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PAPER

Special Section on Data Engineering and Information Management

Modeling N-th Order Derivative Creation Based onContent Attractiveness and Time-Dependent Popularity
Kosetsu TSUKUDA†a) , Masahiro HAMASAKI†b) , Nonmembers, and Masataka GOTO†c) , Member

SUMMARY For amateur creators, it has been becoming popular to create new content based on existing original work: such new content is called
derivative work. We know that derivative creation is popular, but why are
individual derivative works created? Although there are several factors thatinspire the creation of derivative works, such factors cannot usually be observed on the Web. In this paper, we propose a model for inferring latent
factors from sequences of derivative work posting events. We assume asequence to be a stochastic process incorporating the following three factors: (1) the original work’s attractiveness, (2) the original work’s popularity, and (3) the derivative work’s popularity. To characterize content
popularity, we use content ranking data and incorporate rank-biased popularity based on the creators’ browsing behaviors. Our main contributions
are three-fold. First, to the best of our knowledge, this is the first study
modeling derivative creation activity. Second, by using real-world datasetsof music-related derivative work creation, we conducted quantitative experiments and showed the eﬀectiveness of adopting all three factors to model
derivative creation activity and considering creators’ browsing behaviors
in terms of the negative logarithm of the likelihood for test data. Third,
we carried out qualitative experiments and showed that our model is usefulin analyzing following aspects: (1) derivative creation activity in terms of
category characteristics, (2) temporal development of factors that trigger
derivative work posting events, (3) creator characteristics, (4) N-th orderderivative creation process, and (5) original work ranking.
key words: user-generated content, derivative creation, latent variable
model, music content

1.

Introduction

These days not only professional creators but also amateurcreators who used to be just consumers can easily create
content, which is known as user-generated content (UGC),
and make them accessible via the Web. Since not all amateurcreators can create new content from scratch, it is popular touse existing original (1st generation) work as the basis for
new content: such content is called derivative work [1] or
2nd generation work. For example, on YouTube∗ , there aremany videos in which amateur creators dance to an existing
song, or perform a cover of it [2], [3]. To be more specific,
there have been various cases where an original work gains
more popularity with increasing its derivative works such as“Nyan Cat∗∗ ” and “PPAP∗∗∗ ” phenomena. Although original content creators could identify their derivative works byusing the Content ID function and ask YouTube to delete
Manuscript received June 14, 2019.
Manuscript revised November 1, 2019.
Manuscript publicized February 5, 2020.
†
The authors are with National Institute of Advanced Industrial
Science and Technology (AIST), Tsukuba-shi, 305–8568 Japan.
a) E-mail: k.tsukuda@aist.go.jpb) E-mail: masahiro.hamasaki@aist.go.jpc) E-mail: m.goto@aist.go.jp
DOI: 10.1587/transinf.2019DAP0008

them, they do not bother to do that. This is because gaining
the popularity of an original work benefits its creator. Thingiverse∗∗∗∗ is a Web service that facilitates derivative work
creation, where amateur creators can share 3D model dataintended for a 3D printer. On Thingiverse, it is popular for
creators to download original 3D model data created by others, modify it, and upload their new version [4]. In this kindof derivative work creation activity, a creator influenced by
2nd generation content can create 3rd generation content.
Similarly, N-th generation content can be transformed intoN+1-th generation content. Such derivative work creation
activity is called “N-th order derivative creation [5].”When a creator creates a derivative work and uploads
it to the Web, there are various factors that inspire the creation of the derivative work. However, since the factorsthat trigger derivative creation cannot usually be observedon the Web, they are diﬃcult to detect. To get around thisproblem, we assume that when a creator creates a derivative
work, triggering factors can be divided into two categories.
The first one includes factors related to original work features. For example, a creator may cover an original song
because he/she likes the melody, even if the song is not popular among consumers. The second one includes social factors. For example, a creator may dance to an original song
only because the song is popular. Based on this assumption, we propose a probabilistic model to estimate the factorsthat triggered derivative work creation. More specifically,
our model incorporates three factors: (1) an original work’s
attractiveness, (2) an original work’s popularity, and (3) aderivative work’s popularity. The details of each factor are
given in Sect. 3.2. Since the relative influence of the threefactors varies among creators (e.g., one creator may put ahigh priority on factor (1), while another creator may put ahigh priority on factor (2)), our model also incorporates thelatent relationships between creators and each of the threefactors. Moreover, our model uses content ranking information to take into account the popularity of original andderivative works. By referring to the examination model ofa Web search result [6], [7], we model popularity based on
the hypothesis that higher ranked content has a larger influence because such content is, with high probability, viewed
by many creators. By using eﬃcient Bayesian inference
based on the stochastic expectation-maximization (EM) al∗

http://www.youtube.com
http://www.youtube.com/watch?v=QH2-TGUlwu4∗∗∗
http://www.youtube.com/watch?v=0E00Zuayv9Q∗∗∗∗
http://www.thingiverse.com∗∗

c 2020 The Institute of Electronics, Information and Communication Engineers
Copyright ⃝IEICE TRANS. INF. & SYST., VOL.E103–D, NO.5 MAY 2020

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gorithm [8], we can obtain the latent triggers for derivative
work posts.
Modeling derivative creation activity is worth studying
from various viewpoints.

(3) creator characteristics, (4) N-th order derivative
creation process, and (5) original work ranking, andshowed that our model can be used to analyze derivative work creation activity.

• Our model can find original work that has a significant
influence on derivative creation activity. This enables
us to generate original work ranking based on popularity among creators, even though it is common to rank
original works based on popularity among consumers(e.g., rank original works based on the view count).
Such a ranking enables consumers to search for original works from a new viewpoint.
• Given a category (e.g., “3D models of chairs” or “music videos covering songs”), our model can show thecharacteristics of the category in derivative creation activity (e.g., most creators put a high priority on original
work attractiveness in a category). Understanding suchcharacteristics in a category is important from the social scientific point of view.
• Our model can also show creator characteristics (e.g.,a creator puts a high priority on derivative work popularity). There are potentially many applications using
this data such as ads and recommendation. For example, if a creator puts a high priority on original work
attractiveness, it would be useful to recommend original works similar to the original works the creator usedin the past to encourage more derivative work creation.

The remainder of this paper is organized as follows.
Section 2 describes related work in two areas: (1) analysis
of derivative creation activity and (2) modeling influencesin social communities. Section 3 describes the model that
adopts the creator influence factor, which is used in related
work, in addition to the aforementioned three factors. Section 4 presents a Bayesian inference procedure to infer thelatent triggers for derivative work posts. Sections 5 and 6
report on our quantitative and qualitative experiments, respectively. Finally, Sect. 7 concludes this paper.

