Skill-based Team Formation in Software
Ecosystems
Daniel Schall
1
Abstract. This paper introduces novel techniques for the
discovery and formation of teams in software ecosystems. Formation techniques have a wide range of applications including
the assembly of expert teams in open development ecosystems, finding optimal teams for ad-hoc tasks in large enterprises, or working on complex tasks in crowdsourcing environments. Software development performance and software quality are affected by the skills and application domain experiences that the team members bring to the project. Team formation in software ecosystems poses new challenges because
development activities are no longer coordinated by a single organization but rather evolve much more flexibly within
communities. A suitable approach for finding optimal teams
must consider expertise, user load, social distance and collaboration cost of team members. We have designed this model
specifically for the analysis of large-scale software ecosystems
wherein users perform development activities. We have studied our approach by analysing the R ecosystem and find that
our approach is well suited for the team discovery in software
ecosystems.
A key challenge in software ecosystems is to manage quality
of software [8, 9, 15] and addressing nonfunctional requirements (NFRs) in general [4]. Software vendors may require
their plug-in developers to maintain certain quality levels to
deserve an approved status. As shown in earlier research, individual as well as development team skill has a significant effect
on the quality of a software product [5, 7, 12]. The approach in
this work takes a socio-technical view on software ecosystems
wherein ecosystems are understood as the interplay between
the social system and the technical system [11, 13]. Software
development teams composed of members with prior joint
project experience may be more effective in coordinating programmers’ distributed expertise because they have developed
knowledge of who knows what [12]. This paper addresses the
problem of team formation in open, dynamic software ecosystems. In open source development teams are more often than
not formed spontaneously (i.e., they ‘emerge’) based on people’s availability, willingness to collaborate and to contribute
to a certain task.
Potential tasks for expert teams in software ecosystems and
open source development include:
1
• Come up with a software design and/or implementation of
a complex component or subsystem.
• Perform software architecture review of an existing implementation or provide expert opinion about an emerging
technology.
Introduction
Establishing a software ecosystem becomes increasingly important for a companies’ collaboration strategy with other
companies, open source developers and end users. The idea
behind software ecosystems differs from traditional outsourcing techniques [19, 22]. The initiating actor does not necessarily own the software produced by the contributing actors nor
are contributing actors hired by the initiator (e.g., a firm).
All actors as well as software artefacts, however, coexist in an
interdependent way. For example, actors jointly develop applications and thus there is a relationship among the actors.
Software components may depend on each and thus there is a
relationship among the components. This is a parallel to natural ecosystems where the different members of the ecosystems (e.g., the plants, animals, or insects) are part of a food
network where the existence of one species depends on the
rest. In contrast to natural ecosystems, some software ecosystems may be mainly top-down controlled, with most changes
driven by change requests and bug reports coming from other
actors [20]. Other software ecosystems may be controlled in
a bottom-up manner, primarily driven by input from its core
developers [21].
1
Siemens Corporate Technology, Siemensstrasse 90, 1211 Vienna,
Austria, email: [email protected]
To give a concrete example of a potential high-level task, a
complex design or implementation may involve the analysis of
timeseries data including data extraction from a source system, transformation of the data, storage, processing, and visualization. Clearly, this task typically requires multiple people
with distinct skills such as data modelling, statistical knowledge (uni-/multivariate data analysis), data persistence management, and data visualization using various technologies
and toolkits. Indeed, the high-level task needs to be further
decomposed into smaller task. The goals of this work is to
find a team of experts given a set of high level skills. Once
the team has been discovered, detailed task decomposition
and work planning can be performed, which is however not in
the focus of this work.
We provide the following key contributions:
• A novel approach supporting team formation in software
ecosystems based on user expertise, load, social distance
among team members, and collaboration cost.
• Support the discovery of potential mediators if social connectedness in teams is low.
• Analysis of user expertise to recommend the most suitable
team members.
• Evaluation of the concepts using data collected from the
Comprehensive R Archive Network (CRAN) - the largest
public repository of R packages.
The remainder of this paper is organized as follows. In Section 2 we overview related work and concepts. In Section 3
we introduce our team formation approach. Experiments are
detailed in Section 4. The paper is concluded in Section 5.
3
Formation in Ecosystems
Here we present the overall team formation algorithm. We
employ a genetic algorithm that attempts to find the best
team. Genetic algorithms (GAs) mimic Darwinian forces of
natural selection to find optimal values of some function [23].
