Tracking the Dynamics in Crowdfunding

KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

Hongke Zhao, Hefu Zhang Yong Ge Qi Liu, Enhong Chen∗ Anhui Province Key Laboratory of Eller College of Management, Anhui Province Key Laboratory of Big Data Analysis and Application, University of Arizona Big Data Analysis and Application, University of Science and Technology [email protected] University of Science and Technology of China of China {zhhk,zhf2011}@mail.ustc.edu.cn {qiliuql,cheneh}@ustc.edu.cn Huayu Li Le Wu College of Computing and Informatics, School of Computer and Information, UNC Charloe Hefei University of Technology [email protected] [email protected]

ABSTRACT Perks Backers Crowdfunding is an emerging Internet fundraising mechanism by $49,USD raising monetary contributions from the crowd for projects or ventures. In these platforms, the dynamics, i.e., daily funding amount $70,USD on campaigns and perks (backing options with rewards), are the $70,USD most concerned issue for creators, backers and platforms. However, tracking the dynamics in crowdfunding is very challenging and still $70,USD under-explored. To that end, in this paper, we present a focused study on this important problem. A special goal is to forecast the $49,USD funding amount for a given campaign and its perks in the future days. Specically, we formalize the dynamics in crowdfunding as Figure 1: An example of raising-money campaign. campaign level perk level a hierarchical time series, i.e., and . Spe- 1 INTRODUCTION cic to each level, we develop a special regression by modeling the decision making process of the crowd (visitors and backing Crowdfunding, as a particular form of crowdsourcing, is the prac- probability) and exploring various factors that impact the decision; tice of funding a project or venture by raising monetary contribu- on this basis, an enhanced switching regression is proposed at each tions from a large number of people. Recent years have witnessed level to address the heterogeneity of funding sequences. Further, the rapid development of crowdfunding platforms, such as Kick- 1 2 we employ a revision matrix to combine the two-level base forecasts starter.com , Indiegogo.com . In 2015, it was estimated by Forbes for the nal forecasting. We conduct extensive experiments on a that over US $34 billion were raised worldwide in this way, com- real-world crowdfunding data collected from Indiegogo.com. e pared with that the venture capital industry invests $30 billion on experimental results clearly demonstrate the eectiveness of our average each year [3]. approaches on tracking the dynamics in crowdfunding. As the most popular type of crowdfunding, reward-based platforms (e.g., Indiegogo.com) enable people to create projects for KEYWORDS raising money they need, in return for “rewards” (oen vowing future products). When an individual (or a team) wants to raise Crowdfunding, Dynamics, Hierarchical time series money on these platforms, she will create a campaign for her project. ACM Reference format: Figure 1 shows the snapshot for one raising-money campaign on Hongke Zhao, Hefu Zhang, Yong Ge, Qi Liu, Enhong Chen, Huayu Li, Indiegogo.com. From the campaign page, we can see some basic and Le Wu. 2017. Tracking the Dynamics in Crowdfunding. In Proceedings properties of this campaign, e.g., creator, goal, story and also the of KDD’17, August 13-17, 2017, Halifax, NS, Canada., 10 pages. dynamic funding progress, e.g., funded/remaining amount, remain- DOI: hp://dx.doi.org/10.1145/3097983.3098030 ing days. A campaign oen sets several (e.g., 10) types of “rewards” (i.e., perks) with dierent prices, thus backers could make dierent ∗e corresponding author. monetary contributions by selecting dierent perks. e funding sequence is shown in the green rectangle of Figure 1, which is indeed Permission to make digital or hard copies of all or part of this work for personal or a two-level time series, i.e., the dynamic of funding amount on perks classroom use is granted without fee provided that copies are not made or distributed and dynamic of summarized-funding amount on this campaign. for prot or commercial advantage and that copies bear this notice and the full citation In the literature, there are a number of studies on crowdfund- on the rst page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permied. To copy otherwise, or republish, ing [4, 27, 29]. Most of these existing works focus on predicting to post on servers or to redistribute to lists, requires prior specic permission and/or a the campaign success, i.e., reaching the xed funding goals or fee. Request permissions from [email protected]. KDD’17, August 13-17, 2017, Halifax, NS, Canada. 1hps://www.kickstarter.com © 2017 ACM. 978-1-4503-4887-4/17/08...$15.00 2hps://www.indiegogo.com DOI: hp://dx.doi.org/10.1145/3097983.3098030