In Sect. 6, we discuss the application of our model to a realworld dataset and show that our model can be used to obtain
this kind of information.
Our main contributions in this paper are summarized asfollows † .
• To the best of our knowledge, this is the first study
modeling derivative creation activity. Our model cansimultaneously take into account the influences of threefactors: (1) original work attractiveness, (2) original
work popularity, and (3) derivative work popularity.
• We describe the details of inference of model parameters based on the stochastic EM algorithm.
• We quantitatively evaluated our model by using derivative creation data of the music content. Our experimental results show that the model adopting all three factors
achieves the best result in terms 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
behaviors is the most eﬀective to model derivative creation activity.
• We carried out qualitative experiments in terms of (1)category characteristics, (2) temporal development offactors that trigger the derivative work posting events,†
This paper is an extended version of a conference paper [9].
We extend the paper by describing the details of inference of model
parameters and by carrying out the qualitative evaluations in termsof creator characteristics and original work ranking.

2. Related Work
2.1

Analysis of Derivative Creation Activity

A limited number of studies have investigated derivative creation activity. Eto et al. [10] developed a 3Dmodeling application and a model sharing Web service called Modulobe, which allows users to create 3Dmodels from scratch or based on the work of othercreators. They reported that 10.4% of models wereparents of other models and the chains of creation
reached four generations. Cheliotic and Yew [11] examined the remixing activity in the ccMixter online music
community†† . They reported that derivative creation greatly
boosted the output of a community as well as increased thediversity of the output. Hamasaki et al. [1] analyzed
derivative creation activity on Niconico††† , which isone of the most popular video sharing Web services
in Japan. They used explicit citation information between an original work and its derivative works anddiscussed certain statistics (e.g., the number of derivative works of an original work). Hamasaki et al. [12]also developed a Web service called Songrium†††† thathelps a user browse original songs and their derivative
works by visualizing their relations.
All the studies mentioned above analyzed how derivative works had been created by using a network based on
the relationships between the original content and derivative
works. In this work, we focus on why derivative works werecreated and propose a model to estimate the factors and theirinfluences.
2.2

Modeling Influences in Social Communities

Since estimating influences among users in social activities is useful for various applications, such as influentialuser detection [13] and personalized recommendation [14],††http://ccmixter.org
http://www.nicovideo.jp††††
http://songrium.jp†††

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many methods for estimating such influences have been proposed. One major approach is to use an information diffusion model such as the independent cascade model [15].
Although discrete time is assumed with this model, Saito
et al. [16] proposed a model based on Poisson processes
that allows for continuous time modeling. However, theirmodel requires a network of users in which a node corresponds to a user and an edge between users represents theexistence of influence. To overcome this limitation, Iwata
et al. [8] proposed a model that discovers latent influences
between users without a network. Although the cascade
Poisson process [17] models a sequence of cascading events,
the model proposed by Iwata et al. [8], which is called theShared Cascade Poisson Process (SCPP), can handle multiple sequences of adoption events for multiple items by sharing parameters. Iwata et al. [8] used a Bayesian approachto discourage overfitting during parameter inference. Theyevaluated the model by using social bookmark data, whereadopting an item corresponds to bookmarking a Web page.
Tanaka et al. [18] extended the SCPP to estimate the factors that trigger item purchase events. They considered theusers’ view histories for TV advertisements in addition to
influences between users and showed that the SCPP is also
eﬀective in modeling purchase events.
Our model extends the SCPP and the model proposedby Tanaka et al. [18], diﬀering from them in the following
two respects. First, in the other models, there is no needto consider the eﬀect of adopted items such as bookmarked
Web pages and purchased items. However, in derivative 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 bothoriginal works and derivative works. Second, although theother models assume that the popularity of items is constantregardless of time, we assume that content popularity depends on time. Hence, our model incorporates the timedependent popularity of both original works and derivative
works by considering content ranking data and the creators’
ranking browsing behavior.
In our previous work [19], we implemented a public Web service for browsing the derivation factors called
Songrium Derivation Factor Analysis, which was developed by applying our proposed model to the original works
and derivative works uploaded to a video sharing service.
Songrium Derivation Factor Analysis has several functions
that could enable users to browse and watch videos from a
new viewpoint and decide which content they want to use to
create a new derivative work. In our previous paper [19], we
focused on application interfaces realized by the proposedmodel, but did not evaluate the model itself. In this paper,
we describe the details of the proposed model and conduct
quantitative and qualitative evaluations to show the eﬀectiveness of the model.
3.

Model

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 [8], [18].
However, in derivative creation activity, the existence of user
influence is unlikely because no obvious influences among
creators (users) have been observed in derivative creation
activity analysis [1], [10], [11]. Instead, it seems that therich-get-richer phenomenon [20] exists in the activity [1].
Hence, we assume that the popularity of the original andderivative works represents their exposure to creators andthat it 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 popularity) in this section, our proposed model incorporates three of these (setting aside the creator influence factor).
3.1

Notations

In this section, we summarize the notations used in ourmodel. Given a category (e.g., “3D models of chairs” or“music videos covering songs”) and observation time period
T , let I be a set of original works posted to a Web service(e.g., Thingiverse or YouTube) between time 0 and time T .
pp
Let (ti j , ui j ) denote the jth derivative work posting event ofporiginal work i. More specifically, creator ui j ∈ U postspi’s derivative work at time ti j . Here, U is the set of creators. Without loss of generality, we assume that derivative
work posting events are sorted in ascending order of theirpptimestamps: ti j ≤ ti j′ 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 eventsppi. Hence, a set of derivaof i is given by Di = {(ti j , ui j )} Jj=1
tive 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 basedon the popularity computed using statistics such as viewcount. Let (tiko , riko ) denote the kth ranked event of i ∈ I. Thatis, i is ranked at the riko th place at time tiko . We also assume
that the events are sorted in ascending order of their timestamps without loss of generality: tiko ≤ tiko ′ for k < k′ . Let
Kio be the total number of i’s ranked events between time
0 and time T , then a set of ranked events of i is given by
Kio. Therefore, a set of ranked events of all
Oi = {(tiko , riko )}k=1
original works is given by O = {Oi }i∈I .
Similarly, suppose creators can also see the ranking ofderivative works. In the same manner as with the ranked
event of the original work, let (tikc , rikc ) denote the kth ranked
event of i’s derivative work. Let Kic be the total number ofranked events of i’s derivative works between time 0 andtime T ; then a set of ranked
events of i’s derivative works
Kic. Note that Ci includes ranked
is given by Ci = {(tikc , rikc )}k=1
events of all i’s derivative works: (tikc , rikc ) and (tikc ′ , rikc ′ ) can
be ranked events of diﬀerent derivative works. Finally, a setof ranked events of all derivative works of all original works

