Why Did You Cover That Song?: Modeling N-th Order
Derivative Creation with Content Popularity
Kosetsu Tsukuda, Masahiro Hamasaki, and Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST), Japan{k.tsukuda, masahiro.hamasaki, m.goto}@aist.go.jp
ABSTRACTeration content can create 3rd generation content. Similarly, N-th
generation content can be transformed into N+1-th generation content. Such derivative work creation activity is called “N-th orderderivative creation [4].”We know that derivative creation is popular, but why are individual derivative works created? There are various factors that inspire
the creation of derivative works. However, since the factors thattrigger derivative creation cannot usually be observed on the web,they are difficult to detect. To get around this problem, we assume that when a creator creates a derivative work, there are threetriggering factors: (1) original work’s attractiveness, (2) original
work’s popularity, and (3) derivative work’s popularity. Based on
this assumption, we propose a model to estimate the factors thattriggered derivative work creation. Since the relative influence ofthe three factors varies among creators, our model also incorporates the latent relationships between creators and each of the threefactors. Moreover, our model uses content ranking information totake into account the popularity of original and derivative works.
By referring to the examination model of a web search result [7],we model popularity based on the hypothesis that higher ranked
content has a larger influence because such content is, with highprobability, viewed by many creators. By using efficient Bayesianinference based on the stochastic expectation-maximization (EM)algorithm [6], we can obtain the latent triggers for derivative work
posts.
Our main contributions in this paper are as follows. First, to thebest of our knowledge, this is the first study modeling derivative
creation activity. Our model can simultaneously take into accountthe influences of three factors: (1) original work attractiveness, (2)original work popularity, and (3) derivative work popularity. Second, we quantitatively evaluated our model by using derivative creation data of the music content. Our experimental results showthat the model adopting all three factors achieves the best result interms of the log likelihood computed by using test data. We also
show that when we consider the content popularity based on popularity ranking, the method reflecting creators’ browsing behavior isthe most effective to model derivative creation activity. Third, we
carried out qualitative experiments in terms of (1) category characteristics, (2) temporal development of factors that trigger the derivative work posting events, and (3) N-th order derivative creation process and showed that our model can be used to analyze derivative
work creation activity.

Many amateur creators now create derivative works and put themon the web. Although there are several factors that inspire the creation of derivative works, such factors cannot usually be observedon the web. In this paper, we propose a model for inferring latent factors from sequences of derivative work posting events. We
assume a sequence to be a stochastic process incorporating the following three factors: (1) the original work’s attractiveness, (2) theoriginal work’s popularity, and (3) the derivative work’s popularity.
To characterize content popularity, we use content ranking data andincorporate rank-biased popularity based on the creators’ browsing
behavior. Our main contributions are three-fold: (1) to the best of
our knowledge, this is the first study modeling derivative creation
activity, (2) by using a real-world dataset of music-related derivative work creation to evaluate our model, we showed the effectiveness of adopting all three factors to model derivative creation activity and considering creators’ browsing behavior, and (3) we carriedout qualitative experiments and showed that our model is usefulin analyzing derivative creation activity in terms of category characteristics, temporal development of factors that trigger derivative
work posting events, etc.

Keywords
Derivative creation; latent variable model; user generated content

1. INTRODUCTION
The era when only professional creators were able to create andprovide content on the web has passed; now amateur creators who
used to be just consumers can also easily create and provide content. Such content is known as user generated content (UGC). Since
not all amateur creators can create new content from scratch, it ispopular to use existing original (1st generation) work as the basis
for new content; such content is called derivative work [5] or 2nd
generation work. For example, on YouTube1 , there are many videos
in which amateur creators dance to an existing song or perform acover of it. On Thingiverse2 , which is a web service where amateur creators can share 3D model data intended for a 3D printer, it
is popular for creators to download original 3D model data createdby others, modify it, and upload their new version. In this kind ofderivative work creation activity, a creator influenced by 2nd gen1
2

http://www.youtube.com
http://www.thingiverse.com

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2.