625 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

not [22, 27, 29], with small-scale datasets. However, many plat- heterogeneity of dynamics among dierent campaigns, perks forms, such as Indiegogo.com, encourage the “exible goal” instead and dierent funding phases. of the “xed goal” [10], where the success of a campaign is no • We develop a novel two-layer framework that could capture longer a big concern of creators. In fact, for creators, backers and the intrinsic relationship between campaign-level dynamics and platform operators, they all want to understand and forecast the perk-level dynamics, and employ a revision matrix to combine dynamics of campaigns and perks every day, rather than just pre- the base forecasts at two levels for achieving beer nal fore- dict the nal funding results. Specically, successful forecasting of casting of dynamics. the dynamics could benet all three parties: (1) creators can update • We conduct extensive experiments to validate the eectiveness of their campaigns and adjust the perk seings in time based on the our method by comparing with several state-of-the-art methods, dynamics; (2) backers can make beer decisions according to the and report some interesting ndings. current popularities and future dynamics; (3) platform operators can provide beer services, such as management and recommendation of campaigns based on the dynamics. Unfortunately, less eort 2 RELATED WORK has been made towards this goal. To this end, in this paper, we e related work can be grouped into two categories, i.e., the work propose a focused study on tracking and forecasting the dynamics on crowdfunding and the studies on time series forecasting. in crowdfunding in a holistic view. To the best of our knowledge, this is the rst aempt in this area. 2.1 Crowdfunding However, it is a very challenging task. First, there are hierarchical dynamics in longitudinal crowdfunding data, i.e., multiple time Since crowdfunding is a recently emerging market, many prob- series of funding amount for a given campaign and its multiple lems are still under-explored in the literature. In the past, some perks. How to model the hierarchical dynamics is a nontrivial prior studies focused on an important issue: predicting the funding problem. Second, funding dynamics are potentially aected by the results, i.e., success or failure of a campaign, and identifying the visiting crowd’s decision making and various factors, such as social inuence factors [14, 22, 27]. For example, to predict the success features, prices, and time. To track and forecast the dynamics, how or failure of campaigns and also estimate the time of success, [22] to model the eects of these factors in the decision making of crowd formulated the campaign success prediction as a survival analysis is very challenging. At last, the dynamics vary a lot among dierent problem and applied the censored regression approach where one campaigns, perks, and even dierent funding phases. us, how to could perform regression in the presence of partial information. address such heterogeneity is also dicult. Lu et al. [27] inferred the impacts of social media on crowdfund- To conduct this study, we rst collect massive real-world crowd- ing and found the social features could help predict the success funding data with detailed daily transaction information from In- rate of project. Mitra and Gilbert [28] explored the factors which diegogo.com 3. Aer carefully exploring the data, we identify im- lead to successfully funding a crowdfunding project. ey found portant factors that aect the decision making of crowd and the the language used in the project has surprisingly predictive power dynamics of crowdfunding, and construct useful features at both accounting for 58.56% of the variance around successful funding. campaign and perk levels. To address the hierarchy of crowdfund- Besides the studies of predicting nal funding results, some re- ing dynamics, we propose a two-layer framework for modeling the searchers studied the fundraising dynamics for campaigns in their dynamics at both campaign and perk levels. Specic to each level, complete funding durations [19]. However, these studies are mainly we rst develop a single regression model to capture the impacts of from the statistical and empirical perspectives to understand the various factors (e.g., nancial features, social features, time) on the backers’ behaviors, and are still lack of deep and quantitative explo- decision making of the crowd (i.e., visitors and backing probability). rations. In fact, creators, backers and platform operators all want to Further, to address the aforementioned heterogeneity of funding se- track the dynamics of both campaigns and perks every day, rather quences, we propose an enhanced switching regression at each level. than just to predict their nal funding results. Unfortunately, less en we employ a revision matrix to combine the two-level base eort has been made towards this goal. forecasts in order to achieve an optimal nal forecasting. Finally, Besides the task of predicting success, a few studies have ex- we evaluate our approaches by conducting extensive experiments plored the other problems in crowdfunding or the similar service, with our collected data. e experimental results clearly demon- e.g., P2P lending, from data mining perspectives, such as campaign strate the eectiveness of our proposed approaches for tracking recommendations [30], loan recommendations [36, 38], investor and forecasting the dynamics in crowdfunding. Specically, the (backer) recommendations [2], market state modeling [37] and contributions of this paper can be summarized as follows: backing motivation classications [26]. • We propose a focused study on tracking and forecasting the 2.2 Time Series Forecasting dynamics of crowdfunding at both campaign and perk levels using a unique dataset collected from Indiegogo.com. In the literature, time series forecasting has been widely studied [5, 6]. Models for time series forecasting have many forms • We develop a special regression at each level for dynamics in and can describe dierent stochastic processes. For example, the crowdfunding by modeling the funding process. Further, we autoregressive model [1, 8] and vector autoregression model [18] introduce an enhanced switching regression to beer handle the assume that the current value linearly depends on the previous values. However, conventional autoregressive models only include 3e data is publicly available in hp://home.ustc.edu.cn/%7Ezhhk/DataSets.html the response variables without exogenous variables. To address

626 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

Table 1: A Summary of data. Entity Amount Campaign 14,143 (13,227 exible, 916 xed Campaigns) Campaign-level SR Perk-level SR Test Data Perks f^c(.) f^p(.) Perk 83,450 CampaignA 27,721 Creators (Belong to 14,137 Teams), Member SR+R Output 211,812 Backers