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Symbol
I
U
i
p
ui j
p

ti j
o
rik
o
tik
c
rik
c
tik
D
O
C
T
Ji
Kio
Kic

Table 1 Notations used in our model
Description
set of original works
set of creators
original work, i ∈ I
creator of jth derivative work posting event ofporiginal work i, ui j ∈ Utime of jth derivative work posting event of irank of kth ranked event of itime of kth ranked event of irank of kth ranked event of i’s derivative work
time of kth ranked event of i’s derivative work
set of derivative work posting events
set of ranked events of original works
set of ranked events of derivative works
observation period
number of derivative work posting events fori in t ∈ [0, T ]number of ranked events for i in t ∈ [0, T ]number of ranked events for derivative works ofi in t ∈ [0, T ]is given by C = {Ci }i∈I .
Table 1 summarizes the notations used in this paper.
3.2 Factors
3.2.1

Original Work AttractivenessA 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 a song, the features can be the melody, beat,lyrics, etc. We assume that each creator has a diﬀerent preference for original content attractiveness. For example, acreator may put a high priority on original work attractiveness when he/she decides whether or not to create a derivative work of i, while another creator may put a low priority
on it. 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 Fig. 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” in the point process framework [21].
Based on these assumptions, we model the rate at which creator u posts i’s derivative work triggered by i’s attractivenessas follows:fi (u) = αi θ0u ,(1)

where αi ≥ 0 is the original work attractiveness. In otherwords, αi is the rate at which i’s derivative work is posted
without being triggered by the preceding events, and 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
Fig. 1(a), the height of the blue line corresponds to αi θ0u .

Fig. 1time t.

Rate at which creator u posts original work i’s derivative work at

3.2.2

Creator Influence

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′ onother creators are diﬀerent from one creator to another. For
example, if u is a fan of u′ , u′ has a larger influence on u thanon other creators. We also assume that a creator’s influenceon another creator decays over time. This assumption is often used to model information diﬀusion processes between
users [22], [23]. Based on these assumptions, we model therate 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:′αu′ θu′ u e−γp (t−t ) if t′ < t(2)g(i,t′ ,u′ ) (t, u) = 0otherwise,TSUKUDA et al.: MODELING N-TH ORDER DERIVATIVE CREATION BASED ON CONTENT ATTRACTIVENESS AND TIME-DEPENDENT POPULARITY

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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 timewith 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 ift′ ≥ t.
In Fig. 1(b), three creators post original work i’s derivative works. Let the first creator (shown in red) be u′ . The influence of u′ is αu′ θu′ u , which corresponds to h1 in the figure,when u′ posts the derivative work. The influence decreases
as time proceeds.
In derivative creation activity, the derivative work’s attractiveness may also have an influence. We assume that thederivative work’s attractiveness is determined by the creatorof the derivative work. For example, when the creator creates a derivative work by covering an original work’s song,
we think the derivative work’s attractiveness depends on thecreator’s singing voice in the derivative work. Therefore, byconsidering the creator’s influence, we can also consider thederivative work’s attractiveness.
3.2.3

Original Work Popularity

If original work i is popular among consumers, creator u
may create i’s derivative work because his/her derivative
work might also become popular. As mentioned in Sect. 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 influencethan the lower ranked one. This hypothesis comes from theposition bias in the Web search: it has been proved thathigher ranked results receive more user attention and havelarger probabilities of being examined during search sessions [6], [7]. In addition, we assume that each creator has
a diﬀerent preference for original work popularity: one creator may be susceptible to popularity and put a high priority
on original work popularity when he/she decides whether tocreate a derivative work of the original work, while anothercreator may not. As is the case with creator influences, we
also assume that the influence of original work popularity on
a creator decays over time. Based on these assumptions, we
model the rate at which u posts i’s derivative work at time t
based on the influence of i’s popularity as follows:′rb(r′ )ωi θ−1u e−γo (t−t ) if t′ < t(3)ho(i,t′ ,r′ ) (t, u) = 0otherwise,
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 thateach ranked item is viewed dramatically decreases as therank drops [6], [7]. Based on the examination behavior, we
compute the rank bias as rb(r′ ) = r1′ . In Sect. 5.3, we evaluate the usefulness of rank bias. The term ωi ≥ 0 represents
the influence of i’s popularity, θ−1u ≥ 0 represents the prob-

ability that u is influenced by original work
∑ popularity when
he/she creates a derivative work, and u∈U θ−1u = 1. Fi′
nally, e−γo (t−t ) models the decay of influence over time withdecay parameter γo ≥ 0.
In Fig. 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 coro
. Then, the influence deresponds to h2 in Fig. 1(c) at ti1
creases as time proceeds.
3.2.4

Derivative Work Popularity

If original work i’s derivative work created by creator u′
is popular among consumers, creator u may also create i’sderivative work because his/her derivative work might also
become popular even if u is not a fan of u′ . As mentioned
in Sect. 3.1, we assume creators can see the popularity ranking of derivative works. Based on similar assumptions andthe hypothesis described in Sect. 3.2.3, when i’s derivative
work was ranked r′ th at time t′ , we model the rate at which
u posts i’s derivative work at time t based on the influenceof i’s derivative work popularity as follows:′rb(r′ )σi θ−2u e−γd (t−t ) if t′ < t′′(4)hd(i,t ,r ) (t, u) = 0otherwise,
where σi ≥ 0 represents the influence of the popularity of i’sderivative work, θ−2u ≥ 0 represents the probability that u is
influenced by derivative work
∑ popularity when he/she cre′ates 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), (e), and (f) show the influences of i’s first,
second, and third derivative work popularity, respectively:
the first derivative work appears three times in the ranking,while the second and third ones appear one time. Let r′ be
the rank of the first ranked event in Fig. 1(d). The influenceof the first ranked event is rb(r′ )σi θ−2u , which correspondsc. Then, the influence decreases as time
to h3 in Fig. 1(d) at ti1
proceeds.
3.3

Derivative Work Post Rate

Based on the factors described in Sects. 3.2.1 to 3.2.4, therate 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′ ,r′ )∈Oit(t′ ,u′ )∈Dit\uho(i,t′ ,r′ ) (t, u) +∑hd(i,t′ ,r′ ) (t, u),(5)(t′ ,r′ )∈Cit

where Dit\u = {(t′ , u′ )|(t′ , u′ ) ∈ Di and t′ < t ∧ u′ , u} is theset of derivative work posting events before t excluding u’sone; Oit = {(t′ , r′ )|(t′ , r′ ) ∈ Oi and t′ < t} is the set of ranked
events of i before t; and Cit = {(t′ , r′ )|(t′ , r′ ) ∈ Ci and t′ < t}is the set of ranked events of i’s derivative works before t.
Here, λi (t, u) corresponds to h4 in Fig. 1(g).