RELATED WORK

[Analysis of Derivative Creation Activity] A limited number ofstudies have investigated derivative creation activity. Eto et al. [3]developed a 3D modeling application and a model sharing web service called Modulobe, which allows users to create 3D models fromscratch or based on the work of other creators. They reported that
10.4% of models were parents of other models and the chains ofcreation reached four generations. Cheliotic and Yew [1] examined

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DOI: http://dx.doi.org/10.1145/2983323.2983674

2239

the remixing activity in the ccMixter online music community3 .
They reported that derivative creation greatly boosted the output
of a community as well as increased the diversity of the output.
Hamasaki et al. [5] analyzed derivative creation activity on a video
sharing web service called Niconico4 . They used explicit citation
information between an original work and its derivative works anddiscussed certain statistics (e.g., the number of works derived froman original work). All the studies mentioned above analyzed howderivative works had been created by using a network based on therelationships between the original content and derivative works. In
this work, we focus on why derivative works were created and propose a model to estimate the factors and their influences.
[Modeling Influences in Social Communities] Since estimating influences among users in social activities is useful for various
applications, such as influential user detection [14] and personalized recommendation [13], many methods for estimating suchinfluences have been proposed. One major approach is to use
an information diffusion model such as the independent cascade
model [16]. Although discrete time is assumed with this model,
Saito et al. [11] proposed a model based on Poisson processes thatallows for continuous time modeling. However, their model requires a network of users in which a node corresponds to a user
and an edge between users represents the existence of influence.
To overcome this limitation, Iwata et al. [6] proposed a model that
discovers latent influences between users without a network. Although the cascade Poisson process [12] models a sequence of cascading events, the model proposed by Iwata et al., which is called
the shared cascade Poisson process (SCPP), can handle multiple
sequences of adoption events for multiple items by sharing parameters. Tanaka et al. [15] extended the SCPP to estimate the factors that trigger item purchase events. They considered the users’view histories for TV advertisements in addition to influences between users and showed that the SCPP is also effective in modelingpurchase events. Our model extends the SCPP and the model proposed by Tanaka et al. [15], differing from them in the following
two respects. First, in the other models, there is no need to consider
the effect of adopted items such as purchased items. However, inderivative creation activity, adopted items (i.e., derivative works)
also influence other creators’ creation activity. Therefore, we extended the SCPP so that we can handle the effect of both original
works and derivative works. Second, although the other models assume that the popularity of items is constant regardless of time, we
assume that content popularity depends on time. Hence, our model
incorporates the time-dependent popularity of both original works
and derivative works by considering content ranking data and thecreators’ ranking browsing behavior.

ity) in this section, our proposed model incorporates three of these(setting aside the creator influence factor).

3.1

3.2
3.2.1

In an online social activity model, it is common to consider user
preference for content (we refer to the factor as original work attractiveness) and influences among users [6, 15]. However, inderivative creation activity, the existence of user influence is unlikely because no obvious influences among creators (users) havebeen observed in derivative creation activity analysis [1, 3, 5]. Instead, it seemed that the rich-get-richer phenomenon exists in theactivity [5]. Hence, we assume that the popularity of original andderivative works is an important factor in modeling derivative creation activity. Note that although we describe the complete model
as incorporating four factors (original work attractiveness, creator
influence, original work popularity, and derivative work popular-

4

Factors
Original Work Attractiveness (Oatt)

A creator may create original work i’s derivative work because
he/she thinks that i is attractive even if it is not popular. The attractiveness of i can be due to i’s various features; in the case of asong, the features can be the melody, beat, lyrics, etc. We assume
that each creator has a different preference for original content attractiveness. We also assume that the post rate based on original
work attractiveness is constant in the time period from 0 to T as
described in Figure 1(a). Here, the rate at time t represents the instantaneous probability of a creator posting i’s derivative work at
t. This kind of constant rate is known as the “background rate” inthe point process framework [2]. Based on these assumptions, we
model the rate at which creator u posts i’s derivative work triggeredby i’s attractiveness as follows: fi (u) = αi θ0u , where αi ≥ 0 is
the original work attractiveness. The θ0u ≥ 0 represents the probability that u is influenced by original∑work attractiveness when
he/she creates a derivative work, and u∈U θ0u = 1. If u puts
a higher priority on original work attractiveness than other factors,
θ0u becomes large. In Figure 1(a), the height of the blue line corresponds to αi θ0u .