Contribution 1,862,097 Counts, $ 206,151,977 Amount Training Data Campaign-level SWR Perk-level SWR Comment 172,824 Comments, 68,189 Replies Revision Matrix the non-linear dependency of input variables and output variables, f^c f^p R SWR+R Output some other models were applied, such as support vector machine [7] and neural networks [33, 34]. In particular, with the development of deep learning in recent years, many studies found that the re- Figure 2: Overview of our solution. current neural network (RNN) can provide satisfactory results for nonstationary time series forecasting [9, 13]. However, most of for both campaigns and perks, and also construct various features these methods work as a black box, and are lack of explanatory. including both static and time-varying ones. Indeed, developing a forecasting model could not only predict the funding amount but also interpret the decision making of the 3.2 Constructed Features crowd and the factors impacting the decision, which is very needed From this dataset, we construct 24 features for campaigns and 30 for crowdfunding. Unfortunately, lile eort has been made to features for perks. A summary of them is shown in Table 2. track and forecast the dynamics of crowdfunding in this way. 3.2.1 Campaign Features. e campaign features can be grouped into 4 categories, i.e., campaign prole, social media, perk summary 3 PRELIMINARIES and funding progress. e features of campaign prole and social In this section, we rst introduce the working mechanism of In- media are extracted from campaign entities. e features of perk diegogo.com, and also the collected dataset from this website. en summary, i.e., Perk Option, Claimed Num, are extracted from the we introduce the constructed features from the data. corresponding perk entities of a campaign. e features of funding progress and also Available Num are extracted from contribution entities, which are time-varying. 3.1 Indiegogo.com and Dataset ese features are very heterogeneous, including both numer- In crowdfunding services, there are generally three types of ac- ical, categorical data and also text. For consistency, we represent tors: the individual creators or teams who propose the campaigns all features as numerics or numerical vectors [25]. Specically, for to be funded for their ideas, the visiting individuals (i.e., poten- the categorical data with less than 10 dimensions, such as Type, tial backers) who look for campaigns to support, and a platform Owner Type, Currency, and Verication, we adopt the one-hot en- (e.g., Indiegogo.com) that brings these two parties together [12]. coding [36], i.e., converting a categorical variable with n categories Based on the dierent types of rewards for backers, crowdfund- into a n-dimensional binary vector, in which only the value in the ing platforms can be mainly classied into four categories, i.e., corresponding category is set to one and the other values are set donation-based, reward-based, equity-based and lending-based plat- to zero. For the categorical data with more than 10 dimensions, forms [21]. As the most popular type, reward-based platforms such as Category and geo-spatial data, i.e., Country, City, we use follow a mode in which a backer’s primary objective for funding the count encoding, i.e., replacing the variables by the respective is to gain a non-nancial reward, i.e., perk in Indiegogo.com. In- count frequencies of the variables in the dataset. For text data, such diegogo.com also encourages the “exible goal” instead of the “xed as Title, Story, we adopt a doc2vec tool [20] to convert them into goal” and “all-or-nothing” rule [10, 36, 37] for campaigns, which is numerical vectors. Specically, the numerical vector for title is very dierent from other common crowdfunding platforms, such 10-dimensional and the vector for story is 100-dimensional. as Kickstarter.com [2, 14, 22, 27, 30]. at is to say, for one exible 3.2.2 Perk Features. campaign, it is not necessary to raise a xed amount of money in e perk features can be grouped into three the declared durations in order to make this campaign eective. categories, i.e., perk prole, funding progress and the features from Even a less amount of fund (than the exible goal) is collected its campaign. In particular, the funding dynamic of a perk is highly eventually, the funding transaction of this campaign will still be related to its campaign features. us, we also include the features eective. Also, one campaign can continue collecting fund aer of the corresponding campaign as a part of each perk’s feature. the exible goal is reached or over time. In other words, for the We preprocess them in the same way as introduced for campaigns, exible-goal campaigns in Indiegogo.com, the declared goals and except the perk description is represented by a 10-dimensional durations are only for informational purposes. numerical vector. Indiegogo data contains a variety of heterogeneous information 4 PROBLEM AND METHOD OVERVIEW about all entities as shown in Table 1. Entities of each type include various information in the form of unstructured data, such as image, In this section, we rst introduce the problem of tracking the dy- video, and text, and structured data, such as geo-spatial, numerical, namics in crowdfunding, and then overview our proposed method. categorical, and ordinal data. From these entities, we can obtain For beer illustration, Table 3 lists the mathematical notations used the hierarchical dynamics (e.g., daily funding amount time series) in this paper.

627 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

Table 2: e description of features. Feature level Category Feature Type Feature Description Title Title of the campaign Story Detailed description of the campaign in text Team Size Number of members in the crowdfunding team Type Flexible or xed goal Duration Declared funding duration of the campaign Campaign Goal Amount the campaign wants to fund Prole Country Country of the creator City City of the creator Category Category of the campaign, such as Technology, Education Static Owner Type Purpose of the campaign, such as business, individual, non-prot Currency Currency for paying the perks, such USD Campaign Image Num Number of images provided by the campaign Feature Video Num Number of videos provided by the campaign Social or Social Exposure Number of exposure places, e.g.,Facebook, Twier, Youtube, website Media Friend Num Number of friends of funding team in Facebook Verication Whether the campaign was veried in Facebook Perk Option Number of perk options Perk Claimed Num Total claimed number of perks Summary Available Num Total available number of perks Backer Num Number of backers who has contributed to the campaign Funded Amount Amount the campaign has collected Funding Time-varying Funded Percentage Percentage the campaign has funded Progress Comment Num Number of comments the campaign received Reply Num Number of replies the creator has made Description Short description of the perk Perk Featured Whether this perk is recommended by the campaign Static Prole Price Unit price of the perk Perk Claimed Num Claimed number of the perk Feature Funding Sales Num Number of perks have sold Time-varying progress Available Num Available number of the perk Campaign - Campaign Features All the features of the campaign which this perk belongs to

Table 3: Mathematical notations. Symbol Size Description Y c (Y p ) I (K ) × T Daily funding amount matrix for I campaigns (K perks), T funding days; B I × T Daily backer number matrix for I campaigns; Xc (Xp ) I (K ) × T × Mc (Mp ) Campaign (perk) covariant/feature tensor, Mc (Mp ) is the length of covariant/feature vector; Zp K × T × J Unobservable cluster tensor for perks, J is the cluster number of perk sequences; f p (.)(f c (.)) 1 Base forecasts in SR for perks (campaigns); p c 0 × p { p . | ∈ { , ..., }} c { c . | 0 ∈ { , ..., 0 }} f (f ) J (J ) 1 Base forecasts in SWR for perks (campaigns), f = fj ( ) j 1 J , f = fj0 ( ) j 1 J ; 2 Ri (Ki + 1) Revision matrix for campaign i and its Ki perks.