For each team a single number denoting the team’s fitness
is calculated (where larger values are better).
3.1
Genetic Algorithm Outline
There are multiple objectives that need to be optimized. The
objectives are to:
2
Related Work
The success of a project depends not only on the expertise
of the people who are involved, but also on how effectively
they collaborate, communicate and work together as a team
[17, 26]. On the one hand, a team must contain the right set
of expertise, but on the other hand one should determine a
staffing level that, while comprising all the needed expertise,
minimizes the cost and contributes to meeting the project
deadline [10]. The most critical resource for knowledge teams
is expertise and specialized skills in using and handling tools.
But the mere presence of expertise in a team is insufficient
to produce high-quality work. A team must collaborate in an
effective manner. It has been found that prior collaborative
ties have a profound effect on developers’ project joining decisions [12].
In software engineering, team formation is often needed to
perform a development or maintenance activity. A general
trend is the growing number of large scale software projects,
software development and maintenance activities demanding
for the participation of larger groups [6, 14]. In [3], the authors
proposed assignment of experts to handle bug reports based
on previous activity of the expert. Social collaboration on
GitHub including team formation has been addressed in [18].
The authors [2] study the problem of online team formation.
In their work, a setting in which people possess different skills
and compatibility among potential team members is modelled
by a social network. It has to be noted that team formation in
social networks is an NP -hard problem. Thus, optimization
algorithms such as genetic algorithms [29] should be considered in solving the team composition problem [31].
Expertise identification is one of the key challanges and success factors for team work and collaboration [16]. The discovery of experts is becoming critical to ease the communication
between developers in case of global software development or
to better know members of large software communities [30].
Network analysis techniques offer a rich set of theories and
tools to analyse the topological features and human behaviour
in online communities. We have extensively studied the automatic extraction of expertise profiles in our prior research
(see [24, 25, 27]) and build upon our social network based
expertise mining framework.
With regards to team formation in open source communities as well as software ecosystems, there is still a gap in
related work and to our best knowledge there is no existing
approach that supports formation based on mined expertise
profiles.
• maximize the average expertise score for given skills
• minimize the average cost
• minimize the average distance
The team with the best trade-off among these objectives
shall obtain the highest fitness and will be recommended as
the best fitting team. The required team skills are stated by
customers who wish to assign a specific complex task to a
team of experts — be it within a corporation or outsourcing
a specific task to the crowd. Our assumption is that such complex tasks demand for the expertise of multiple team members. Within our formation approach, additional constraints
can be considered such as one person shall only cover one skill
and not multiple ones. Indeed, in practice people are familiar
with multiple topics thereby covering multiple skills. Factors
such as matching user load with complexity, effort, and deadline of a task are not in focus of this work. The reader may
refer to [25] for further information on these topics.
The main computational steps of our formation approach
are introduced and elaborated in detail in Algorithm 1. The
relevant lines in Algorithm 1 are specified in parenthesis.
1. Based on the set S = {s1 , s2 , . . . , sn } of demanded skills,
prepare a mapping structure that holds skills, users U , and
expertise ranking scores (lines 6-9). In this step, current
user load is evaluated (based on previously assigned tasks)
and users with high load are filtered out.
2. Initialize a population of individuals. An individual is a
team consisting of n team members where n can be configured. The parameter n is given by the size of the skill set
S if each team member has to provision exactly one skill
(line 12).
3. Loop until max iterations have been reached and compute
the main portion of the genetic algorithm based search
heuristic. Finally, after this loop select the team with the
highest fitness (lines 14-48).
4. Depending on the ecosystems community structure and the
demanded set of skills, teams may have good or poor connectivity in terms of social links among team members.
Therefore, construct a subgraph of the social collaboration
graph GS containing only the nodes from the best team
and their edges between each other. Analyse the connectivity of this subgraph by computing the average number
of neighbours (lines 50-51).
5. If connectivity is low, try to find a dedicated coordinator
who is ideally connected to all team members through social links. The role of the coordinator is to mediate communication among members and strengthen team cohesion
(line 53-56).
Algorithm 1 Formation algorithm.
