

House property H13

Car property H14

Occupation H15

Scale of company H16

Order status H17

Figure 2 Index system of P2P lending investment risk key influencing factors selection


where default denotes default risk S indicates explainedvariable and L demonstrates control variable

As reported in Table 1 the regression coefficient ofinterest rate is 00573 and the marginal utility is 00221which reveal that there is a positive significance between theinterest rate and the default risk at 1 significance levelsAge and occupation are also significantly positive at the 1level But the number of investors has no significant impacton the default risk in comparison with other three factorserefore when analyzing the key influencing factors se-lection of P2P lending investment risk H4 should be re-moved and H1 H7 and H15 are retained

Considering that FCBGSO+MFD cannot recognizeand learn the application background lack of activethinking and personal perception we extract the attributeswith a significant impact on default risk using the artificialprior knowledge in this work Credit rating plays an im-portant role in the process of investors making investmentdecisions as illustrated in Table 2 In the P2P lendingindustry investors need to consider on whom the funds areinvested in and the specific amount allocated for eachorder so as to maximize the expected investment incomeand reduce the return risk Credit rating is an importantinput to solve such combinatorial optimization problem soit has important reference value for the key influencingfactors selection of P2P lending investment risk [5 51] Inaddition the borrowerrsquos historical information is a nicecomplement to the credit rating e higher the repaymentrate of historical borrowings on time the lower the ratiobetween historical overdue times and historical borrowingtimes which indicates the borrowers convey a message toinvestors that the borrowers are trusted and welcomed bythe market e lower the default risk perceived by in-vestors the smaller the risk compensation erefore H10(historical borrowings) and H11 (historical overdue times)of borrowers are of great significance in the analysis of keyinfluencing factors selection of P2P lending investment risk[48 49]

In summary the results achieved by the key influencingfactors selection method of P2P lending investment risk areshown in Table 3 e attributes selected by the artificialprior knowledge are H6 H10 and H11 which are added intothe attribute subset (H1 H7 and H15) one by one en asmall and reasonable number of attribute subsets areachieved which are shown in Table 4 We use ELM tocalculate the classification accuracy of each attribute subsetand the subset with the highest accuracy is the key influ-encing factors of P2P lending investment risk Because thehigher the classification accuracy of the subset is the morerelevant between the subsetrsquos attributes and the default risk

e maximal and average classification accuracies ofcombinations 1ndash10 are displayed in Table 4 In Table 4combination 1 is the original dataset combination 2 is thepreliminary attribute subset attained by FCBGSO+MFDcombination 3 is the retaining attributes after removing thenonsignificant correlation variable in combination 2 usingthe probit regression method and combinations 4ndash10 arethe attribute subsets by adding H6 H10 and H11 intocombination 3 one by one

e maximal and average classification accuracies of theattribute subsets (combinations 4ndash10) are markedly higherthan that of combination 2 which indicates the proposedapproach can achieve a better result than theFCBGSO+MFD namely the combination of the artificialintelligence method the traditional statistical method andthe artificial prior knowledge performs better than everysingle one of them After removing H4 in combination 2 bythe probit regression the accuracy of combination 3 isslightly lower than that of combination 2 but the decrease iswithin the acceptable range It implies that H4 is not a keyinfluencing factor of P2P lending investment risk emaximal and average accuracies of combination 9 are higherthan the other combinations erefore H1 H7 H10 H11and H15 in combination 9 are the key influencing factors ofP2P lending investment risk It indicates that the proposedapproach dramatically reduces the redundant attributesekey influencing factors of P2P lending investment risk areexactly achieved which provides high-quality data for theprediction of P2P lending investment risk

43 Comparison Analysis To verify the effectiveness andcredibility of the proposed approach we compare it with thefollowing methods in literatures [19 29 50 52] Literatures[19 50] adopt swarm intelligence algorithms combined withMFD for the key influencing factors selection e literature[29] uses a rough set theory combined with artificial fishswarm algorithm for attribute selection e literature [52]employs the statistical method and the artificial priorknowledge to extract the key influencing factors In Table 5the maximal and average classification accuracies of theproposed approach are superior to that of other algorithmswhich denotes its validity and effectiveness Moreover incomparison with the literatures [19 29 50 52] the maximalclassification accuracies achieved by the proposed approachare increased by 19 percentage points 18 percentage points23 percentage points and 4 percentage points respectivelye average accuracies are raised by 19 percentage points 18percentage points 21 percentage points and 2 percentagepoints respectively Given the above the key influencingfactors selected by the proposed method perform the bestfollowed by literature [19 29 52] and literature [50] is the