4.1 Problem Statement amount sequences, i.e., Y c (i,τ ), B(i,τ ) in previous τ days before t c p For I campaigns with T funding days4, we have the daily funding and their current features X (i, t) and X (ki , t), where τ represents c c (t − τ : t). Please note that, we do not use the previous-days series amount time series Y = (Y (i, t))I ×T , backer number time series c c of funding amount and backer number on perks, i.e., Y p , Bp , as B = (B(i, t))I ×T , and the campaign features X = ((X (i, t))I ×T . Ki represents the number of perks of i-th campaign, and ki ∈ the input variables even though they are available in our data. e {1,..., Ki } represents the ki -th perk of this campaign. For all the K reason is that the time series of funding amount and backer number PI on perks are sparser compared with those on campaigns. More (K = i=1 Ki ) perks, we also have their daily funding amount time p p p p importantly, according to the crowdfunding mechanism, all the series Y = (Y (k, t))K×T , and perk features X = (X (k, t))K×T . Each Y c (i, t) or Y p (k, t) represents the funding amount of i-th backers of perks come from their campaign visitors. e rationality campaign or k-th perk at its t-th funding day. will be demonstrated in the experiments. Formally, the task can be Our goal is to learn a model F(.) which can be used to forecast formulated as: c p the daily funding amount, i.e., Y (i, t + h),Y (ki , t + h), for i-th Y c (i, t + h) campaign and its perks in next h days, when given their funding p Y (1, t + h) c c p  L  = F(Y (i,τ ), B(i,τ ), X (i, t), X (ki , t)) + ϵ, 4  ...  For beer presentation in matrix, we use a notation T to represent the  L   p  funding days for all campaigns though their durations may be dierent. Y (Ki , t + h)      L 

628 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

where ki ∈ {1,..., Ki } and ϵ is the error vector. To forecast the Infected Visitors. e intrinsic objective of crowdfunding is to time series in next h days, we rst focus on predicting the values at aract massive contributions from the “crowd”, thus the propaga- current day t and the estimations in following days t + h can also tion is crucial for a campaign. Crowdfunding mechanism encour- be derived by taking the current estimations as input variables. ages the backers to share their backed campaigns to their friends via virtual social relations, e.g., Facebook, Twier, or real-life rela- 4.2 Method Overview tions, and indeed, backers are also willing to do that. What’s more, Since the dynamics in crowdfunding are two-level time series, we researchers have found that the prior fundings on a campaign have propose a hierarchical model F(.) for fully considering the character- great eects on its dynamics in the following durations [32]. us, istics of hierarchy and making full use of the available information. previous backers inuence the current and following propagation of Specically, F(.) contains the campaign-level base forecasts (i.e., a specic campaign and also its current underlying visitors. Specif- c c p p i f (.), f ), the perk-level base forecasts (i.e., f (.) or f ), and a ically, we model the infected visitors PUt at current time t by the combination of them using a revision matrix R. Figure 2 shows propagation of the backers in previous τ days on campaign i as: the overview of our method. Specically, we rst independently i p T learn the base forecasts for campaigns (gray shapes) and perks PUt = (α ) · B(i,τ ), (1) (white shapes). At each level, we propose two kinds of structures p for the base forecasts, i.e., Single Regression (denoted as SR, f c (.) where α is the coecient vector to weight the propagation inu- and f p (.)) and SWitching Regression (denoted as SWR, f c and ences of backers in previous τ days. f p ) based on the understanding of decision making of the crowd Spontaneous Visitors. Besides the visitors infected by the (visitors and backing probability) and assumptions on funding se- propagation of previous-days backers, there are also some spon- quences. en for a target campaign (purple) and its perks (blue), taneous visitors arriving at any funding days of a campaign. e we use a revision matrix to get the nal results by combining the spontaneously arriving visitors may be aracted by the properties estimations of these two-level forecasts. of a campaign. Specically, we suppose that the spontaneous visi- i tors on campaign i at time t, SUt , follow a Poisson distribution [23] 5 STRUCTURES OF BASE FORECASTS as follows: In this section, we dene the structures of base forecasts: the single i exp(−λi )λi Pois(SU = m|λi ) = , (2) regression model, i.e., f c (.) and f p (.), and the switching regres- t m! sion model, i.e., f c and f p . Specically, we dene the structures where λi is the parameter for mean visiting in a unit time. As of base forecasts by exploring the mechanism of crowdfunding described above, to capture the impacts of time-varying covariants and modeling the decision making of “crowd”. e two-level base of perks, we allow parameter λi to be a function of the time-varying forecasts have the similar forms. us, we detail the structures of campaign covariants Xc (i, t) [23]: perk-level base forecasts, and then directly give the structures of p T c campaign-level base forecasts. λi = (ξ ) · X (i, t), (3)