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4.

Inference

Given derivative work posting events D, original works
ranked events O, and derivative works ranked events C, we
infer the model parameters in Table 2 by using the stochastic EM algorithm. Following Iwata et al. [8], we assume
that a set of i’s derivative work posting events Di is generated from a marked point process [24] at a rate of λi (t, u).
Based on this assumption, the likelihood of the function of
D is described as follows:
P(D|O, C, α, ω, σ, Θ, γ)
 J
 ∫
i
T ∑
∏
 ∏

p
p

λi (ti j , ui j ),λi (t, u)dtexp −
=
0

i∈I

(6)

j=1

u∈U

where α = {αl }l∈I∪U , ω = {ωi }i∈I , σ = {σi }i∈I , Θ ={θu }u∈U+ , θu = {θuu′ }u′ ∈U\u , and γ = {γp , γo , γd }. Here, U+
denotes U ∪ {0, −1, −2}, where 0, −1, and −2 represent virtual creators who are used for original work attractiveness,original work popularity, andwork popularity,re( derivative)∫T∑
spectively. The term exp − 0 u∈U λi (t, u)dt represents
the probability that no creator posts i’s derivative work between time 0 and time T . The integral part can be analytically calculated as follows:
∫ T∑
Ji
(
p )
1 ∑
αui j 1 − e−γp (T −ti j )λi (t, u)dt = αi T +γp j=1
0 u∈U
Ki
(
)
ωi ∑
o
rb(riko ) 1 − e−γo (T −tik )+γo k=1
o

Ki
(
)
σi ∑
c
+
rb(rikc ) 1 − e−γd (T −tik ) .
γd k=1c(7)

Following Iwata et al. [8], we introduce latent variables
zi j ∈ {0, 1, · · · , Dit\u + |Oit | + |Cit |} to indicate the index of
the latent trigger of the jth derivative work posting event oforiginal work i. The terms zi j = 0, Dit\u +1 ≤ zi j ≤ Dit\u +|Oit |, Dit\u + |Oit | + 1 ≤ zi j ≤ Dit\u + |Oit | + |Cit | indicatethat the event was triggered due to the influence of original
work attractiveness, original work popularity, and derivative
work popularity, respectively, and zi j = j′ (1 ≤ j′ ≤ Dit\u )indicates that the event was triggered due to the influenceof the creator who posted the j′ th derivative work of i. By
using the latent variables, the derivative
work post rate in∑
Eq. (5) can be written as λi (t, u) = z λi (t, u, z), where
Table 2
Symbol
αi
αu
ωi
σi
θu′ u
γp , γo , γdParameters of proposed model

Description
original work attractiveness of i, αi ≥ 0
influence of u, αu ≥ 0
popularity of i, ωi ≥ 0
popularity of i’s derivative work, σi ≥ 0transition probability from u′ to u,∑
θu′ u ≥ 0, u∈U\u′ θu′ u = 1
decay parameter, γp ≥ 0, γo ≥ 0, γd ≥ 0

λi (t, u, z) =
fi (u)
if z = 0






if 1 ≤ z ≤ Dit\ug(i,tizp ,upiz ) (t, u)



o
o
ho(i,tiz′ ,riz′ ) (t, u) if Dit\u + 1 ≤ z ≤ Dit\u + |Oit |





hd(i,tc ,rc ) (t, u) if Dit\u + |Oit | + 1 ≤ z.
iz′′ iz′′(8)Here, z′ = z − Dit\u and z′′ = z − Dit\u − |Oit |.
By combining Eqs. (6), (7), and (8), the joint distribuition of D and latent variables Z = {{zi j } Jj=1}i∈I is given by:P(D, Z|O, C, α, ω, σ, Θ, γ)

Ji
∏

(
p )
1 ∑
αui j 1 − e−γp (T −ti j )exp αi T +=γp j=1
i∈I
Ki
(
)
ωi ∑
o
rb(riko ) 1 − e−γo (T −tik )+γo k=1

Kic
Ji
) ∏
(
σi ∑
p
p

c
−γd (T −tikc ) λi (ti j , ui j , zi j ).
+rb(rik ) 1 − e
γd k=1j=1o(9)

We assume a Gamma prior for each of the original
work attractiveness scores αi as follows:
P(αi |a, b) =1 a a−1b αi exp(−bαi ),
Γ(a)

(10)

where a and b are hyperparameters. In this study, following
Iwata et al. [8], we set a = b = 1. We also assume a Gamma
prior for each creator influence αu , original work popularity ωi , and derivative work popularity σi . In addition, we
assume a Dirichlet prior over θu , u ∈ U+ as follows:Γ(β |U|) ∏ β−1P(θu |β) =θ ′(11)
Γ(β)|U| u′ ∈U\u uu
We use a Gamma prior for α, ω, and σ, and a Dirichlet priorfor Θ to analytically calculate the marginalization over theparameters. The marginalized joint distribution is computed
by integrating out those parameters as follows: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 ∑ ∑p
η(zi j )(ti j − tizi j )
∝ exp −i∈I j:zi j ,0

×

Kio
∏∏
i∈I k=1

Ki∏∏crb(riko ) Miki∈I k=1

rb(rikc )Nik∏ Γ(Li + a) ∏ Γ(Lu + a)
×(T + b)Li +a u∈U (Ru + b)Lu +ai∈I∏ Γ(Mi + a) ∏ Γ(Ni + a)×(Roi + b) Mi +a i∈I (Rci + b)Ni +ai∈ITSUKUDA et al.: MODELING N-TH ORDER DERIVATIVE CREATION BASED ON CONTENT ATTRACTIVENESS AND TIME-DEPENDENT POPULARITY975(

Γ (β |U|)×Γ (β)|U|)|U+ | ∏ ∏u′ ∈U\u Γ (Luu′ + β)u∈U+Γ (Lu + β |U|),∂S (γp )/∂γp,∂2 S (γp )/∂2 γpwhere S (γp ) is given by:∑∑p
S (γp ) = − γp(ti j − tizi j )i∈I j:1≤zi j ≤|Dit\u |∑−(Lu + a) log(Ru + b).