3. MODEL

3

Notations

Given a category (e.g., “3D models of chairs” or “music videos
covering songs”) and observation time period T , let I be a setof original works posted to a web service (e.g., Thingiverse or
YouTube) between time 0 and time T . Let (tpij , upij ) denote thejth derivative work posting event of original work i. More specifically, creator upij ∈ U posts i’s derivative work at time tpij . Here,U is the set of creators. Without loss of generality, we assume
that derivative work posting events are sorted in ascending order of
their timestamps: tpij ≤ tpij ′ for j < j ′ . When Ji represents thetotal number of i’s derivative works posted during the observation
time period, a set of derivative work posting events of i is giveniby Di = {(tpij , upij )}Jj=1. Hence, a set of derivative work posting
events of all original works is given by D = {Di }i∈I .
Suppose creators can see the ranking of original works on the
web service, where original works are ranked based on the popuo
larity computed using statistics such as view count. Let (toik , rik)
denote the kth ranked event of i ∈ I. That is, i is ranked at theorik
th place at time toik . We also assume that the events are sorted
in ascending order of their timestamps without loss of generality:
toik ≤ toik′ for k < k′ . Let Kio be the total number of i’s ranked
events between time 0 and timeo T , then a set of ranked events of i is
Kiogiven by Oi = {(toik , rik)}k=1. Therefore, a set of ranked eventsof all original works is given by O = {Oi }i∈I .
Similarly, suppose creators can also see the ranking of derivative
works. In the same manner as with the ranked event of the originalcwork, let (tcik , rik) denote the kth ranked event of i’s derivativecwork. Let Ki be the total number of ranked events of i’s derivative
works between time 0 and time T ; then a set of ranked
events ofKicc
i’s derivative works is given by Ci = {(tcik , rik)}k=1. Note that Ci
includes ranked events of all i’s derivative works. Finally, a set of
ranked events of all derivative works of all original works is given
by C = {Ci }i∈I .

3.2.2

Creator Influence (Cinf)

Creator u may create original work i’s derivative work because
creator u′ posted i’s derivative work; in other words, u is influenced by u′ . We assume that the influences of u′ on other creators
are different from one creator to another. For example, if u is a

http://ccmixter.org
http://www.nicovideo.jp2240

(c) Original work ’s popularity

T

Rate

0

T

0

(d) 1st deriva"ve work popularity

TT(f) Total eﬀect

Rate

Rate

(b) Creator inﬂuence

Rate

0

0

(e) 2nd deriva"ve work popularity

Rate

Rate

(a) Original work ’s a!rac"veness

0

T

0

T

Figure 1: Rate at which creator u posts original work i’s derivative work at time t.
fan of u′ , u′ has a larger influence on u than on other creators.
We also assume that a creator’s influence on another creator decays
over time. This assumption is often used to model information diffusion processes between users [10]. Based on these assumptions,
we model the rate at which u posts i’s derivative work at time t
based on the influence of u′ who posted i’s derivative work at time′t′ as follows. g(i,t′ ,u′ ) (t, u) = αu′ θu′ u e−γp (t−t ) if t′ < t, and 0′
otherwise, where αu′ ≥ 0 is the influence of u on other creators,
θu′ u∑≥ 0 represents the strength of the relation between u′ and u,
and u∈U \u′ θu′ u = 1, where U \ u′ is the set of creators excluding u′ . Hence, αu′ θu′ u means the influence of u′ on u. Finally,′e−γp (t−t ) models the decay of influence over time with decay parameter γp ≥ 0. Note that if u′ posts i’s derivative work after u, u′does not influence u: g(i,t′ ,u′ ) (t, u) = 0 if t′ ≥ t.
In Figure 1(b), two creators post original work i’s derivative
works. Let the first creator (shown in red) be u′ . The influence ofu′ is αu′ θu′ u , which corresponds to h1 in the figure, when u′ posts
the derivative work. The influence decreases as time proceeds.