5.1 Single Regression Model, f p (.), f c (.) where ξ p is the coecient vector to weight the covariants. us, i In SR, we suppose the funding amount time series of campaigns or the spontaneous visitors of a campaign SUt can be computed as: perks can be modeled by a single model. Specically, at perk level, Z ∞ p i i i SR has the form of f (.). In fact, SR can explore the previous-days E(SUt ) = Pois(SUt ) d(SUt ) = λi . (4) funding dynamics and also capture the impacts of time-varying 0 i covariants (perk features) and time by an inbuilt parametric Hazard In summary, we can infer the underlying visitors Ut of campaign function [11, 23]. i at time t by: Dierent from other conventional time series problems, crowdfunding is a nancial service in which a complete funding activity i i i p T p T c Ut = E(PUt + SUt ) = (α ) · B(i,τ ) + (ξ ) · X (i, t). (5) contains two processes, i.e., user visiting and visitor backing. at is, a campaign may obtain more contributions if it can aract fre- Aer modeling the current visitors of one campaign, in the quent visits. Also, not all the visitors will contribute her visiting following, we will introduce the second factor which inuences the campaigns. A visitor of campaign i will contribute to this campaign funding dynamics, i.e., backing probability of selecting a perk. only if her evaluation on this campaign is higher than a threshold. 5.1.2 Backing Probability of Selecting a Perk: g(.). In this study, If so, this visitor will back this campaign by selecting a perk based we explore the Hazard model [11, 23] to approximate the back- on her evaluation and comparison of perks. erefore, in f p (.), we ing probability of crowd, i.e, g(t, x), where x is the abbreviation try to model the funding process by two components, i.e., current of Xp (k , t). Hazard function is widely-used in COX of survival visitors, and backing probability of selecting a perk. i analysis, which is the instantaneous rate of occurrence of the event. 5.1.1 Modeling Visitors. We assume the current visitors of a Specically, we explore the density function, i.e., g(t, x), for the campaign come from two ways: infected by previous backers, and the probability of event. In our study, the event refers to the backing spontaneous visitors. e visitors of a perk are essentially the current behavior [23]. e reason for exploring proportional Hazard to visitors on its campaign, because all users rst access campaigns approximate the backing probability is that Hazard can reect the rather than perks. impacts of both time and features on event which are all important

629 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

in the dynamics of crowdfunding. In survival analysis, the proba- 5.2 Switching Regression Model bility density function can be derived from the denition of Hazard According to our observations, dierent campaigns and perks have model h(t): great heterogeneities, and even for one campaign or perk, its funding dynamic at dierent funding phases may vary a lot. us, P (t ≤ Tb ≤ t + ∆t |Tb ≥ t) g(t) g(t) c p h(t) = lim = = , training a single model, i.e., f (.) or f (.) is inadequate. Also, ∆t→0 ∆t 1 − G(t) S(t) some studies have found that the time series have the clustering where Tb is the random variable which represents the time until characteristics, that is, the sequences in the same cluster have the the event occurs, i.e., backing the campaign by selecting a specic similar growth paern [24]. us, in this subsection, we introduce perk, and g(t),G(t), S(t) are respectively the probability density an enhanced switching regression model, i.e., SWR, based on a function, cumulative distribution function and survivor function of more reasonable assumption, i.e., funding amount sequences of campaigns and perks respectively form dierent clusters in which Tb. Specic to perk ki of campaign i at time t, Hazard function has the following form: sequences have dierent dynamic paerns. We also take the perk- p { p | ∈ { }} level base forecasts f = fj (.) j 1,..., J as examples to intro- p T p p h(t |x) = h0(t) exp((β ) · X (ki , t)), (6) duce SWR, where fj (.) is the base forecast for j-th perk sequence p cluster and J is the number of clusters. fj (.) has the similar form where h0(t) is a baseline function, which is perk independent and p p a function of time. Hazard function can capture the impacts of with f (.) in SR, but each fj (.) has its own parameters. both time and time-varying covariants by the baseline function Besides the observable variables, i.e., Y c ,Y p , B, Xc , Xp , in f p , and the risk proportion. A campaign and its perks share a same we also assume there are some unobservable cluster indicator vari- p p p h0(t) function since they conform a same funding timeline. Term ables, such that Z = (Z (k, t))K×T , where Z (ki , t)) can be p T p exp((β ) X (ki , t)) is the proportional risk associated with the abbreviated as z and z = (z1,..., zJ ). Specically, zj ∈ {0, 1} covariates. e baseline function is arbitrary nonnegative perk- and |z| = 1, where zj = 1 means the funding amount sequence p p independent of time for parameter functions. In our study, we adopt (Y (ki ,τ ),Y (ki , t)) of ki -th perk at time slice t belongs to the j-th a Gompertz distribution form [17, 31]: sequence cluster of perks, and vice versa. at is to say, a funding sequence at a given specic time only belongs to one specic clus- h0(t) = exp (γ0 + γ1t). (7) ter. Please note that, the clustering object is sequence segments rather than complete funding sequences of perks so that a perk Aer dening the form of proportional Hazard model h(t), the may belong to dierent clusters in dierent time slices. us, for density function, i.e., g(t, x), can be derived. e details of deriva- perk ki at time t, we have: tion are shown in Appendix A. In summary, we can get the form of p the base forecast, i.e., f (.), as follows. YJ p p c p p zj p Y (ki , t) = f (B(i,τ ), X (i, t), X (ki , t)|Θ ) + ϵt , (9) p j j Y p (k , t) = f p (B(i,τ ), Xc (i, t), Xp (k , t)|Θp ) + ϵ j=1 i i t L = p T , + p T Xc , |Xp , + p , p L pki ((α ) B(i τ ) (ξ ) (i t))g(t (ki t)) ϵt where Θj are the parameters learned from the sequence segments in j-th cluster. Similarly, we can also get the campaign-level base p p p p c where pki is the unit price of perk ki , Θ = (α , ξ , β ,γ). Pa- forecasts f . rameters Θp can be learned by maximum likelihood estimation or equally least square when the error follows Gaussian distribution: 6 MODEL LEARNING AND FORECAST p I K T In this section, we rst detail the learning process for f , in the X Xi X p c c p 1 p p 2 same way, f (.), f (.), f can also be learned. en, for a given L(Θ ) = arg min (Y (ki , t) − Y (ki , t)) Θp 2 (8) target campaign and its perks, we propose to revise the forecasts i=1 ki =1 t=τ L by an optimization combination of the two-level base forecasts for + λp ||Θp || , 2 the nal forecasting. p where λ is a regularization parameter and ||.||2 denotes the L2 norm, which is used to avoid overing. 6.1 Learning Base Forecasts in SWR p p Now, we have given the specic structure of f (.). Similarly, we Because Zp in f p is unobservable, we can learn Θ and cluster c j dene the structure of base forecast f (.) for campaign level as: the sequence segments simultaneously by an EM-process. Since the clusters are hard restraint, we can achieve learning through c c c c c c Y (i, t) = f (Y (i,τ ), X (i, t)|Θ ) + ϵt two steps, i.e., estimating the cluster variables Zp , optimizing the c T c c T c c c p Zp L = ((α ) Y (i,τ ) + (ξ ) X (i, t))g(t |X (i, t)) + ϵt . parameters Θj with current . p Estimating Zp . Donate Θ (o) as the parameters in o-th iteration. Please note that, in the campaign-level modeling, there is not j In each iteration, we estimate Zp , i.e., let each z = 1 i: a declared price for each campaign. us, for consistency, we use j c the funding amount observation Y (i,τ ) rather than the backer J p p p , c . j = arg min |Y (ki , t) − f 0 (.|Θ 0 (o))|. (10) number observation B(i τ ) in f ( ). j0=1 j j