Table 1 Regression analysis between different influencing factorsand default risk

Variable names Probit regression equationExplainedvariable(default)

coefficient Pgt |z| dydxInterest rate 00573lowastlowastlowast le0001 00221Number of investors 00007 0402 00003Age 00182lowastlowastlowast 0008 00070Occupation 00495lowastlowastlowast 0004 00191

Persudo R2 0304LR chi2(4) 3367Probgt chi2 00000

lowastlowastlowast lowastlowast and lowast indicate statistical significance at 10 5 and 1 significancelevels respectively


worst It also illustrates that the proposed key influencingfactors selection approach by combining qualitative andquantitative analysis is more reasonable and scientific

44 Parameter Analysis In the proposed selection methodof key influencing factors of P2P lending investment riskFCBGSO is employed as a search strategy To improve theperformance of FCBGSO its main parameters should beanalyzed including iterations population size initial local-decision range and maximal local-decision range

To verify the performance of FCBGSO it is comparedwith GSO [53] IGSO [54] DGSO [55] and BGSO [56] asshown in Figure 3(a) As the iterations increase the MFDdifference curves between attribute subset selected by thefive algorithms and the original dataset of P2P lending godown first and level off (the smaller the MFD difference isthe better the algorithm performs) Additionally the con-vergence speed and precision of FCBGSO are significantlybetter than GSO IGSO DGSO and BGSO We advise to setthe maximum of iterations at 20

In Figure 3(b) with the increasing of population sizethe MFD difference decreases continuously When the sizeof the population reaches 30 the performance of FCBGSO

Table 2 Key influencing factors analysis of P2P lending investment risk achieved by artificial prior knowledge

Attributes Names Explanation

H6 Credit rating

Literatures [5 48] indicate that credit rating canreflect a borrowerrsquos credit status reveal his credit riskand avoid adverse selection in investment Creditrating is an important input for combinatorial

optimization problem to balance investment earningsand return risk which is of great significance to key

influencing factors selection of P2P lendinginvestment risk

H10 Historical borrowings Literatures [49 50] illustrate that the borrowerrsquoshistorical information is an important factor affectingthe investment risk It embodies in the number ofhistorical overdue and historical borrowings e

higher the repayment rate of historical borrowings ontime the lower the ratio between historical overduetimes and historical borrowing times It indicates thatthe borrowers convey a message to investors that theborrowers are trusted and welcomed by the market

and the risk compensation is smaller

H11 Numbers of historical overdue

Table 3 Key influencing factors selection analysis of P2P lending investment risk

Originaldataset

Preliminary influencingfactors

Nonsignificant relevantattributes

Attributes selected by artificialprior knowledge

Number of attributes 17 4 1 3Attribute subsets H1 H2 H17 H1 H4 H7 H15 H4 H6 H10 H11

Table 4 Classification accuracy analysis before and after keyinfluencing factors selection of P2P lending investment risk

Combinations Attribute subsetsClassificationaccuracy ()Max Mean

Combination 1 H1 H2 H17 856250 778227Combination 2 H1 H4 H7 H15 766234 661543Combination 3 H1 H7 H15 745342 657832Combination 4 H1 H6 H7 H15 864198 783466Combination 5 H1 H7 H10 H15 776398 706136Combination 6 H1 H7 H11 H15 893750 795277Combination 7 H1 H6 H7 H10 H15 869565 800076Combination 8 H1 H6 H7 H11 H15 888199 824711Combination 9 H1 H7 H10 H11 H15 931250 839844Combination 10 H1 H6 H7 H10 H11 H15 900621 826736ldquoMaxrdquo and ldquoMeanrdquo respectively indicate the maximal and the averageclassification accuracies of the P2P lending subsets

Table 5 Comparison analysis between the proposed approach andother method

Methods Selected keyinfluencing factors

Reductionrate ()

Classificationaccuracy ()Max Mean

Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844


tends to be stable So the population size should be set at30

Figure 3(c) analyzes the relationship between the initiallocal-decision range and the performance of FCBGSO If theinitial local-decision range is undersize it may affect itsconvergence speed If the initial local-decision range isoversize the algorithm easily traps into local optima Asthere are 17 attributes in the P2P lending dataset the radiusof the initial local-decision range varies from 1 to 17 Whenthe initial local-decision range is 8 the algorithm performs atits best We advise to set the initial local-decision range at 8