3.2.4

Derivative Work Popularity (Dpop)

If original work i’s derivative work created by creator u′ is popular among consumers, creator u may also create i’s derivative work
because his/her derivative work might also become popular even if
u is not a fan of u′ . Based on similar assumptions and the hypothesis described in Section 3.2.3, when i’s derivative work was rankedr′ th at time t′ , we model the rate at which u posts i’s derivative
work at time t based on the influence of i’s derivative work pop′
ularity as follows. hd(i,t′ ,r′ ) (t, u) = rb(r′ )σi θ−2u e−γd (t−t ) if′
t < t, and 0 otherwise, where σi ≥ 0 represents the influenceof the popularity of i’s derivative work, θ−2u ≥ 0 represents theprobability that u is influenced by derivative∑ work popularity when
he/she creates a derivative work, and u∈U θ−2u = 1. Finally,′e−γd (t−t ) models the decay of influence over time with decay parameter γd ≥ 0.
Figure 1(d) and (e) show the influences of i’s first and second
derivative work popularity, respectively. Let r′ be the rank of thefirst ranked event in Figure 1(d). The influence of the first ranked
event is rb(r′ )σi θ−2u , which corresponds to h3 in Figure 1(d) at
tci1 . Then, the influence decreases as time proceeds.

3.2.3 Original Work Popularity (Opop)
If original work i is popular among consumers, creator u may
create i’s derivative work because his/her derivative work mightalso become popular. As mentioned in Section 3.1, we assume creators can see the popularity ranking of original works. When two
original works are ranked, we hypothesize that the higher ranked
one has a larger influence than the lower ranked one. This hypothesis comes from the position bias in the web search: it has
been proved that higher ranked results receive more user attention
and have larger probabilities of being examined during search sessions [7]. In addition, we assume that each creator has a different preference for original work popularity. As is the case withcreator influences, we also assume that the influence of original
work popularity on a creator decays over time. Based on theseassumptions, we model the rate at which u posts i’s derivative
work at time t based on the influence of i’s popularity as fol′lows: ho(i,t′ ,r′ ) (t, u) = rb(r′ )ωi θ−1u e−γo (t−t ) if t′ < t, and′0 otherwise, where r represents the rank of i at time t′ , and function rb computes the rank bias. As reported in studies on behavior analysis of search result examination, the probability that eachranked item is viewed dramatically decreases as the rank drops [7].
Based on the examination behavior, we compute the rank bias asrb(r ′ ) = r1′ . In Section 5.3, we evaluate the usefulness of rankbias. The term ωi ≥ 0 represents the influence of i’s popularity,
θ−1u ≥ 0 represents the probability that u is influenced by original work popularity when he/she creates a derivative work, and∑−γo (t−t′ )models the decay of influu∈U θ−1u = 1. Finally, eence over time with decay parameter γo ≥ 0.
In Figure 1(c), the original work i appears four times in the popularity ranking. Let r′ be the rank of the first ranked event. The
influence of the event is rb(r′ )ωi θ−1u , which corresponds to h2 inFigure 1(c) at toi1 . Then, the influence decreases as time proceeds.

3.3

Derivative Work Post Rate

Based on the factors described in Sections 3.2.1 to 3.2.4, the rate
at which u posts i’s derivative work at t is given by:∑λi (t, u) = fi (u) +g(i,t′ ,u′ ) (t, u)+∑(t′ ,u′ )∈Dit\uho(i,t′ ,r′ ) (t, u) +(t′ ,r ′ )∈Oit∑

hd(i,t′ ,r′ ) (t, u),(1)(t′ ,r ′ )∈Cit

where Dit\u = {(t′ , u′ )|(t′ , u′ ) ∈ Di and t′ < t ∧ u′ ̸=u}, Oit = {(t′ , r′ )|(t′ , r′ ) ∈ Oi and t′ < t}, and Cit ={(t′ , r′ )|(t′ , r′ ) ∈ Ci and t′ < t}. Here, λi (t, u) corresponds
to h4 in Figure 1(f).

4.

INFERENCE

Given D, O, and C, we infer the model parameters by using thestochastic EM algorithm. Following Iwata et al. [6], we assume
that a set of i’s derivative work posting events Di is generated froma marked point process [9] at a rate of λi (t, u). Based on this assumption, the likelihood of the function of D is given by:
P (D|O, C, α, ω, σ, Θ, γ)
( ∫
) J
i
T ∑
∏
∏
=
exp −
λi (t, u)dt
λi (tpij , tpij ), (2)
i∈I

0

u∈U

j=1

where α = {αl }l∈I∪U , ω = {ωi }i∈I , σ = {σi }i∈I , Θ ={θ u }u∈U+ , θ u = {θuu′ }u′ ∈U \u , and γ = {γp , γo , γd }. Here,U+ denotes U ∪ {0, −1, −2}, where 0, −1, and −2 represent virtual (creators for Oatt, Opop,)and Dpop, respectively. The term∫T ∑exp − 0represents the probability that nou∈U λi (t, u)dt
creator posts i’s derivative work between time 0 and time T .