630 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

p Zp Ki 1 1 ······ 1 Optimizing Θj . Aer estimating , we optimize the current p 1 K -1 -1 ··· -1 L p i parameters Θ (o). In each iteration, the loss function (Θj (o)) is   j  1 -1 Ki -1 ··· -1  1   dened as: Ri =  ...... . Ki +1  ......   . . .  I Ki T J  ···  p 1 X X X X  1 -1 -1 Ki -1  L(Θ (o)) = arg min z (Y p (k , t) − Y p (k , t))2   j p j i i  1 -1 ······ -1 Ki  Θ (o) 2   j i=1 ki =1 t=τ j=1   L   p || p || us, the nal estimations for campaign i and perk ki are: + λj Θj (o) 2. (11) XKi c 1 c p Yf (i, t) = (KiY (i, t) + Y (ki , t)), For optimizing the above function, we adopt the alternating least Ki + 1 k =1 squares (ALS) [39]. ALS is a popular optimization method with L i L 1 X accurate parameter estimation and fast convergence rate, which p c p 0 p Yf (ki , t) = (Y (i, t) − Y (ki , t) + KiY (ki , t)), computes each parameter by xing the other parameters when Ki + 1 0 ki minimizing the object function. Specically, the updating rules for L L L 0 { } L p where ki = 1,...,ki−1,ki+1,..., Ki represent the other perks of some representative parameters in (Θj (o)) are as follows: the target campaign except current perk ki . We can see that, the ∂L ∂L matrix revises the nal estimations by considering both perk-perk p ← p − , p ← p − , αj (o) αj (o) ηα p ξj (o) ξj (o) ηξ p and perks-campaign relations. e revision optimizes the nal ∂α (o) ∂ξ (o) j j estimations especially when the individual base forecasting for ∂L p p ∂L target campaign or perk performs bad. We will empirically examine γ (o) ← γ (o) − ηγ , β (o) ← β (o) − ηβ , ∂γ (o) j j p that in the experiments. ∂βj (o) p p p p 7 EXPERIMENT where Θj (o) = (αj (o), ξj (o),γ (o), βj (o)) are the parameters in o-th iteration, and η = (ηα ,ηξ ,ηγ ,ηβ ) are the learning rates. e In this section, we construct experiments with the collected dataset details of gradients are given in Appendix B. Repeat these two steps to evaluate the performances of our approaches. until convergence. 7.1 Experimental Setup 6.2 Revise Forecasts by Optimal Combination We partition the dataset into subsets based on the declared funding We have learned the campaign-level and perk-level base forecasts, durations of campaigns and construct experiments mainly on two i.e., f c and f p , respectively. Next we introduce how to get the nal subsets whose durations are 30 and 60 days. Specically, for 30-days forecasting for given target campaign i and its Ki perks by combin- campaigns and perks, we construct observations and features in ing the independent estimations of the two-level base forecasts. their duration (30 days) and the following 15 days aer that. Simi- In the literature, researchers have proposed some combination larly, for 60-days campaigns and perks, we construct observations strategies, such as “boom-up” and “top-down” strategies for hi- and features in their durations (60 days) and the following 30 days. erarchical time series data [15]. Specically, boom-up strategies For each subset, we partition the data into a training set and a test aempt to produce forecasts at the lowest level and aggregate them set, i.e., we randomly select 20% elements from Y c as the test set. to the upper levels of the hierarchy, while top-down methods pro- Consequently, the other variables in the corresponding places, e.g., duce forecast at the top level and then disaggregate to the lower B, Xc , Xp , will also be selected. e remaining elements are used levels using proportions. ese two types of strategies are not for training. We process each subset ve times in this way. e suitable for the problem in crowdfunding, because processing base reported results are averaged over ve-round tests. Table 4 shows forecasts at lower (perk) level suers the sparsity while processing one-round data partitioning. base forecasts at campaign level will not consider the relations of perks in a same campaign. To this end, we propose to produce Table 4: Data partitioning. #Training Sequences #Test Sequences independent forecasts at both campaign and perk levels, and then Sub sets use a revision matrix to get the nal estimations. e proof of Campaign Perk Campaign Perk optimality of this combination strategy can be found in [15, 16]. 30 days 8,000 88,663 2,000 23,204 c p p T 60 days 8,000 93,986 2,000 22,984 Specically, we denote (Y (i, t),Y (1, t),...,Y (Ki , t)) asY (i, t) which represent the estimations for target campaign i and its perks L L L D 7.1.1 Comparison Methods. We compare the following meth- at t by the base forecasts. Y (i, t) are the nal estimations for them ods on forecasting the dynamics, i.e., daily funding amount, for aer the revision. at is, H campaigns and perks. Y (i, t) = RiY (i, t), (12) • Switching Regression with Revision (SWR+R): training switching regression models (i.e., f c, f p ) for campaigns and perks H D where Ri is the revision matrix for campaign i and its perks which independently and then using the revision matrix to combine can provide an optimal combination of the independent estimations them for the nal results. Empirically, the cluster numbers for of base forecasts. Specically, Ri has the following form: campaigns and perks are respectively set as 4 and 8.