Figure 3(d) investigates the relationship between themaximal local-decision range and the performance ofFCBGSO e maximal local-decision range should begreater than or equal to the initial local-decision range sothe range of maximal local-decision range varies from 8 to17 e algorithm achieves the best result when the maximal

local-decision range is 12 or 13 erefore the maximallocal-decision range should be set at 12 or 13

5 Conclusion

To exactly predict the investment risk of P2P lending weneed to scientifically and rationally analyze its key influ-encing factors But existing traditional statistical approachescannot find the exact key influencing factors of the P2Plending investment risk and the attributes achieved byartificial intelligencemethodsmay not be the key influencingfactors of P2P lending investment risk To tackle the aboveissues a key influencing factors selection approach of P2Plending investment risk is proposed using the combinationof FCBGSO MFD probit regression and artificial priorknowledge On one hand the proposed FCBGSOwith a highsearching efficiency combined with MFD tends to perform

0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)

0 2 4 6 8 10 12 14 16 18Initial local-decision range

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)

7 9 11 13 15 17Maximal local-decision range

05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)

Figure 3 Performance impact analysis of FCBGSO with different parameters (a) Iterations (b) Population size (c) Initial local-decisionrange (d) Maximal local-decision range


well when it comes to dealing with the high-dimensionaloriginal dataset of P2P lending and the preliminary attributesubset is achieved On the other hand the nonsignificantrelevant attributes with the default risk in the preliminaryattribute subset are removed using the probit regressionmethod After that a small and reasonable number of at-tribute subsets are attained by combining the retaining at-tributes and the attributes achieved by the artificial priorknowledge e attribute subset with the best accuracyassessed using ELM is efficiently achieved from the attributesubsets namely it is the key influencing factors of P2Plending investment risk Finally the experimental results onthe real P2P lending dataset of Renrendai demonstrate thevalidity and effectiveness of the proposed approach Inaddition the proposed FCBGSO performs better than otherbinary heuristic algorithms with respect to the convergencespeed and precision

In future work we will attempt to use an ensembleclassifier of ELMs with a high classification ability to predictthe investment risk of P2P lending We believe thatpromising results can be achieved which can provide newresearch ideas for the investment risk prediction of P2Plending

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the Anhui Provincial NaturalScience Foundation under grant nos 1908085QG298 and1908085MG232 the National Nature Science Foundation ofChina under grant nos 91546108 and 71490725 the NationalKey Research and Development Plan under grant no2016YFF0202604 the Fundamental Research Funds for theCentral Universities nos JZ2019HGTA0053 and JZ2019HGBZ0128 and the Open Research Fund Program of KeyLaboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology) Ministry ofEducation

References

[1] H Zhang H Zhao Q Liu T Xu E Chen and X HuangldquoFinding potential lenders in P2P lending a hybrid randomwalk approachrdquo Information Sciences vol 432 pp 376ndash3912018

[2] M Herzenstein U M Dholakia and R L Andrews ldquoStra-tegic herding behavior in peer-to-peer loan auctionsrdquo Journalof Interactive Marketing vol 25 no 1 pp 27ndash36 2011

[3] Q Tuo H Zhao and Q Hu ldquoHierarchical feature selectionwith subtree based graph regularizationrdquo Knowledge-BasedSystems vol 163 pp 996ndash1008 2019

[4] M Dash and H Liu ldquoFeature selection for classificationrdquoIntelligent Data Analysis vol 1 no 3 pp 131ndash156 1997

[5] Y Guo W Zhou C Luo C Liu and H Xiong ldquoInstance-based credit risk assessment for investment decisions in P2Plendingrdquo European Journal of Operational Research vol 249no 2 pp 417ndash426 2016

[6] L Larrimore L Jiang J Larrimore D Markowitz andS Gorski ldquoPeer to peer lending the relationship betweenlanguage features trustworthiness and persuasion successrdquoJournal of Applied Communication Research vol 39 no 1pp 19ndash37 2011

[7] J Yao J Chen J Wei et al ldquoe relationship between softinformation in loan titles and online peer-to-peer lendingevidence from RenRenDai platformrdquo Electronic CommerceResearch vol 18 pp 1ndash19 2018

[8] Z Xiao Y Li and K Zhang ldquoVisual analysis of risks in peer-to-peer lending marketrdquo Personal and Ubiquitous Computingvol 22 pp 1ndash14 2018

[9] L Gonzalez and Y K Loureiro ldquoWhen can a photo increasecredit e impact of lender and borrower profiles on onlinepeer-to-peer loansrdquo Journal of Behavioral and ExperimentalFinance vol 2 pp 44ndash58 2014