where


γp if 1 ≤ zi j ≤ Dit\uη(zi j ) = 
γ
Dit\u + 1 ≤ zi j ≤ Dit\u + |Oit |
o if



γ if Dc
it\u + |Oit | + 1 ≤ zi j .
(13)Here, Mik and Nik are the number of posting events triggered by the kth ranked event of i and kth ranked event of∑Kio
i’s derivative work, respectively. The terms Mi = k=1
Mik∑Kic
and Ni = k=1 Nik represent the total number of posting
events triggered by ranked events of i and ranked eventsof∑ Jii’s derivative work, respectively. Furthermore, Li =j=1 δ(zi j , 0) is the number of posting events triggered by
i’s attractiveness, where δ(x, y)∑= 1∑if i x = y, and δ(x, y) ′= 0otherwise. The term Luu′ = i∈I Jj=1
δ(uizi j , u)δ(ui j , u ) is
the numberofposting
eventswhereutriggered u′ ’s post,∑and Lu = u′ ∈U\u Luu′ is the total number of posting events
triggered by u. Here, uizi j = 0 if zi j = 0, uizi j = −1
if Dit\u + 1 ≤ zi j ≤ Dit\u + |Oit |, and uizi j = −2 if
Dit\u + |Oit | + 1 ≤ zi j , which represent virtual creators. In
addition, Ru for each creator u ∈ U is given by:
)
1 ∑(
Ru =
1 − e−γp (T −t) ,(14)
γp t∈Duwhere Du is a set of timestamps of derivative work posting
events of u, and Roi and Rci for i are computed as follows:Kio∑γp ← γp −

(12)

(18)

(19)

u∈U

The β is estimated using the fixed point iteration
method [23]. The update rule is given by:∑∑u′ ∈U\u (Ψ(Luu′ + β) − Ψ(β))
u∈U+
∑
β←β
,
(20)
|U| u∈U+ (Ψ(Lu + β |U|) − Ψ(β |U|))where Ψ is the digamma function.
Finally, we can make the point estimates of the integrated out parameters as follows:α̂i =Li + a
,
T +b

α̂u =

Lu + a,Ru + b(21)

where α̂i and α̂u can be used to find attractive original works
and influential creators, respectively,ω̂i =Mi + a,Roi + bσ̂i =Ni + a,Rci + b(22)

where ω̂i and σ̂i can be used to find popular original works
and popular derivative works, respectively, and L ′ +βuu
if u = 0 ∨ u = −1 ∨ u = −2
 Lu +β|U|(23)
θ̂uu′ =  Luu′ +βotherwise,
Lu +β(|U|−1)which can be used to analyze influences between creators
including virtual creators.

Roi =

)
( )(
1
o
rb riko 1 − e−γo (T −tik ) ,γo k=1

(15)

Rci =

Ki
)
( )(
1 ∑
c
rb rikc 1 − e−γc (T −tik ) .
γc k=1(16)

In this section, we answer the following research questions
based on our quantitative experimental results:

Based on the marginalized joint distribution in Eq. (12),
we developed a stochastic EM procedure for the iteration. In
the E-step, given the current state of all but one variable zi j ,the new latent assignment of zi j is sampled from the following probability:

RQ1 Is adopting three factors, which are original work attractiveness, original work popularity, and derivative
work popularity, eﬀective to model derivative creation
activity? (Sect. 5.2)
RQ2 What kinds of ranking bias methods are eﬀective tomodel derivative creation activity? (Sect. 5.3)

5. Quantitative ExperimentscP(zi j = y|D, Z\i j , O, C, γ, β, a, b)()
P D, Z\i j , zi j = y|O, C, γ, β, a, b(
) ,∝P D\i j , Z\i j |O, C, γ, β, a, b

5.1
(17)

where y ∈ {0, 1, · · · , Dit\u +|Oit |+|Cit |}, and \i j represent theprocedure excluding the jth derivative work posting event ofi.
In the M-step, we estimate the decay parameters γ andDirichlet parameter β by maximizing the logarithm of thejoint likelihood in Eq. (12). We estimate γ using Newton’s
method. For example, the update rule of γp is given by:

DatasetIn our experiments, we used derivative creation activity dataof music content on Niconico, which is one of the mostpopular video sharing Web services in Japan. On Niconico, any user can upload and view videos, and derivative
creation activity of music content occurs frequently: according to Songrium, as of the end of May 2019, morethan 300,000 original song videos and more than 680,000
derivative videos had been uploaded to Niconico. Most
original songs are created using singing synthesizer software called VOCALOID [25]; we restricted ourselves toIEICE TRANS. INF. & SYST., VOL.E103–D, NO.5 MAY 2020

976

Fig. 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.

Category
Sing
Dance
Play

Table 3 Statistics of our dataset
|I|
|O|
|D|
|C|
4,035
64,973
199,320
67,627396
30,9259,420
22,954583
38,726
5,526
20,492|U|
18,715
1,153
692

original song videos of this type. With respect to derivative works, 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
song on 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 9/30/2013. Data between 1/1/2010
and 3/31/2013 were used as training data and data between
4/1/2013 and 9/30/2013 were used as test data. In each category, we eliminated original works that had fewer than two
derivative works and creators who posted fewer than threederivative works during the training period.
We also collected ranking data. On Niconico, users cansee 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 createdbased on several statistics of the previous day (e.g., viewcount 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 9/30/2013. Since
only daily ranking data is available on Niconico, the timestamp in all our experiments is measured in days.
Table 3 lists the statistics of the dataset used in the experiments.
5.2 Combination of Factors
5.2.1

Settings[Comparison Models] Recall that we introduced four factors that can be used to model derivative creation activity.
Hereafter, let Oatt, Uinf, Opop, and Dpop denote original
work attractiveness, creator influence, original work popularity, and derivative work popularity, respectively. As
mentioned in Sect. 3, we hypothesize that a model adopting Oatt, Opop, and Dpop is the most eﬀective. To evaluate this hypothesis, the following six models were compared: (1) Oatt, (2) Oatt+Uinf, (3) Oatt+Uinf+Opop+Dpop,(4) Oatt+Opop, (5) Oatt+Dpop, and (6) Oatt+Opop+Dpop,
where Oatt+Uinf, for example, represents the model thatcombines the factors of Oatt and Uinf. Among the six models, (2) corresponds to SCPP [8] and (6) is our proposedmodel.
[Evaluation Metric] Predictive performance is one of
the most commonly used metrics to evaluate the appropriateness of a learned model [8], [26]. Predictive performanceis computed using the negative logarithm of the likelihoodfor posting events (t, u) during the test period from T to T ′ .
The logarithm of the likelihood is given by:∑  ∫ T ′ ∑
 ∑