1: input: skills S, population size p size,
2: elitism elitism k, max iterations max iter
3: output: best individual - team with the highest fitness
4: # init mappings of skills, users, scores
5: M ← ∅
6: for Skill s ∈ S do
7:
m ← getRankingScoreM apping(s)
8:
M [s] ← m # add mapping
9: end for
10: # initialize population of
11: # randomly composed individuals
12: P ← createP opulation(S, M, p size)
13: iter ← 0 # iteration counter
14: while iter++ < max iter do
15:
# new population
16:
P 0 ← createEmptyP opulation(p size)
17:
# obtain a ranked list
18:
R ← rankP opulationByF itness(P)
19:
# elitism - copy small part of the fittest
20:
for i = 0 . . . elitism k − 1 do
21:
# add to population
22:
P 0 [i] ← getIndividualByRankIndex(R, i)
23:
end for
24:
# build new population
25:
i ← elitism k
26:
while i < p size do
27:
# stochastically select from P
28:
I[] ← rouletteW heelSelection(P)
29:
# crossover
30:
if randomN umber < crossover rate then
31:
# assign new offspring
32:
I[0] ← crossover(I[0], I[1])
33:
end if
34:
# mutation
35:
if randomN umber < mutation rate then
36:
# assign mutated individual
37:
I[0] ← mutate(I[0])
38:
end if
39:
# add new offspring
40:
P 0 [i++] ← I[0]
41:
end while
42:
# assign the new population
43:
P ← P0
44:
# evaluate population - total fitness
45:
evaluate(P)
46: end while
47: # this is the best team
48: I ← f indBestIndividual(P)
49: # construct a graph GI based on I
50: GI ← extractSubGraph(GS , I)
51: if checkConnectivity(GI ) < ζ then
52:
# find node to increase connectivity
53:
u ← f indCoordinator(GI )
54:
if u 6= null then
55:
addN ode(GI , u)
56:
end if
57: end if
58: # extract the node set NI ⊂ U from GI
59: NI ← getN odes(GI )
60: return NI # node set of best team members
3.2
Detailed Computational Steps
In the following we detail the steps in the algorithm and explain additional functions that are invoked while executing
the formation algorithm.
3.2.1
Rank Expertise by Skills
Expertise profiles are not created in a predefined, static manner. Expertise is calculated based on actual community contributions. However, we do not attempt to analyse detailed user
contributions in terms of software versioning control systems
but rather focus on ‘high-level’ package metadata thereby following a less privacy intrusive approach. The method used for
determining the expertise scores is not within the focus of this
work due to space limits. The interested reader may refer to
[27, 28] for information on the basic approach.
3.2.2
Basic Selection Strategies
An initial set of candidate solutions are created and their corresponding fitness values are calculated. This set of solutions
is referred to as a population and each solution as an individual (i.e., the team composed of team members). The individuals with the best fitness values are selected and combined
randomly to produce offsprings, which make up the next population. The approach of selecting a subset of individuals with
the best fitness values is called elitism. Elitism is realized by
copying the fittest individuals to the next population.
To maintain a demanded population of individuals, individuals are selected and undergo crossover (mimicking genetic
reproduction). For the team formation approach this means
that team members are swapped between two teams. The basic part of the selection process is to stochastically select from
one generation to create the basis of the next generation (see
rouletteW heelSelection in line 28). The requirement is that
the fittest individuals have a greater chance of survival than
weaker ones. This replicates nature in that fitter individuals
will tend to have a better probability of survival and will go
forward. Weaker individuals are not without a chance. In nature such individuals may have genetic coding that may prove
useful to future generations [1].
Individuals are also subject to random mutations. However,
the probability of mutation is low because otherwise the genetic algorithm would be just a random search procedure. In
our work we apply a ‘smart’ approach to mutation and do
not select a replacement team member at random. Rather, a
new team member is predicted and voting is performed by
the existing team members.
3.2.3
Relationship-driven Mutation
In traditional GAs, which are agnostic to the underlying nature of the population, mutation takes place by exchanging a
gene by a random gene thereby maintaining genetic diversity.
Here we perform prediction of edges between existing team
members and newly randomly selected team members. If a
threshold is surpassed, the randomly suggested team members is added to the team. This prediction approach ensures a
much higher likelihood that the new team member will work
within the team more effectively. We propose random forests
for predicting edges between pairs of users. Random forests
are a simple yet effective and robust method for classification problems. Prediction of edges between pairs of users is
performed by modelling features describing the relationship
between two nodes u and v. At a high level, these features include common neighbours, the jaccard similarity index, joint
community interest, and joint package dependencies.