[10] X Chen B Huang andD Ye ldquoe role of punctuation in P2Plending evidence from Chinardquo Economic Modelling vol 68pp 634ndash643 2018

[11] Z Zhang L Bai Y Liang and E Hancock ldquoJoint hypergraphlearning and sparse regression for feature selectionrdquo PatternRecognition vol 63 pp 291ndash309 2017

[12] J Liu Y Lin M Lin S Wu and J Zhang ldquoFeature selectionbased on quality of informationrdquo Neurocomputing vol 225pp 11ndash22 2017

[13] D Huang and T W S Chow ldquoEffective feature selectionscheme using mutual informationrdquo Neurocomputing vol 63no 1 pp 325ndash343 2005

[14] J Liu Y Lin Y Li W Weng and S Wu ldquoOnline multi-labelstreaming feature selection based on neighborhood roughsetrdquo Pattern Recognition vol 84 pp 273ndash287 2018

[15] A Ferone ldquoFeature selection based on composition of roughsets induced by feature granulationrdquo International Journal ofApproximate Reasoning vol 101 pp 276ndash292 2018

[16] X-Y Luan Z-P Li and T-Z Liu ldquoA novel attribute reductionalgorithm based on rough set and improved artificial fish swarmalgorithmrdquo Neurocomputing vol 174 pp 522ndash529 2016

[17] Y Chen Q Zhu and H Xu ldquoFinding rough set reducts withfish swarm algorithmrdquo Knowledge-Based Systems vol 81pp 22ndash29 2015

[18] K Mukherjee J K Ghosh and R C Mittal ldquoVariogramfractal dimension based features for hyperspectral data di-mensionality reductionrdquo Journal of the Indian Society ofRemote Sensing vol 41 no 2 pp 249ndash258 2013

[19] C Zhang Z Ni L Ni and N Tang ldquoFeature selection methodbased on multi-fractal dimension and harmony search al-gorithm and its applicationrdquo International Journal of SystemsScience vol 47 no 14 pp 3476ndash3486 2016

[20] Z W Ni H W Xiao Z J Wu et al ldquoAttribute selectionmethod based on improved discrete glowworm swarm op-timization and fractal dimensionrdquo Pattern Recognition andArtificial Intelligence vol 26 no 12 pp 1169ndash1178 2013

[21] C A M Lima A L V Coelho R C B Madeo andS M Peres ldquoClassification of electromyography signals usingrelevance vector machines and fractal dimensionrdquo NeuralComputing and Applications vol 27 no 3 pp 791ndash804 2016

[22] H Dong T Li R Ding and J Sun ldquoA novel hybrid geneticalgorithm with granular information for feature selection andoptimizationrdquo Applied Soft Computing vol 65 pp 33ndash462018


[23] S Jadhav H He and K Jenkins ldquoInformation gain directedgenetic algorithm wrapper feature selection for credit ratingrdquoApplied Soft Computing vol 69 pp 541ndash553 2018

[24] H Ghimatgar K Kazemi M S Helfroush and A AarabildquoAn improved feature selection algorithm based on graphclustering and ant colony optimizationrdquo Knowledge-BasedSystems vol 159 pp 270ndash285 2018

[25] S Tabakhi P Moradi and F Akhlaghian ldquoAn unsupervisedfeature selection algorithm based on ant colony optimiza-tionrdquo Engineering Applications of Artificial Intelligencevol 32 pp 112ndash123 2014

[26] YWanMWang Z Ye and X Lai ldquoA feature selectionmethodbased on modified binary coded ant colony optimization al-gorithmrdquo Applied Soft Computing vol 49 pp 248ndash258 2016

[27] P Moradi and M Gholampour ldquoA hybrid particle swarmoptimization for feature subset selection by integrating a novellocal search strategyrdquo Applied Soft Computing vol 43pp 117ndash130 2016

[28] B Xue M Zhang and W N Browne ldquoParticle swarm op-timisation for feature selection in classification novel initi-alisation and updating mechanismsrdquo Applied Soft Computingvol 18 pp 261ndash276 2014

[29] Y Chen Z Zeng and J Lu ldquoNeighborhood rough set re-duction with fish swarm algorithmrdquo Soft Computing vol 21no 23 pp 6907ndash6918 2017