2241

Following Iwata et al. [6], we introduce latent variables zij ∈{0, 1, · · · , Dit\u + |Oit | + |Cit |} to indicate the index of thelatent trigger of the jth derivative work posting event of original
work i. The terms zij = 0, Dit\u + 1 ≤ zij ≤ Dit\u + |Oit |,Dit\u + |Oit | + 1 ≤ zij ≤ Dit\u + |Oit | + |Cit | indicatethat the event was triggered due to the influence of Oatt, Opop,and Dpop, respectively. zij = j ′ (1 ≤ j ′ ≤ Dit\u ) indicates that the event was triggered due to the influence of the creator who posted the j ′ th derivative work of i. By using the latentvariables, the derivative∑ work post rate in Equation (1) can be written as λi (t, u) =z λi (t, u, z), where λi (t, u, z) = fi (u) if
z = 0, g(i,tp ,up ) (t, u) if 1 ≤ z ≤ Dit\u , ho(i,to ′ ,ro ′ ) (t, u)
iz iz
iz
iz
if Dit\u + 1 ≤ z ≤ Dit\u + |Oit |, and hd(i,tc ′′ ,rc ′′ ) (t, u)
iz
iz
if Dit\u + |Oit | + 1 ≤ z. Here, z ′ = z − Dit\u andz ′′ = z − Dit\u − |Oit |.
Since the integral part in Equation (2) can be analytically calculated, by combining the above equations, the joint distribution of Diand latent variables Z = {{zij }Jj=1}i∈I is given by:

Category
Sing
Dance
Play

|U|
18,715
1,153692

5. QUANTITATIVE EXPERIMENTS
In this section, we answer the following two research questions:(1) is adopting three factors (Oatt, Opop, and Dpop) effective tomodel derivative creation activity? (Section 5.2) and (2) what kindsof ranking bias methods are effective to model derivative creation
activity? (Section 5.3)

5.1

DatasetWe used derivative creation activity data of music content on
Niconico, which is one of the most popular video sharing web services in Japan. On Niconico, any user can upload and view videos,and derivative creation activity of music content occurs frequently:
as of the end of April 2016, more than 140,000 original song videos
and more than 590,000 derivative videos had been uploaded to
Niconico. Most original songs are created using singing synthesizer software called VOCALOID; we restricted ourselves to original song videos of this type. Niconico maintains three categories
of derivative works: (1) sing: covering an original song, (2) dance:
dancing to an original song, and (3) play: playing an original songon a musical instrument such as a guitar or piano. We crawled
original songs (i.e., original works) posted between 1/1/2010 and
3/31/2013 and their derivative works posted between 1/1/2010 and
6/30/2013. Data between 1/1/2010 and 3/31/2013 were used astraining data and data between 4/1/2013 and 6/30/2013 were usedas test data. In each category, we eliminated original works that
had fewer than two derivative works and creators who posted fewer
than three derivative works during the training period.
We also collected ranking data. On Niconico, users can see
the top 100 daily ranking of original songs and the top 100 daily
rankings for derivatives in each of the sing, dance, and play categories. Ranking data on one day is created based on several
statistics of the previous day (e.g., view count and comment count)so that the ranking data represent the work’s aggregated popularity. We crawled the top 100 ranking data in each of the original
song and three derivative content categories between 1/1/2010 and
6/30/2013. Since only daily ranking data is available on Niconico,the timestamp in all our experiments is measured in days.
Table 1 lists the statistics of the dataset used in the experiments.