3.2.4
Fitness Function
The last important ingredient of our GA based approach is
the design of a workable fitness function. A fitness function
is a type of objective function that is used to provide a single number. The idea is to discard ‘bad’ team configurations
(i.e., individuals) and to breed new ones from the good configurations. The search heuristic is terminated when either the
overall fitness converges or the maximum number of iterations
have been reached.
The fitness function computes the value ΦI as
ΦI = w1 ∗ expertise + w2 ∗ cost + w3 ∗ distance
(1)
where w1 + w2 + w3 = 1. Each of the input factors
expertise, cost, distance needs to be scaled between 0 and
1. ΦI is computed when invoking the function evaluate (see
Algorithm 2 Fitness function.
1: input: skills S, individual I, ranking score mapping M
2: output: fitness value ΦI ∈ [0, 1] of individual I
3: metrics ← ∅ # metrics as basis for fitness
4: score ← 0 # team expertise score
5: popularity ← 0 # popularity - to approximate cost
6: for Skill s ∈ S do
7:
u ← I[s] # get member by skill
8:
rs ← M [s][u] # expertise score by skill
9:
# perform feature scaling
max(M [s])−rs
10:
rs0 ← 1 − max(M
[s])−min(M [s])
11:
score ← score + rs0
12:
# get user degree in GS
13:
ku ← degree(GS , u)
14:
# perform feature scaling
−ku
15:
ku0 ← kmax
kmax
16:
popularity ← popularity + ku0
17: end for
18: # add average team expertise score to metrics
19: addM etric(metrics, score/|S|)
20: # add average popularity to metrics
21: # higher community popularity means higher cost
22: addM etric(metrics, popularity/|S|)
23: dist ← 0 # social distance
24: Q ← queue(I)
25: while Q 6= ∅ do
26:
u ← poll(Q)
27:
for v ∈ Q do
28:
# unweighted shortest path distance
29:
# d(u, v) computed in GS
30:
duv = d(u, v)
31:
if duv 6= null then
32:
# perform feature scaling
33:
# lower values are better
34:
# max(GS ) is diameter of graph
S )−duv
35:
d0uv ← max(G
max(GS )−1
36:
dist ← dist + d0uv
37:
end if
38:
end for
39: end while
40: GI ← extractSubGraph(GS , I)
41: # add average distance to metrics
42: addM etric(metrics, dist/|edges(GI )|)
43: ΦI ← 0
44: for m ∈ metrics do
45:
ΦI ← ΦI + wm ∗ metric
46: end for
Algorithm 1 line 45). Later on ΦI is used to rank the population by fitness (see Algorithm 1 line 17) as well as when
calling f indBestIndividual (see Algorithm 1 line 48).
Algorithm 2 details the computational steps of an individual I’s fitness as defined by Eq. 1. An approximation of a
cost factor is provided by community popularity in terms of
number of neighbours in the social graph GS . Thus, according
to this logic more popular users are also more expensive. A
perfect fitness score, given a set of skills S, would be 1. This
is however impossible to achieve because expertise is also influenced by the user degree in GS . Thus, a suitable tradeoff
among these factors has to be found. The individual with the
highest fitness within the population is then selected and recommended as the best team.
3.2.5
Coordinators
Based on the set of demanded skills and community structure,
it may not be possible to find teams with good connectivity among the team members. The last steps in Algorithm 1
would be to check the connectivity of I and to find a dedicated
node who is ideally connected to all nodes in I to mediate
communication. All nodes in U matching this constraint are
then ranked based on their averaged expertise given the skill
set S. The discovered node acting is potential team coordinator is added to the final team.
4
Experimental Evaluation
4.1
R Ecosystem
In this section we present our experiments. We focus on one
part of the R ecosystem called the Comprehensive R Archive
Network (CRAN). Other R-based communities not considered
in this research are, for example, Bioconductor2 . We have implemented a Web crawler to download3 and parse R software
package meta information available as HTML pages. This information includes contributing authors and package dependencies. In addition, CRAN provides so called CRAN task
views, which are used in our analysis as skill or topic information. As an example, a given task view Bayesian Inference
would be a single skill.
Figure 1 shows the package authorship graph GA .