[30] X Zhu Z Ni L Ni F Jin M Cheng and J Li ldquoImproveddiscrete artificial fish swarm algorithm combined with margindistance minimization for ensemble pruningrdquo Computers ampIndustrial Engineering vol 128 pp 32ndash46 2019

[31] X Zhu Z NiM Cheng F Jin J Li andGWeckman ldquoSelectiveensemble based on extreme learning machine and improveddiscrete artificial fish swarm algorithm for haze forecastrdquoAppliedIntelligence vol 48 no 7 pp 1757ndash1775 2018

[32] X Chen Y Zhou Z Tang and Q Luo ldquoA hybrid algorithmcombining glowworm swarm optimization and complete 2-opt algorithm for spherical travelling salesman problemsrdquoApplied Soft Computing vol 58 pp 104ndash114 2017

[33] R Karthikeyan and P Alli ldquoFeature selection and parametersoptimization of support vector machines based on hybridglowworm swarm optimization for classification of diabetic ret-inopathyrdquo Journal of Medical Systems vol 42 no 10 p 195 2018

[34] K N Krishnanand and D Ghose ldquoGlowworm swarm opti-misation a new method for optimising multi-modal func-tionsrdquo International Journal of Computational IntelligenceStudies vol 1 no 1 pp 93ndash119 2009

[35] K N Krishnanand and D Ghose ldquoGlowworm swarm opti-mization for simultaneous capture of multiple local optima ofmultimodal functionsrdquo Swarm Intelligence vol 3 no 2pp 87ndash124 2009

[36] K N Krishnanand and D Ghose ldquoGlowworm swarm basedoptimization algorithm for multimodal functions with col-lective robotics applicationsrdquo Multiagent and Grid Systemsvol 2 no 3 pp 209ndash222 2006

[37] H Cui J Feng J Guo and T Wang ldquoA novel single mul-tiplicative neuron model trained by an improved glowwormswarm optimization algorithm for time series predictionrdquoKnowledge-Based Systems vol 88 pp 195ndash209 2015

[38] B Wu C Qian W Ni and S Fan ldquoe improvement ofglowworm swarm optimization for continuous optimizationproblemsrdquo Expert Systems with Applications vol 39 no 7pp 6335ndash6342 2012

[39] M Taherkhani and R Safabakhsh ldquoA novel stability-basedadaptive inertia weight for particle swarm optimizationrdquoApplied Soft Computing vol 38 pp 281ndash295 2016

[40] C Gan W Cao M Wu and X Chen ldquoA new bat algorithmbased on iterative local search and stochastic inertia weightrdquoExpert Systems with Applications vol 104 pp 202ndash212 2018

[41] H T Liang and F H Kang ldquoAdaptive mutation particleswarm algorithm with dynamic nonlinear changed inertiaweightrdquo Optik vol 127 no 19 pp 8036ndash8042 2016

[42] R Cheng Y Bai Y Zhao X Tan and T Xu ldquoImproved fireworksalgorithm with information exchange for function optimizationrdquoKnowledge-Based Systems vol 163 no 1 pp 82ndash90 2019

[43] B B Mandelbrot and J A Wheeler ldquoe fractal geometry ofnaturerdquo American Journal of Physics vol 51 no 3pp 286-287 1983

[44] C TrainaJr A Traina L Wu et al ldquoFast feature selectionusing fractal dimensionrdquo Journal of Information and DataManagement vol 1 no 1 pp 158ndash171 2000

[45] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquo Neurocomputing vol 70no 1ndash3 pp 489ndash501 2006

[46] Y Cai X Liu Y Zhang and Z Cai ldquoHierarchical ensemble ofextreme learning machinerdquo Pattern Recognition Lettersvol 116 pp 101ndash106 2018

[47] X Li W Mao andW Jiang ldquoMultiple-kernel-learning-basedextreme learning machine for classification designrdquo NeuralComputing and Applications vol 27 no 1 pp 175ndash184 2016

[48] H Yum B Lee and M Chae ldquoFrom the wisdom of crowds tomy own judgment in microfinance through online peer-to-peer lending platformsrdquo Electronic Commerce Research andApplications vol 11 no 5 pp 469ndash483 2012

[49] K Xie Z Mao and J Wu ldquoLearning from peers the effect ofsales history disclosure on peer-to-peer short-term rentalpurchasesrdquo International Journal of Hospitality Managementvol 76 pp 173ndash183 2019

[50] Y J Lu Z W Ni X H Zhu et al ldquoAttribute reductionmethod based on MapReduce-based improved discreteglowworm swarm algorithm and multi-fractal dimensionrdquoPattern Recognition and Artificial Intelligence vol 31 no 6pp 537ndash547 2018