631 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

900 90 Daily Funding Amount Daily Funding Amount Daily Funding Amount Daily Funding Amount 800 Daily Backer Number 80 Daily Backer Number Daily Backer Number Daily Backer Number 6 0.6 4 0.4

600 60 600 60 3 0.3 4 0.4

400 40 2 0.2 300 30 0.2 2 200 1 20 0.1

10 20 30 40 10 20 30 40 20 40 60 80 20 40 60 80 Funding Days Funding Days Funding Days Funding Days (a) Campaign 30days (b) Perk 30days (c) Campaign 60days (d) Perk 60days Figure 3: Funding series display.

• Switching Regression (SWR): training switching regression Table 5: e running time (seconds). models (i.e., f c, f p ) for campaigns and perks independently. e Methods SWR+R SWR SR+R SR RF AR AVE seings of SWR are the same as those in SWR+R. Training 1,860 1,860 254 254 1.52 9.69 - Test 0.73 0.18 0.59 0.12 0.25 0.09 0.05 • Single Regression with Revision (SR+R): training single regression models (i.e., f c (.), f p (.)) for campaigns and perks inde- their durations. Besides, in the start-up days, the funding amount pendently and then using the revision matrix to combine them is relatively small and grows slowly, while aer the declared dura- for the nal results. tions, the funding time series decays over time. ese inspire us to • Single Regression (SR): training single regression models (i.e., explore the time eect (i.e., h0(t)) and cluster the time series at the f c (.), f p (.)) for campaigns and perks. granularity of sequence segments rather than the complete series of campaigns and perks. • Random Forest (RF): training random forest regressions for campaigns and perks, in which the input variables are the same 7.2.2 Eiciency Results. Table 5 records the running time (sec- as those in SR and SWR. onds) of dierent methods for training and test on all the con- • Autoregressive Model (AR): training autoregressive models [1, structed datasets. We can see that our models need more time than 8] for campaigns and perks using the daily funding observations. others for training. However, in tests, our two-level base forecasts, • Average (AVE): using the averages of funding amount in previ- i.e., SWR and SR, run faster than RF. ous τ days to predict the current funding. In these methods, the 7.2.3 Forecasting Performances. For beer training and forecast- parameters τ are all set as 5. ing, we scaled the time series variables using ln(.) function, i.e., 7.1.2 Evaluation Metrics. To evaluate the forecasting perfor- Y c (i, t) = ln(Y c (i, t) + 1). Figure 4 shows the forecasting performances, here we select two widely-used metrics, i.e., the Root mances with respect to the predicting days, i.e., h. Overall, our Mean Squared Error (RMSE) [34] and Mean Relative Squared Er- methods, i.e., SWR+R, SWR, SR+R, SR and the ensemble method, ror (MRSE) [8] for evaluation. Specically, their denitions are: i.e., RF, perform signicantly beer than AR and AVE which lose s the predicting abilities with the accumulation of errors over time. PN − 2 N Second, in the campaign-level tests, SWR+R performs best; while in i=1(yi yî ) 1 X yî 2 RMSE = , MRSE = ( − 1) , the perk-level tests, SWR performs best. e possible reason is that N N yi i=1 the base forecasts SWR (also SR) predict more accurately for perks, where N is the number of predictions, yi is the i-th real observation i.e., perk-level base forecasts work beer than campaign-level ones value and yî is the corresponding estimated value. (the perk instances for training are much more than campaigns’), so that, aer revising, the performances on campaigns become beer 7.2 Experimental Results while performances on perks turn to a lile worse. Even so, clearly, We rst plot the funding time series and analyze the characteristics, both SWR+R and SWR have the satisfactory performances com- and then report the forecasting results. pared with other methods, e.g., the values of RMSE or MRSE are reduced by more than 50% in most cases. ird, from the compar- 7.2.1 Funding Series Analysis. We mainly have two types of isons of SR and SWR, we can see the eectiveness of clustering for time series observations, daily contributions (backer numbers), and funding sequences. Finally, our methods perform much beer for daily funding amount for both campaigns and perks. e funding perks while AR and AVE have worse results for perks. at is be- time series of campaigns and perks are shown in Figure 3. From cause the time series of perks are much sparser and more unstable these gures, we can see that: 1) the adjacent daily funding amount so that it is more dicult to predict for AR and AVE in which only is highly correlated, so that we exploit the variables in previous the response variables are taken into consideration. Dierently, our c days (e.g., Y (i,τ ) and B(i,τ )) in our approaches; 2) the series of models explore the relations of perks and campaigns so that they both campaigns and perks at dierent funding time have dierent work well for perks. dynamic paerns, e.g., 30-days campaigns and perks have observable peaks at the end of their declared durations, 60-days campaigns 7.2.4 Parameter Eects. We also test the eects of the common and perks have observable peaks at both the end and middle of parameter, i.e., τ , of the corresponding methods. We report the

632 KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada

3 3 3 4

2 2 2

2 RMSE RMSE RMSE RMSE

1 1 1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Predicting Days Predicting Days Predicting Days Predicting Days (a) Campaign 30days (b) Perk 30days (c) Campaign 60days (d) Perk 60days