−
logλi (t, u), (24)
L=
λ
(t,
u)dt
i


i∈I

T

u∈U

(t,u)∈Dtestiwhere Dtest
is the test data for i. When the value of −L isismall, the predictive performance is high. To examine theinfluence of the length of the test period on our results, we
examined spans of test data from one month (4/1/2013 to
4/30/2013) up to six months (4/1/2013 to 9/30/2013). In every case, the model was trained using data between 1/1/2010
and 3/31/2013, and the test period began on 4/1/2013.
5.2.2

Experimental Results

Figure 2 shows the negative log-likelihood during each test
period in each category. During each test period, the modelthat achieved the best performance is marked with “*”. In
the “sing” category, Oatt+Opop+Dpop exhibited the best
result for all test periods. In the “dance” and “play” categories, it did not perform the best for all test periods, but
it stably exhibited high performance in all categories during all test periods. To evaluate the stability of the models, we computed the average rank of each model over six
test periods in each category. We also computed the average rank of each model over 3 categories × 6 test periods= 18 test periods. Table 4 lists the results. We can seethat Oatt+Opop+Dpop achieved the highest average rankover 18 test periods with relatively small standard deviation.
Although Oatt+Uinf exhibited the best results for five test
periods in the “play” category, the results in Table 4 indicate the instability of the model because its average ranks
in both “sing” and “dance” categories were low. By comparing Oatt+Uinf+Opop+Dpop with Oatt and Oatt+Uinf,
we can show the usefulness of adopting all four factors
rather than adoption only Oatt or Oatt+Uinf. Similarly,

TSUKUDA et al.: MODELING N-TH ORDER DERIVATIVE CREATION BASED ON CONTENT ATTRACTIVENESS AND TIME-DEPENDENT POPULARITY

977

Fig. 3

Negative logarithm of likelihood of each ranking bias method.

Table 4 Average rank of each model over six test periods in each category. “All” means average rank over 18 test periods. Numbers in parentheses indicate standard deviations.
Model
Oatt
Oatt+Uinf
Oatt+Uinf+Opop+Dpop
Oatt+Opop
Oatt+Dpop
Oatt+Opop+Dpop

Sing
6.0 (0.0)
3.7 (0.47)
2.0 (0.0)
5.0 (0.0)
3.3 (0.47)
1.0 (0.0)

Dance
6.0 (0.0)
4.7 (0.75)
2.3 (0.47)
3.0 (1.53)
3.7 (0.47)
1.3 (0.47)Play
4.5 (0.76)
1.5 (1.12)
3.8 (1.07)
6.0 (0.0)
1.8 (0.37)
3.3 (0.47)

All
5.5 (0.83)
3.28 (1.56)
2.72 (1.04)
4.67 (1.53)
2.94 (0.91)
1.89 (1.1)

comparison results between Oatt+Opop, Oatt+Dpop, andOatt+Opop+Dpop indicate the usefulness of adopting bothOpop and Dpop. Finally, by comparing Oatt+Opop+Dpop
and Oatt+Uinf+Opop+Dpop, we can conclude that our proposed model adopting Oatt, Opop, and Dpop is the mosteﬀective to model derivative creation activity.

Algorithm 1 Calculate degrees of three factors for jthderivative work posting event of i
Require: P(zi j |D, Z\i j , O, C, γ, β, a, b)
1: E f ⇐ P(zi j = 0|D, Z\i j , 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(zi j = y|D, Z\i j , O, C, γ, β, a, b)
5:
else
6:
Ehd ⇐ Ehd + P(zi j = y|D, Z\i j , O, C, γ, β, a, b)
7:
end if8:y⇐y+1
9: end while
10: return E f , Eho , Ehd

these results, we conclude that Reciprocal, which reflects
the creators’ browsing behaviors, is the most eﬀective formodeling derivative creation activity.

5.3 Ranking Bias Method Comparison
6. Qualtitative Experiments
5.3.1

Settings

As mentioned in Sect. 3.2.3, our model uses the reciprocal
rank method to bias the content ranking based on the creators’ browsing behaviors of a ranked list (hereafter, “Reciprocal”). To evaluate its eﬀectiveness, we compared it withthe following two methods. The first method, “Linear,” linearly decreases the ranking bias:
101 − riko

.
(25)
100
Here, rb(rikc ) is also computed in 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:
rb(riko ) = rb(rikc ) = 1 regardless of the content rank. With
this method, it is assumed that all ranked content has equal
influence.
We used the negative logarithm of the likelihood as anevaluation metric, as in Sect. 5.2.1.
rb(riko ) =5.3.2

Experimental Results

Figure 3 shows the comparison 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

In this section, we report on the qualitative analysis results interms of (1) category characteristics, (2) temporal development of factors that trigger derivative work posting events,(3) creator characteristics, (4) N-th order derivative creation
process, and (5) original work ranking.
6.1

Category Characteristics

By using the posterior distribution of latent variables in
Eq. (17), we can analyze the impact of each of the threefactors (Oatt, Opop, and Dpop) that trigger derivative work
posting events in a category. Algorithm 1 shows the pseudocode for computing the strengths of the three factors for thejth derivative work posting event of i. In the pseudo-code,
E f , Eho , and Ehd correspond to the strength of original work
attractiveness, original work popularity, and derivative work
popularity, respectively, where E f + Eho + Ehd = 1. By summing E f of all derivative works of all original works in a
category, we can obtain the strength of Oatt in the category.
In the same manner, we can obtain the strength of Eho andEhd in a category.
Table 5 lists the ratios of the three factors during thetraining period. The ratios of the three factors vastly diﬀeredfrom one category to another. In the “sing” category, the ratios of Opop and Dpop were both high, while that of Oatt
was low. These results indicate that the creators in this category are susceptible to fads and put a high priority on content popularity. In the “dance” category, the ratio of Dpop

IEICE TRANS. INF. & SYST., VOL.E103–D, NO.5 MAY 2020

978Fig. 4 Estimated number of derivative work posting events triggered by each of three factors permonth. Vertical axis represents the number of derivative works posted in a month.
Table 5

Ratios of estimated factors (%)

FactorOriginal work attractiveness (Oatt)
Original work popularity (Opop)
Derivative work popularity (Dpop)

Sing
14.6
40.0
45.4

Dance
17.3
21.7
61.0

Play
42.5
40.0
17.5

was higher than those of the other two factors. In this category, not all creators can compose their own choreography.
Hence, a creator often posts a derivative work in which thecreator dances to the original song with the original choreography. After that, other creators also post derivative works
in which they imitate the choreography. The results in Table 5 show that our model described this category’s characteristics well. In the “play” category, the ratio of Oatt washigh compared to those of the other two categories. This indicates that creators in this category often play their favorite
original songs without being aﬀected by fads.
6.2 Temporal Development of Factors
By using Algorithm 1, we can also analyze the temporaldevelopment of factors that trigger the derivative work posting events of each original work. In this section, we reporton the temporal development of factors per month. Given
original work i, we computed the sum of E f for each i’sderivative work posting event every month. Similarly, we
computed the sum of Eho and Ehd every month.
Figure 4 shows example results for three original songs
that we selected for this evaluation. In each category, weshow 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 in the horizontal axis is the month when the original work’s first derivative
work was posted. The blue, orange, and red bars indicate thenumber of posting events caused by the factor of Oatt, Opop,and Dpop, respectively. Again, we can observe the characteristics of each category. In the “sing” category, in theearly period of derivative creation activity, Oatt and Opop
had large influences. We could 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 influenceof Dpop increased as time proceeded. We also observed that
Oatt had some influence even at the end period of the graph.