P (D, Z|O, C, α, ω, σ, Θ, γ)
[
Ji
(
)
∏
p
1 ∑
αuij 1 − e−γp (T −tij )=exp αi T +γp j=1
i∈I
(
)
o
ωi ∑
o
+
rb(rik) 1 − e−γo (T −tik )
γo
k=1

Kic
Ji
(
) ∏
c
σi ∑
c
λi (tpij , tpij , zij ). (3)rb(rik) 1 − e−γd (T −tik ) 
+
γd
j=1
Kio

k=1

We assume a Gamma prior for each of the original work attractiveness scores αi as P (αi |a, b) ∝ αa−1
exp(−bαi ), where a andib are hyperparameters. In this study, following Iwata et al. [6], we
set a = b = 1. We also assume a Gamma prior for each creator
influence αu , influence of original work popularity ωi , and influence of derivative work popularity σi . In addition,a∏ we assume
β−1
Dirichlet prior over θ u , u ∈ U+ as P (θ u |β) ∝ u′ ∈U \u θuu′ .
We use a Gamma prior for α, ω, and σ and a Dirichlet prior forΘ to analytically calculate the marginalization over the parameters.
The marginalized joint distribution is computed by integrating out
those parameters:
P (D, Z|O, C, γ, β, a, b)∫∫∫∫=
P (D, Z|O, C, α, ω, σ, Θ, γ)P (α|a, b)
× P (ω|a, b)P (σ|a, b)P (Θ|β)dαdωdσdΘ.

Table 1: Statistics of our dataset.
|I|
|O|
|D|
|C|
4,035 64,973 199,320 67,627
396 30,925
9,420 22,954
583 38,726
5,526 20,492

5.2

(4)

Combination of Factors[Comparison Models] As mentioned in Section 3, we hypothesize that a model adopting Oatt, Opop, and Dpop is the most effective. To evaluate this hypothesis, the following six models werecompared: (1) Oatt, (2) Oatt+Cinf, (3) Oatt+Cinf+Opop+Dpop,(4) Oatt+Opop, (5) Oatt+Dpop, and (6) Oatt+Opop+Dpop, where
Oatt+Cinf, for example, represents the model that combines thefactors of Oatt and Cinf. Among the six models, (2) corresponds to
SCPP [6] and (6) is our proposed model.
[Evaluation Metric] Predictive performance is one of the mostcommonly used metrics to evaluate the appropriateness of a learned
model [6, 8]. Predictive performance is computed using the negative logarithm of the likelihood for posting events (t, u) during the′test period fromthe likelihood is given by( T∫ to′ T∑. The logarithm)of∑
∑
T
L =
−
λ
(t,
u)dt
i
i∈I
u∈U
(t,u)∈D test logλi (t, u),T

Based on the marginalized joint distribution, we developed astochastic EM procedure for the iteration. In the E-step, given thecurrent state of all but one variable zij , the new latent assignmentof zij is sampled from the following probability:
P (zij = y|D, Z\ij , O, C, γ, β, a, b)()(5)
P D, Z\ij , zij = y|O, C, γ, β, a, b()∝,
P D\ij , Z\ij |O, C, γ, β, a, b
where y ∈ {0, 1, · · · , Dit\u + |Oit | + |Cit |}, and \ij represents
the procedure excluding the jth derivative work posting event of i.
In the M-step, we estimate the decay parameters γ and Dirichletparameter β by maximizing the logarithm of the joint likelihoodin Equation (4). Following Iwata et al. [6], γ is estimated using
Newton’s method and β is estimated using the fixed point iteration method [10]. Finally, we can make the point estimates of theintegrated out parameters αi , αu , ωi , σi , and θuu′ .

iwhere Ditest is the test data for i. When the value of −L is small,the predictive performance is high. To examine the influence of thelength of the test period on our results, we examined spans of test

2242

㻝㻡
㻝㻞
㻥
㻢
㻟
㻜

㻤

*

Sing
*

*

㻠

*
1 mo.

㻢

2 mo.

3 mo.

㻟
㻝

Sing

*

㻢

Dance

㻠

*

㻠
㻜

*
*

㻤

*

㻞

*

㻞
㻜

㻝㻞

*

Play

㻞

Reciprocal
㻠

㻤

㻝㻢

㻠

*

Dance

LinearUniform

Oa +Cinf
Oa +Cinf+Opop+Dpop
Oa
Oa +Opop
Oa +Opop+Dpop
Oa +Dpop

*
*

㻞

*

㻝

2 mo.

3 mo.

*
*

㻜

㻜

1 mo.

*

㻟 Play

1 mo.

2 mo.

3 mo.

1 mo.

2 mo.