[51] C Serrano-Cinca and B Gutierrez-Nieto ldquoe use of profitscoring as an alternative to credit scoring systems in peer-to-peer (P2P) lendingrdquo Decision Support Systems vol 89pp 113ndash122 2016

[52] J-T Han Q Chen J-G Liu X-L Luo and W Fan ldquoepersuasion of borrowersrsquo voluntary information in peer topeer lending an empirical study based on elaboration like-lihood modelrdquo Computers in Human Behavior vol 78pp 200ndash214 2018

[53] M Marinaki and Y Marinakis ldquoA glowworm swarm opti-mization algorithm for the vehicle routing problem withstochastic demandsrdquo Expert Systems with Applicationsvol 46 pp 145ndash163 2016

[54] Y Chen S Wang W Han Y Xiong W Wang and L Tong ldquoAnew air pollution source identification method based on remotelysensed aerosol and improved glowworm swarm optimizationrdquoIEEE Journal of Selected Topics in Applied Earth Observations andRemote Sensing vol 10 no 8 pp 3454ndash3464 2017

[55] Y Q Zhou Z X Huang and H X Liu ldquoDiscrete glowwormswarm optimization algorithm for TSP problemrdquo ActaElectronica Sinica vol 40 no 6 pp 1164ndash1170 2012

[56] M Li X Wang Y Gong Y Liu and C Jiang ldquoBinaryglowworm swarm optimization for unit commitmentrdquoJournal of Modern Power Systems and Clean Energy vol 2no 4 pp 357ndash365 2014


Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

ldquopromoting developmentmdashstandardizing developmentmdashbeing vigilant of riskrdquo to the ldquoimproving Internet financialsupervisionrdquo in 2018 indicates that the standardizationcontrol of Internet financial investment risk is imperativeerefore it is urgent to explore the investment risk of P2Plending To research the investment risk we should analyzethe key influencing factors of P2P lending investment riskwhich can provide high-quality data for the prediction ofP2P lending investment risk

A key influencing factors selection approach for P2Plending investment risk is essential to reduce irrelevant attri-butes with the investment risk in an original dataset of P2Plending and retain key influencing factors In fact there is a largeamount of noisy or irrelevant features with investment risk inthe real datasets of P2P lending Existing key influencing factorsselection approaches usually use traditional statistical methodsand attribute selection algorithms based on artificial intelligence[3 4] e statistical methods are commonly used in the se-lection of key influencing factors of P2P lending investmentrisk while there is no application of artificial intelligencemethods at least to our knowledge e traditional statisticalmethods are only limited to the discussion of the impact of asingle factor on the borrower for the order default risk but itignores the fusion and the crossover of multiple informationFor instance the credit rating of each loan has an importantimpact on investment risk which is presented by Guo et al [5]Larrimore et al examined the relationship between language useand investor decision-making [6] e soft information in loantitles has a significant influence on whether the loan is suc-cessful e results also suggest that investors do not investblindly based on returns [7] Xiao et al proposed a visualanalysis method which analyzes and detects risk in P2P lendingdeals [8] Perceived age of P2P lending orders shows a strongsignal of ability and experience and more mature perceived ageis more attractive to investors [9] Chen et al investigated theamount of punctuation used in loan descriptions can influencethe investment default risk using data from Renrendai (one ofthe largest P2P lending platforms in China) [10] To sumup thetraditional statistical methods such as regression analysis havesmall calculations and simple operations when they analyze theinfluencing factors of P2P lending investment risk

For feature selection based on artificial intelligence there aretwomain points one is the evaluation criterion selection and theother one is the search strategy With respect to evaluationcriterion various evaluation methods are used to evaluatefeature subsets Different evaluation methods have great re-lationship with the optimal subset For example informationtheory [11ndash13] distance analysis [4] rough sets [14ndash17] andfractal dimension [18ndash20] Fractal dimension is treated as anevaluation criterion which attracts many scholarsrsquo attentions Ithas two advantages [21] on one hand the number of an optimalfeature subset can be determined by calculating its fractal di-mension which can dramatically reduce computationalamount on the other hand the fractal dimension performs wellwhen it comes to solving high-dimensional datasets and non-linear problems Most existing feature selection approachesbased on fractal dimension use only a single fractal dimensionwhich may not precisely describe the original datasets [20]because of their complicated distribution In contrast