Rick Katz
Greg Young
Wanhua Su
Alexandra Laflamme−Sanders
extRemes
lago
Huan Cheng
SpatialVx
distillery
smoothie
BASIX
in2extRemes
GeneFeST
Eric Gilleland
Bastian Pfeifer
Ulrich Wittelsbuerger
PopGenome
Bob Handsaker
A. G. Taylor
S. D. Cohen
C. A.J. Appelo
Liangying Zhang
R. Serban
D. Gillespie
Holly Janes
S. R. Charlton
D. Shumaker
D. L. Parkhurst
Tom Kraljevic
Spencer Aiello
Tim Hoar
RadioSonde
phreeqc
Amy Wang
Petr Maj
iid.test
Ariel Rao
h2o
Yanming Li
esd4all
replicationDemos
cyclones
Alexandra Imbert
clim.pact
Bin Nan
anm
MSGLasso
Nello Blaser
Rasmus E. Benestad
Luisa Salazar Vizcaya
knnflex
Yan Liu
Dennis D. Boos
Alejandro Cáceres
Yubo Zou
Atina Dunlap Brooks
PrecipStat
Yuzheng Zhang
Dorit Hammerling
Rlab
Yingwei Peng
qqplotter
Hexin Zhang
Tia Lerud
MLPAstats
CNVassoc
Douglas Nychka
Nathan Lenssen
Edsel A. Peña
CNVassocData
gcmrec
Doug Nychka
LatticeKrig
smcure
Emmanuel Sharef
gvlma
Elizabeth H. Slate
Juan R. González
survrec
Robert L. Strawderman
Stephan Sain
splinesurv
David Ruppert
Added Fortran
Alan C. Hindmarsh
Stephen Sain
Chao Cai
Piotr Romanski
ordBTL
David M. Spooner
John Paige
fields
Jiajia Zhang
Songfeng Wang
FSelector
Rene Gomez
International Potato Center
William Roca
Marc Ghislain
Giuseppe Casalicchio
exsic
mcpd
Barry Hurley
Merideth Bonierbale
Jie Zhou
Vilma Hualla
Tobias Kuehn
quipu
NPHMC
Lars Kotthoff
Talal Rahwan
Erich Studerus
Pablo Carhuapoma
Reinhard Simon
divagis
Felipe de Mendiburu
Leonard Judt
TransModel
llama
Michael Braun Original Fortran
monographaR
Jorge Nunez
Stef de Haan
Sangkyun Lee
H. Welsh
Zachary Jones
KappaV
Fraser Ian Lewis
agricolae
Thomas F. Coleman
Lluís Armengol
Fraser Lewis
datacheck
sparseHessianFD
Lingbing Feng
Marta Pittavino
Marcelo Reginato
Xavier Solé
SNPassoc
Dan Dkin
J. O’Neill
abn
Vincent Bonhomme
Sarah Ivorra
Cedric Gaucherel
Evan Saitta
Jorge J. More
Jun Peng
Sandrine Picq
Asher Wishkerman
Telmon
Wenbin Lu
Hinrich W. H.
GohlmannChiara Forcheh
Anyiawung
Elisabet Guinó
Burton S. Garbow
Maren Rebke
Ulrike von Luxburg
Kenneth Hillstrom
Neus Martinez
loe
tgcd
Hoksan Yip
Momocs
Alberto Murta
Yoshikazu Terada
SVMMaj
Lieven Clement
BaSTA
Anu Sironen
Reinhard Furrer
Jason Collison
Alexander Duerre
smds
Geert Verbeke
hoardeR
GeneticTools
REPPlab
isopam
simco
ALKr
Pushpike Thalikarathne
gaussquad
Patrick J. F. Groenen
Enyelbert Muñoz
PamGeneMixed
sscor
Sebastian Schmidtlein
GENEAread
Daniel Fischer
orthopolynom
cluster.datasets
Hannes Feilhauer
aBioMarVsuit
LDRTools
Frederick Novomestky
liso
Eero Liski
Zhou Fang
Vincent T. van Hees
autopls
goalprog
Daniel Vogel
rportfolios
gMWT
GGIR
Owen Jones
matrixcalc
Carsten Oldenburg
Severine Sabia
Ziv Shkedy
Fernando Colchero
Jose Francisco Loff
Linda R. Petzold
Ricardo Kriebel
Georgi NalbantovNorbert
Willem Talloen
truncdist
Alain Berro
beadarrayFilter
Raquel Iniesta
Marion Deville
Robert Maillardet
OjaNP
Emmanuel Rousseaux
BayHap
Richard Brent
Bradford B. Worrall
Ed Ionides
Stephen
Michele M.