This indicates the possibility that some creators happened tofind the original song (e.g., by keyword search) and decided
to cover the song because they were attracted to the song. In
the “dance” category, a limited number of creators who cancompose original choreography posted derivative works inthe early period (see blue bars in the first two months). After that, many other creators were influenced by such derivative works and posted new derivative works. The influenceof Opop was low throughout the period. In the first half ofthe period in the “play” category, many creators who put ahigh priority on Opop or Dpop posted this original work’s
derivative works; while in the last half, creators who put ahigh priority on Oatt kept posting derivative works.
6.3

Creator Characteristics

Given a creator, we aggregated E f , Eho , and Ehd for each of
his/her derivative work posting events into the three factors
and normalized their sum to 1. This enables us to analyze
the ratio at which a creator is influenced by each of three factors. Figure 5 shows the results where each dot represents
a creator. In each category, we plot the top 250 creators interms of the number of derivative works for visibility. In the“sing” category, although most creators put a high priority
on Opop and/or Dpop, creators in circle A put a high priority on Oatt. For a creator in circle A, it would be usefulto recommend original works similar to the original works
he/she used in the past to encourage more derivative work
creation. In the “dance” category, creators in circle B werelikely to be those who can compose original choreography.
We can also use this finding for recommendation. In the“play” category, creators in circle C put a high priority on
Dpop contrary to other creators. For these creators, it would
be helpful to recommend popular content in the derivative
work ranking.
6.4

N-th Order Derivative Creation Process

By using the posterior distribution of latent variables, we
can visualize the derivative creation process of an original
work. To visualize the process, for each derivative work, we
detected y, which is the maximum value in Eq. (17). Wheny was equal to 0 or indicated the index of the original work’s
ranked event, derivative work creation was triggered by theoriginal work; when y indicated the index of the ranked

TSUKUDA et al.: MODELING N-TH ORDER DERIVATIVE CREATION BASED ON CONTENT ATTRACTIVENESS AND TIME-DEPENDENT POPULARITY

979

Fig. 5 Creator distributions based on ratio at which a creator is influenced by each of three factors.
Each dot represents one creator.

Fig. 6 Derivative works creation process of an original work in “dance” category. 0 represents theoriginal work, and the number j ≥ 1 give the indices of the derivative works.

event of the j′ th derivative work, derivative work creation
was triggered by the j′ th derivative work.
Figure 6 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 jthderivative work. An edge between numbers indicates thatthe lower content creation was triggered by the upper one.
In this derivative creation process, the 1st derivative work
played an important role because it triggered many derivative creations. We also observed that 9th order derivative
creation (82nd derivative work) occurred in this process.
6.5 Original Work Ranking
Finally, we show that we can generate original work ranking
in a new light based on the estimated parameters. Popularity
is an important metric when an original work ranking is generated. For example, it is common to rank videos based on
their view count. The ranking based on view count reflects
the popularity among consumers or viewers. It is also possible to consider the popularity among creators, where one of
the simplest ways is to rank original works according to thetotal number of derivative works. However, this popularity
includes various kinds of factors: in our case, Oatt, Opop,and Dpop. On the other hand, by using our model, we cangenerate original work rankings based on each of the threefactors. In this section, due to space limitations, we discuss
the ranking based on Oatt.
Given a category and rank threshold l, we generate the
top l original work ranking, denoted as R1 , where origi-

Table 6 Spearman’s rank correlations between ranking based on numberof derivative works and that based on original work attractiveness. “All”
means ranking that takes into account derivative works in all three categories.
l
10
30
50
100

Sing
0.170
-0.0372-0.199-0.0439Dance-0.0909
0.238
0.286
0.105

Play
-0.3160.202
0.08320.357

All-0.3330.272
0.00101
0.0883nal works are ranked in descending order of the number ofderivative works during the test period. We also generate
the original work ranking, denoted as R2 , where l original
works in R1 are re-ranked in descending order of αi . Recall
that αi in Eq. (21) represents i’s attractiveness at the end of
the test period. Then Spearman’s rank correlation between
R1 and R2 is computed.
In addition, we generate two original work rankings
considering all three categories at once: (1) the ranking
where original works are ranked based on the sum of thenumber of derivative works in three categories, and (2) the
ranking where original works are ranked based on the sumof αi in three categories.
Table 6 lists the results. Overall, the rank correlations
were low. These results indicate that original work ranking
based on original work attractiveness largely diﬀers fromthat based on the number of derivative works, and our proposed model enables consumers to see the ranked list oforiginal works in a new light.

IEICE TRANS. INF. & SYST., VOL.E103–D, NO.5 MAY 2020

980

7.