multifractal dimension (MFD) can describe the distribution ofdataset in different aspects [19] which is regarded as theevaluation criterion of feature subsets in this work In regard tosearching strategy finding an optimal feature subset of anoriginal dataset is a combinatorial optimization problem [17]erefore heuristic algorithms provide good searching strate-gies for the feature selection methods for example geneticalgorithm (GA) [22 23] ant colony optimization (ACO)[24ndash26] particle swarm optimization (PSO) [27 28] and ar-tificial fish swarm algorithm (AFSA) [29] However the com-plex coding process of GA is hard to be implemented [30 31]ACO has the disadvantages of the blindness search in the earlystage slow convergence speed and huge computing resourceconsumption PSO easily traps into local optimal solution[30 31] AFSAhas the weaknesses of lack of population diversityand slow convergence rate in the later stage In contrastglowworm swarm optimization (GSO) has the advantages ofsimplicity of implementation strong robustness and good andfast global convergence [32] which can be used as a searchingstrategy for solving a feature selection problem [33]We attemptto propose a fireworks coevolution binary glowworm swarmoptimization (FCBGSO) as the searching strategy in this work

Based on the above analysis first and foremost the tra-ditional statistical methods cannot solve the high-dimensionalnonlinear problem and the analysis is one-sided so it is dif-ficult to exactly analyze the key influencing factors of the P2Plending investment risk In addition the artificial intelligencemethods perform well when it comes to coping with high-dimensional and nonlinear datasets but it cannot recognizeand learn the application background lack of active thinkingand personal perception and the selected attributes may not bethe key influencing factors of P2P lending investment riskerefore we proposed a novel approach to find the keyinfluencing factors of P2P lending investment risk whichcombines MFD FCBGSO the probit regression and the ar-tificial prior knowledgeemission is attained in four steps inthe first step we take the proposed FCBGSO as a searchstrategy and treat MFD as an evaluation criterion for featuresubsets en the preliminary attribute subset extracted fromthe original dataset of P2P lending is attained using thecombination of FCBGSO and MFD In the second step thenonsignificant relevant attributes with the default risk areremoved from the preliminary subset using the probit re-gression In the third step a small and reasonable number ofattribute subsets are achieved by combining the retaining at-tributes after removing and the attributes obtained by theartificial prior knowledge In the final step considering theadvantages of extreme learning machine (ELM) such as goodgeneralization ability and the extremely fast learning speedELM is used to assess the classification accuracies of thesesubsets and the attribute subset with the best accuracy is thekey influencing factors of P2P lending investment risk

e contributions of the proposed approach are pre-sented as follows

(1) A novel approach for key influencing factors selec-tion of P2P lending investment risk is proposedusing the combination of FCBGSO MFD the probitregression and the artificial prior knowledge















lt rid(t) li(t)lt lj(t)1113882 1113883

(2)



(3)


d lt rs




Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (4)





111386811138681113868111386811138681113868111386811138681113872 11138731113966 11139671113966 1113967

(5)




(6)






Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (7)



0 else

⎧⎪⎨

⎪⎩(8)

S xi( 1113857 1

1 + exp minus xi( 1113857 (9)




If randlt μ1 then

XEAprime (t) round

12


XEAPrime

(t) round12


XEBprime (t) round

12


XEBPrime

(t) round12


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


prime (t) XEAPrime




XEAPrime





If randlt μ2 then



(11)



r ri

d times e

2

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (12)










Dq

limr⟶0

1q minus 1

timeslog1113936 p

qi

log r qne 1

limr⟶0

logpi 1113936 pi

log r q 1

r isin r1 r21113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)





f

1113944q


1113971

(14)




1113944

L

i1bigi xj1113872 1113873 1113944

L

i1big ωiji + bi( 1113857 yi (15)



Hβ Y (16)

where H



⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

NtimesL

Y

yT1⋮yT

N

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ntimesm

and β

βT1⋮βT

L

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ltimesm



PA PBPE


Crossover

Subpopulation layer

Competitive

mechanism

P (t) P (t + 1)

Population

segmentation

Crossover





β HdaggerT (17)






1113969 q 2 3 4 5 6




prime




















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018





















lt rid(t) li(t)lt lj(t)1113882 1113883

(2)



(3)


d lt rs




Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (4)





111386811138681113868111386811138681113868111386811138681113872 11138731113966 11139671113966 1113967

(5)




(6)






Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (7)



0 else

⎧⎪⎨

⎪⎩(8)

S xi( 1113857 1

1 + exp minus xi( 1113857 (9)