Sale R. Williams
ABCoptim
PST
Steven Carnie
John Burkardt
Martin Kroll
credule
Víctor Moreno
Jung−Ying Tzeng
Carles Breto
Olga Borovkova
OptGS
Jyrki Möttönen
spuRs
Hannu Oja
Steve Ellner
Dao Nguyen
Sebastian Funk
Edward L. Ionides
FastKM
Michael Lavine
googlePublicData
Sara Taskinen
ICSNP
MNM
MuFiCokriging
httk
Markus Matilainen
Dave Tyler
Alexandre Janon
popEpi
CosmoPhotoz
Malte Jastrow
Omkar Muralidharan
J. Pitkaniemi
Jospeh Hilbe
financial
Lukasz Komsta
Olivier Roustant
DiceOptim
DiceKriging
quantchem
T. Wagner
KrigInv
Vincent Moutoussamy
Rick ReevesMarguerite A. Butler
AHR
Matthias Brueckner
Yann Richet
Nicolas Bousquet
dtt
David Ginsbourger
GPareto
Victor Picheny
Cleve Moler
outliers
Clement Walter
subplex
MarkedPointProcess
Martin Schlather
ouch
Gilles Defaux
Edward Sudicky
Rene Therrien
Aaron A. King
SoPhy
Guanhua Chen
Heike Schuhmacher
Wolfgang Lederer
Heike Schumacher
simex
fastM
moonsun
mblm
Clement Chevalier
Jérôme Guélat
regtest
Jens Oehlschlägel
kergp
Paul Lemaitre
rindex
bit
James Lovato
Andrew Robinson
S. Marmin
DiceView
Barry W. Brown
Andre Moitinho
RenextGUI
Nicolas Durrande
Yves Deville
GPlab
Energie Atomique
Laurent Gilquin
RsimMosaic
UPMASK
codadiags
Service d’Etudes
Acho Arnold
Jens Oehlschl
RCEIM
msme
equivalence
fanovaGraph
Joseph Guillaume
Brett T. McClintock
ref
Alberto Krone−Martins
Renext
Olivier Jacquet
K. Seppa
mixfdr
multimark
Werner Brannath
bit64
AGSDest
COUNT
Thomas Muehlenstaedt
Jana Fruth
Taieb Touati
sensitivity
Esa Ollila
Stephen P. Ellner
Joseph M. Hilbe
Xavier Bay
Alexis Jinaphanh
colcor
Jaakko Nevalainen
Jean−Francois Cardoso
Rachel Marceau
Carles Martinez Breto
Fang−Chi Hsu
Daniel C. Reuman Seija Sirkia
Bradley Efron
Jonathan Elliott
LOGIT
safi
M. Rantanen
Jari Miettinen
JADE
SpatialNP
James Wason
Jimena Davis
Sebastien Da Veiga
Loic Le Gratiet Nisha Sipes
David E. Tyler
ICS
moments
Simulation du Comportement
Robert
Pearce
Bernardo
Ramos
Helen Wearing
fICA
BSSasymp
pomp
R. Woodrow Setzer
Gilles Pujol
John Wambaugh
RandomFieldsUtils
Bruce E. Kendall
tsBSS
Klaus NordhausenIngo Bulla
Rafael S. de Souza
Bertrand Le Nezet
Matthew J. Ferrari
spnet
mistral
Mickael Binois
Jessica Franco
Delphine Dupuy
DiceEval
C. Helbert
Rien van Genuchten
Bernd Huwe
DiceDesign
kin.cohort
Carl A. Mendoza
Andrew Sila
Guillaume Damblin
vectoptim
Nilanjan Chatterjee
Manuel Wiesenfarth
Thomas Terhoeven−Uselmans
Thomas Terhoeven−Urselmans
soil.spec
SwissAir
Yusuke Sugomori
Pius Korner−Nievergelt
Carl Morris
Peter M. J. Herman
Ryan Curtin
blmeco
Joseph Kelly
RcppMLPACKRcppDL
ecolMod
AdaptFitOS
Rgbp
Niki Zumbrunnen
rootSolve
ReacTran
Theresa Albrecht
Rene Locher
Filip Meysman
diagram
Franscesca Mazzia
Jeff Cash
Tobias Roth
LIM
James Orr
Dick van Oevelen
bvpSolve
Tatyana Krivobokova
plot3D
Peter VandeHaar
shape
Larry Schaeffer
Julius Kipyegon Kones
Aurélien Proye
PlayerRatings
Brendan Malone
Olivier Lepais Bas Kempen
Barbara Hellriegel
Jim Orr
AdaptFit
carcass
Chris Ferro
FedData
Pius Korner
birdring
Filip J. R. Meysman
Hannes Reuter
Murray Lark
Heloise Lavigne
Jean−Marie Epitalon
seacarb
NetIndices
evd
GSIF
Fraenzi Korner−Nievergelt
Bernard Gentili
Andreas F. Hofmann
Francesca Mazzia
AquaEnv
Lutz Duembgen
Hans−Juergen Auinger
Alec G. Stephenson
Yunro Chung
Anastasia Ivanova
Michael G. Hudgens
FAwR
Bettina Almasi
Henrik Andersson
femmeR
deTestSet
diffEq
plot3Drgl