3 mo.

㻜

1 mo.

2 mo.

3 mo.

1 mo.

2 mo.

3 mo.

Figure 2: Negative logarithm of likelihood of each model. Vertical axis and horizontal axis represent negative log-likelihood
and test periods (e.g., “1 mo.” is first set of test data), respectively.

Figure 3: Negative logarithm of likelihood of each ranking bias
method.
Algorithm 1 Calculate degree of three factors for jth derivative
work posting event of i
Require: P (zij |D, Z\ij , O, C, γ, β, a, b)
1: Ef ⇐ P (zij = 0|D, Z\ij , O, C, γ, β, a, b), Eho ⇐ 0, Ehd ⇐ 0,y⇐1
2: while y ≤ |Oit | + |Cit | do
3:
if y ≤ |Oit | then4:
Eho ⇐ Eho + P (zij = y|D, Z\ij , O, C, γ, β, a, b)
5:
else
6:
Ehd ⇐ Ehd + P (zij = y|D, Z\ij , O, C, γ, β, a, b)
7:
end if8:y ⇐y+19: end while
10: return Ef , Eho , Ehd

data from one month (4/1/2013 to 4/30/2013) up to three months(4/1/2013 to 6/30/2013).
[Results] Figure 2 shows the negative log-likelihood during eachtest period in each category. The model that achieved the best performance is marked with “*”. In the “sing” and “dance” categories,
Oatt+Opop+Dpop exhibited the best result for all test periods. In
the “play” category, it did not perform the best, but it stably exhibited high performance in all categories during all test periods.
Although other models exhibited the best results in the “play” category, they were unstable because their average ranks in both the“sing” and “dance” categories were low. From these results, weconclude that our proposed model adopting Oatt, Opop, and Dpop
is the most effective to model derivative creation activity.

Table 2: Ratios of estimated factors (%).
FactorSing Dance
Original work attractiveness (Oatt) 14.6
17.3
Original work popularity (Opop)
40.0
21.7
Derivative work popularity (Dpop) 45.4
61.0

5.3 Ranking Bias Method Comparison

Play
42.5
40.0
17.5

[Settings] As mentioned in Section 3.2.3, our model uses the reciprocal rank method to bias the content ranking based on the creators’ browsing behavior of a ranked list (hereafter, “Reciprocal”).
To evaluate its effectiveness, we compared it with the following
two methods. The first method, “Linear,” linearly decreases the
101−r oocranking bias, rb(rik) = 100 ik . Here, rb(rik) is also computedin the same manner. With this method, it is assumed that content
influence does not dramatically decrease when the content position in the ranking decreases compared to Reciprocal. The second
method, “Uniform,” does not take into account the ranking bias:ocrb(rik) = rb(rik) = 1 regardless of the content rank. With thismethod, it is assumed that all ranked content has equal influence.
We used the negative logarithm of the likelihood as an evaluation
metric, as in Section 5.2.
[Results] Figure 3 shows the results of the three ranking bias
methods. Reciprocal outperformed the other two methods for all
test periods in all categories. In addition, Linear always outperformed Uniform: this result indicates the usefulness in considering
the rank position of content. Based on these results, we conclude
that Reciprocal, which reflects the creators’ browsing behavior, isthe most effective for modeling derivative creation activity.

the category. In the same manner, we can obtain the strength of
Eho and Ehd in a category.
Table 2 lists the ratios of the three factors during the training
period. The ratios of the three factors vastly differed from one category to another. In the “sing” category, the ratios of Opop andDpop were both high, while that of Oatt was low. These results
indicate that the creators in this category are susceptible to fads andput a high priority on content popularity. In the “dance” category,
the ratio of Dpop was high. In this category, not all creators cancompose their own choreography. Hence, a creator often posts a
derivative work in which the creator dances to the original songwith the original choreography. After that, other creators also post
derivative works in which they imitate the choreography. The results show that our model described this category’s characteristics
well. In the “play” category, the ratio of Oatt was high. This indicates that creators in this category often play their favorite original
songs without being affected by fads.