If randlt μ1 then

XEAprime (t) round

12


XEAPrime

(t) round12


XEBprime (t) round

12


XEBPrime

(t) round12


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


prime (t) XEAPrime




XEAPrime





If randlt μ2 then



(11)



r ri

d times e

2

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (12)










Dq

limr⟶0

1q minus 1

timeslog1113936 p

qi

log r qne 1

limr⟶0

logpi 1113936 pi

log r q 1

r isin r1 r21113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)





f

1113944q


1113971

(14)




1113944

L

i1bigi xj1113872 1113873 1113944

L

i1big ωiji + bi( 1113857 yi (15)



Hβ Y (16)

where H



⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

NtimesL

Y

yT1⋮yT

N

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ntimesm

and β

βT1⋮βT

L

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ltimesm



PA PBPE


Crossover

Subpopulation layer

Competitive

mechanism

P (t) P (t + 1)

Population

segmentation

Crossover





β HdaggerT (17)






1113969 q 2 3 4 5 6




prime




















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018











Xj(t) minus Xi(t)

⎛⎝ ⎞⎠ (7)



0 else

⎧⎪⎨

⎪⎩(8)

S xi( 1113857 1

1 + exp minus xi( 1113857 (9)




If randlt μ1 then

XEAprime (t) round

12


XEAPrime

(t) round12


XEBprime (t) round

12


XEBPrime

(t) round12


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


prime (t) XEAPrime




XEAPrime





If randlt μ2 then



(11)



r ri

d times e

2

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (12)










Dq

limr⟶0

1q minus 1

timeslog1113936 p

qi

log r qne 1

limr⟶0

logpi 1113936 pi

log r q 1

r isin r1 r21113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)





f

1113944q


1113971

(14)




1113944

L

i1bigi xj1113872 1113873 1113944

L

i1big ωiji + bi( 1113857 yi (15)



Hβ Y (16)

where H



⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

NtimesL

Y

yT1⋮yT

N

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ntimesm

and β

βT1⋮βT

L

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ltimesm



PA PBPE


Crossover

Subpopulation layer

Competitive

mechanism

P (t) P (t + 1)

Population

segmentation

Crossover





β HdaggerT (17)






1113969 q 2 3 4 5 6




prime




















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018











Dq

limr⟶0

1q minus 1

timeslog1113936 p

qi

log r qne 1

limr⟶0

logpi 1113936 pi

log r q 1

r isin r1 r21113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)





f

1113944q


1113971

(14)




1113944

L

i1bigi xj1113872 1113873 1113944

L

i1big ωiji + bi( 1113857 yi (15)



Hβ Y (16)

where H



⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

NtimesL

Y

yT1⋮yT

N

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ntimesm

and β

βT1⋮βT

L

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

Ltimesm



PA PBPE


Crossover

Subpopulation layer

Competitive

mechanism

P (t) P (t + 1)

Population

segmentation

Crossover





β HdaggerT (17)






1113969 q 2 3 4 5 6




prime




















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018










β HdaggerT (17)






1113969 q 2 3 4 5 6




prime




















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018
















prime



Order information


Interest rate H1

Loan amounts H2

Repayment period H3


Payment method H5

Credit rating H6

Age H7


Marriage H9

Income level H10



House property H13

Car property H14

Occupation H15


Order status H17






















H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018



























H6 Credit rating









Originaldataset










Reductionrate ()


Literature[19] H1 H3 H4 H7 7647 741290 649641

Literature[29] H10 H12 H13 8235 750000 659587

Literature[50] H1 H4 H7 H16 7647 706250 626507

Literature[52] H1 H2 H3 H6 7647 887500 819134

Proposedmethod

H1 H7 H10 H11H15

7059 931250 839844






5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018












5 Conclusion


0 10 20 30 40 50 60 70 80 90 100Iterations

05

1

15

2

25

3

35D

iffer

ence

of m

ultif

ract

al d

imen

sion

FCBGSOIGSOBGSO

DGSOGSO

(a)

0 6 12 18 24 30 36 42 48 54 60Population size

0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n(b)


0

05

1

15

2

25

3

Diff

eren

ce o

f mul

tifra

ctal

dim

ensio

n

(c)


05

1

15

2D

iffer

ence

of m

ultif

ract

al d

imen

sion

(d)





Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018










Data Availability




Acknowledgments


References


































































Journal of












Journal of







Volume 2018






Volume 2018


















































Journal of












Journal of







Volume 2018






Volume 2018








a novel key influencing factors selection approach of p2p

Documents