Conclusion

We proposed a probabilistic model for inferring latent factors and their influences in derivative creation activity. The
model incorporates three factors: (1) original work attractiveness, (2) original work popularity, and (3) derivative
work popularity. Our model takes into account content popularity obtained from content ranking data. Our experimental results using real-world derivative creation data showedthat our model adopting all three factors achieved the best
result in terms of the log likelihood. With respect to content
popularity, we showed that using reciprocal rank in content
ranking that reflects creators’ browsing behaviors achieved
the best result. In our qualitative experiments, we showed
the usefulness of our model in various aspects including category characteristic analysis (e.g., original work attractiveness has a large influence in the “play” category), visualizing the spread of derivative works creation activity, etc. The
limitation of our model is that it presupposes the existenceof the ranking information. Such information can be easily
obtained in other domains such as 3D models and recipes
since the popularity-based rankings of original and derivative works are usually generated from some statistics suchas the view count and the favorite count of each work. We
therefore believe that our model is general and independentof content types.
For future work, we are interested in extending ourmodel by considering additional factors. For example, someoriginal works may be often used to create derivative works
during Christmas. Considering such seasonality [27] is one
possible direction to extend our model.
Acknowledgments
This work was supported in part by JST ACCEL Grant
Number JPMJAC1602, Japan.
References[1] M. Hamasaki, H. Takeda, and T. Nishimura, “Network analysis of
massively collaborative creation of multimedia contents: Case studyof hatsune miku videos on nico nico douga,” UXTV, pp.165–168,
Oct. 2008.
[2] C. Cayari, “The YouTube eﬀect: How YouTube has provided new
ways to consume, create, and share music,” International Journal of
Education & the Arts, vol.12, no.6, pp.1–28, 2011.
[3] L.A. Liikkanen and A. Salovaara, “Music on YouTube: user engagement with traditional, user-appropriated and derivative videos,”Computers in Human Behavior, vol.50, pp.108–124, Sept. 2015.
[4] S. Papadimitriou and E.E. Papalexakis, “Towards laws of the 3dprintable design web,” WebSci, pp.255–256, June 2014.
[5] M. Goto, “Grand challenges in music information research,”
Dagstuhl Follow-Ups: Multimodal Music Processing, vol.3,
pp.217–225, 2012.
[6] L.A. Granka, T. Joachims, and G. Gay, “Eye-tracking analysis ofuser behavior in www search,” SIGIR, pp.478–479, July 2004.
[7] T. Joachims, L. Granka, B. Pan, H. Hembrooke, and G. Gay, “Accurately interpreting clickthrough data as implicit feedback,” SIGIR,
pp.154–161, Aug. 2005.

[8] T. Iwata, A. Shah, and Z. Ghahramani, “Discovering latent influence
in online social activities via shared cascade poisson processes,”
KDD, pp.266–274, Aug. 2013.
[9] K. Tsukuda, M. Hamasaki, and M. Goto, “Why did you cover thatsong?: Modeling n-th order derivative creation with content popularity,” CIKM, pp.2239–2244, Oct. 2016.
[10] K. Eto, M. Hamasaki, K. Watanabe, Y. Kawasaki, and T. Nishimura,“Modulobe: A creation and sharing platform for articulated models
with complex motion,” ACE, pp.305–308, Dec. 2008.
[11] G. Cheliotis and J. Yew, “An analysis of the social structure of remix
culture,” C&T, pp.165–174, June 2009.
[12] M. Hamasaki and M. Goto, “Songrium: A music browsing assistance service based on visualization of massive open collaboration
within music content creation community,” WikiSym, pp.4:1–4:10,
Aug. 2013.
[13] X. Song, Y. Chi, K. Hino, and B.L. Tseng, “Information flow modeling based on diﬀusion rate for prediction and ranking,” WWW,
pp.191–200, May 2007.
[14] X. Song, B.L. Tseng, C.Y. Lin, and M.T. Sun, “Personalized recommendation driven by information flow,” SIGIR, pp.509–516, Aug.
2006.
[15] J. Yang and J. Leskovec, “Modeling information diﬀusion in implicit
networks,” ICDM, pp.599–608, 2010.
[16] K. Saito, M. Kimura, K. Ohara, and H. Motoda, “Learning
continuous-time information diﬀusion model for social behavioral
data analysis,” ACML, pp.322–337, 2009.
[17] A. Simma and M.I. Jordan, “Modeling events with cascades of poisson processes,” UAI, pp.546–555, July 2010.
[18] Y. Tanaka, T. Kurashima, Y. Fujiwara, T. Iwata, and H. Sawada,“Inferring latent triggers of purchases with consideration of social
eﬀects and media advertisements,” WSDM, pp.543–552, Feb. 2016.
[19] K. Tsukuda, K. Ishida, M. Hamasaki, and M. Goto, “Songrium
Derivation Factor Analysis: A web service for browsing derivation
factors by modeling n-th order derivative creation,” IEICE Trans.
Inf. & Syst., vol.E101-D, no.4, pp.1096–1106, April 2018.
[20] A.L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol.286, no.5439, pp.509–512, Oct. 1999.
[21] D.L. Snyder and M.l I. Miller, Random Point Processes in Time andSpace, Springer, 1991.
[22] M. Gomez-Rodriguez, D. Balduzzi, and B. Schölkopf, “Uncovering
the temporal dynamics of diﬀusion networks,” ICML, pp.561–568,
June 2011.
[23] S. Myers and J. Leskovec, “On the convexity of latent social network
inference,” in Advances in Neural Information Processing Systems
23, pp.1741–1749, Dec. 2010.
[24] G. Last and A. Brandt, Marked point processes on the real line : thedynamic approach, Probability and its applications, Springer-Verlag,
1995.
[25] H. Kenmochi and H. Ohshita, “Vocaloid - commercial singing
synthesizer based on sample concatenation,” INTERSPEECH,
pp.4009–4010, 2007.
[26] A. Karatzoglou, X. Amatriain, L. Baltrunas, and N. Oliver, “Multiverse recommendation: N-dimensional tensor factorization forcontext-aware collaborative filtering,” RecSys, pp.79–86, Sept.
2010.
[27] H. Kim, N. Takaya, and H. Sawada, “Tracking temporal dynamics
of purchase decisions via hierarchical time-rescaling model,” CIKM,
pp.1389–1398, Nov. 2014.

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Kosetsu Tsukuda
received the Ph.D. degrees in Informatics from Kyoto University,
Japan in 2014. He is currently a Researcher
at the National Institute of Advanced Industrial
Science and Technology (AIST), Japan. His
research interests lie in the areas of data mining, information recommendation, and information retrieval regarding user-generated content and music content. He has received nine
awards including IPSJ Computer Science Research Award for Young Scientists and IPSJ Yamashita SIG Research Award.

Masahiro Hamasaki
received the Ph.D. degree in informatics from the Graduate University for Advanced Studies (SOKENDAI), Japan
in 2005. He is currently the Leader of the Media Interaction Group at the National Instituteof Advance Industrial Science and Technology(AIST), Japan. His research interests include
Web mining, semantic Web, and social media
analysis. He is a member of the JSAI, the IPSJ,
and ACM.

Masataka Goto
received the Doctor ofEngineering degree from Waseda University in
1998. He is currently a Prime Senior Researcher
at the National Institute of Advanced Industrial
Science and Technology (AIST), Japan. Overthe past 27 years he has published more than
270 papers in refereed journals and international
conferences and has received 51 awards, including several best paper awards, best presentation
awards, the Tenth Japan Academy Medal, andthe Tenth JSPS PRIZE. In 2016, as the Research
Director he began OngaACCEL Project, a 5-year JST-funded research
project (ACCEL) on music technologies.