6. QUALTITATIVE EXPERIMENTS

6.2

Temporal Development of Factors

By using Algorithm 1, we can also analyze the temporal development of factors that trigger the derivative work posting eventsof each original work. This section reports the temporal development of factors per month. Given original work i, we computed thesum of Ef for each i’s derivative work posting event every month.
Similarly, we computed the sum of Eho and Ehd every month.
Figure 4 shows example results for the three original songs that
we selected for this evaluation. In each category, we show the temporal development of factors for one original work. The horizontal
axis represents months in the training period, and the vertical axis
represents the number of derivative works posted in a month. The
first month on the horizontal axis is the month when the original
work’s first derivative work was posted. The blue, orange, and redbars indicate the number of posting events caused by Oatt, Opop,and Dpop, respectively. Again, we can observe the characteristics

In this section, we report on the qualitative analysis results interms of (1) category characteristics, (2) temporal development offactors that trigger derivative work posting events, and (3) N-th order derivative creation process.

6.1 Category Characteristics
By using the posterior distribution of latent variables in Equation(5), we can analyze the impact of each of the three factors (Oatt,
Opop, and Dpop) that trigger derivative work posting events in a
category. Algorithm 1 shows the pseudo-code for computing thestrengths of the three factors for the jth derivative work posting
event of i. In the pseudo-code, Ef , Eho , and Ehd correspond to
the strength of Oatt, Opop, and Dpop, respectively, where Ef +Eho + Ehd = 1. By summing Ef of all derivative works of all
original works in a category, we can obtain the strength of Oatt in

2243

Original work popularity (Opop)

Original work a!rac"veness (Oa!)
120

25

Sing

100

Deriva"ve work popularity (Dpop)
25

Dance

20

20

15

15

10

10

5

5

Play

80
60
40
20
0
Apr-10

Oct-10

Apr-11

Oct-11

Apr-12Oct-120
Nov-100May-11

Nov-11

May-12

Nov-12

Jul-10Jan-11

Jul-11

Jan-12

Jul-12

Jan-13Figure 4: Estimated number of derivative work posting events triggered by each of three factors per month. Vertical axis represents
the number of derivative works posted in a month.
and 11th derivative works played an important role because they
triggered many derivative creations. We also observed that 10thorder derivative creation (30th, 32nd, and 33rd derivative works)
occurred in this process.

7.

CONCLUSION

We proposed a model for inferring latent factors and their influences in derivative creation activity. For future work, we areinterested in applying our model to other derivative creation datasuch as data on Thingiverse. We are also interested in extending
our model by considering additional factors. For example, someoriginal works may be often used to create derivative works during Christmas. Considering such seasonality is one possible way toextend our model.

Acknowledgements

Figure 5: Derivative work creation process of an original workin “dance” category. 0 represents the original work, and j ≥ 1
represents the jth derivative work.

This work was partly supported by MEXT KAKENHI Grant Number (15H06887) and CREST, JST.

8.

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of each category. In the “sing” category, in the early period of thederivative creation activity, Oatt and Opop had a large influence.
We estimate that some derivative works created in the period became popular; after that, other creators who put a high priority on
Dpop also posted the original work’s derivative work. This is why
the influence of Dpop increased as time proceeded. We also observed that Oatt had some influence even at the end period of thegraph. This indicates the possibility that some creators happened
to find the original song (e.g., by keyword search) and covered thesong. In the “dance” category, a limited number of creators who
can compose original choreography posted derivative works in theearly period (see the blue bars in the first two months). After that,many other creators were influenced by such derivative works andposted new derivative works. In the first half of the test period in the“play” category, many creators who put a high priority on Opop or
Dpop posted this original work’s derivative works; while in the lasthalf, creators who put a high priority on Oatt kept posting derivative
works.

6.3 N-th Order Derivative Creation Process
By using the posterior distribution of latent variables, we canvisualize the derivative creation process of an original work. To visualize the process, for each derivative work, we detected y, whichis the maximum value in Equation (5). When y was equal to 0 or
indicated the index of the original work’s ranked event, derivative
work creation was triggered by the original work; when y indicatedthe index of the ranked event of the j ′ th derivative work, derivative
work creation was triggered by the j ′ th derivative work.
Figure 5 shows the derivative creation process of an original
work in the “dance” category. In the figure, 0 represents an original work, and j ≥ 1 represents the jth derivative work. An edge
between numbers indicates that the lower content creation was triggered by the upper one. In this derivative creation process, the 9th2244