0.4 0.4 0.4 0.4 SWR+R SWR 0.3 SR+R SR RF AR 0.2 0.2 0.2 AVE MRSE MRSE MRSE 0.2 MRSE

0.1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Predicting Days Predicting Days Predicting Days Predicting Days (e) Campaign 30days (f) Perk 30days (g) Campaign 60days (h) Perk 60days Figure 4: Forecasting performances. results when forecasting the dynamics only in next one days in Anhui Provincial Natural Science Foundation (No.1708085QF140). Figure 5. In most cases, all methods will achieve beer results, Qi Liu gratefully acknowledges the support of the Youth Innovation i.e., smaller RMSE and MRSE, as τ becomes larger. Please note Promotion Association of CAS (No. 2014299). that, in all cases, our model, i.e., SWR, has the best performances. REFERENCES e comparison results between SR, SWR, RF, AR and AVE clearly [1] Hirotugu Akaike. 1969. Fiing autoregressive models for prediction. Annals of demonstrate the robustness of SWR and also the importance of our the institute of Statistical Mathematics 21, 1 (1969), 243–247. constructed features on tracking and forecasting the dynamics of [2] Jisun An, Daniele ercia, and Jon Crowcro. 2014. Recommending investors funding time series in crowdfunding. for crowdfunding projects. In 23rd WWW. ACM, 261–270. [3] Chance Barne. 2015. Trends show crowdfunding to surpass VC in 2016. Forbes, June 9 (2015). [4] Paul Belleamme, omas Lambert, and Armin Schwienbacher. 2014. Crowd- 8 CONCLUSION funding: Tapping the right crowd. Journal of Business Venturing 29, 5 (2014), In this paper, we presented a focused study on tracking and fore- 585–609. [5] George EP Box, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung. 2015. casting the dynamics in crowdfunding in a holistic view. For con- Time series analysis: forecasting and control. John Wiley & Sons. structing this study, we rst collected massive real-world crowd- [6] Peter J Brockwell and Richard A Davis. 2006. Introduction to time series and forecasting. Springer Science & Business Media. funding data with detailed daily transaction information from In- [7] Li-Juan Cao and Francis Eng Hock Tay. 2003. Support vector machine with diegogo.com and generated various features at both campaign and adaptive parameters in nancial time series forecasting. IEEE Trans. on NN 14, 6 perk levels. We then formalized the problem as the prediction (2003), 1506–1518. [8] Biao Chang, Hengshu Zhu, Yong Ge, Enhong Chen, Hui Xiong, and Chang Tan. with hierarchical time series and proposed a two-layer solution 2014. Predicting the popularity of online serials with autoregressive models. In framework. Specically, for both campaign and perk levels, we 23rd CIKM. ACM, 1339–1348. developed two regression models, i.e., SR and SWR, by exploring [9] Jerome T Connor, R Douglas Martin, and Les E Atlas. 1994. Recurrent neural networks and robust time series prediction. IEEE trans. on NN 5, 2 (1994), 240– the decision making of crowd and the clustering characteristic of 254. funding sequences. For a given target campaign and perks, we [10] Douglas J Cumming, Gael¨ Leboeuf, and Armin Schwienbacher. Crowdfunding models: Keep-it-all vs. all-or-nothing. In Paris December 2014 nance meeting. employed a revision matrix to combine the independent estima- [11] Lloyd D Fisher and Danyu Y Lin. 1999. Time-dependent covariates in the Cox tions of two-level base forecasts. Finally the experimental results proportional-hazards regression model. Annual review of public health 20, 1 on our collected data clearly demonstrated the eectiveness of our (1999), 145–157. [12] Raymond P Fisk, Lia Patr´ıcio, Andrea Ordanini, Lucia Miceli, Marta Pizzei, and solutions, especially SWR and the combination. A Parasuraman. 2011. Crowd-funding: transforming customers into investors In the future, we will test other combination strategies for the through innovative service platforms. Journal of service management 22, 4 (2011), two-level base forecasts, e.g., boom-up strategies, which produces 443–470. [13] C Lee Giles, Steve Lawrence, and Ah Chung Tsoi. 2001. Noisy time series forecasts at the perk level and aggregates them to the campaigns. prediction using recurrent neural networks and grammatical inference. Machine learning 44, 1-2 (2001), 161–183. [14] Michael D Greenberg and Elizabeth M Gerber. 2014. Learning to fail: experiencing ACKNOWLEDGMENTS public failure online through crowdfunding. In SIGCHI Conference on Human Factors in Computing Systems. ACM, 581–590. is research was partially supported by grants from the National [15] Rob J Hyndman, Roman A Ahmed, George Athanasopoulos, and Han Lin Shang. Science Foundation for Distinguished Young Scholars of China 2011. Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis 55, 9 (2011), 2579–2589. (Grant No. 61325010), the National Natural Science Foundation of [16] Rob J Hyndman, Alan J Lee, and Earo Wang. 2016. Fast computation of reconciled China (Grants No. 61672483, U1605251, 61602234, 61572032) and the forecasts for hierarchical and grouped time series. Computational Statistics &

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2.5 4 4

2 RMSE RMSE RMSE 1.5 2 RMSE 2 1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 τ τ τ τ (a) Campaign 30days (b) Perk 30days (c) Campaign 60days (d) Perk 60days

0.9 0.6 0.9

0.4

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SWR SR MRSE 0.2 MRSE MRSE MRSE RF 0.3 0.2 0.3 AR AVE

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 τ τ τ τ (e) Campaign 30days (f) Perk 30days (g) Campaign 60days (h) Perk 60days Figure 5: Eects of parameter τ .

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