Stefanie von Felten
Bertrand Iooss
Frederik De Laender
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limSolve
OceanView
Karline Soetaert
Yvonne Badke
Christian Reimer
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synbreed
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pvclass
ByeongChris−Carolin
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StackOverflow
Thomas Unternährer
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Jeff Sonas
Manuela Huso
Matthew A. Etterson
James Rae
Jean−Pierre Gattuso
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MultiCNVDetect
Rob Robinson
mev
Leo Belzile
Oliver Behr
Manuela M. P. Huso
Markus Baaske
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R. Kyle Bocinsky Dylan
pRSR
Ivo Niermann
Alexander J. McNeil
logcondens
SimRAD
Dan Dalthorp
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Christian Genest Jeff D. Hamann
Gerard Heuvelink
QRMlib
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Scott Ulman
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Mehmet Balcilar
JointGLM
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Martin W. Ritchie
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Guenther Walther
PhySim
Andrea Rau Dolph Schluter
Ruo Xu
Lucia H. C. Anjos
EvoRAG
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Manuel Gentile
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reporttools
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ExceedanceTools
Quinn Payton
Ken Kleinman
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pequod
SurvRegCensCov
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Filippo Santambrogio
artfima
selectMeta
Kaspar Rufibach
rtkpp
rneos
Marc Weber
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sltl
bestglm
Luciano Seta
Stanislas Hubeaux
pear
nncRda
Changjiang Xu
modehunt
Dick Brus
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FitAR
OrdFacReg
Alberto Mirisola
ebdbNet
smacpod
Hao Lin
DeducerMMR
FGN
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DiversitySampler
Earl Brown
Matthew K. Lau
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JohnsonDistribution hcc
dynia
P. Sing
spcosa
S. R. Borrett
Yun Shi
Aude Longeville
ARTP
Jinkun Xiao
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HTSDiff
Leanna King
pcenum
Kathrin Weyermann
William Wheeler
logcondiscr
rtkore
Miguel Sousa Lobo
Yixin Chen
modelcf
Rmixmod
Florent Langrognet
glmlep
Kai Yu
HTSCluster
Stephen Boyd
Angel Felicisimo
D. J. Brus
Jaap de Gruijter
Henry Bart Jr
RobustEM
G. Govaert
Herve Lebret
Dennis Walvoort
Christophe Biernacki
J. J. de Gruijter
Lieven Vandenberge
Aurora Cuartero
Abdel El−Shaarawi
rwm
Rmpi
D. E. Hines
MixAll
Parmeet Bhatia
Martin Andersen
Lieven Vandenberghe
VecStatGraphs2D
rddtools
censNID
FitARMA
Fadoua Balabdaoui
enaR
Vincent Kubicki
Joachim Dahl
Qizhai Li
VecStatGraphs3D
FRAPO
cleangeo
POT
RFA
Justin Q. Veenstra
arfima
Zinovi Krougly
Alexandre Brulet
Hao Yu
Serge Iovleff
cccp
Emmanuel Blondel
Mathieu Ribatet
Farzad Sabzikar
Kendall
mleur
ltsa
rsatscan
Pablo Garcia Rodriguez
A. I. McLeod
Ying Zhang
Laura Hauser
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DTK
koRpus
OrdMonReg
systemfit
gogarch
Juan Carlos Ruiz Cuetos
Maria Eugenia Polo Garcia
Lin Wang
LGEWIS
Remi Lebret
Xin Dang
Aishat Aloba
blockcluster
J. C. Cuetos
BEQI2
versions
GRaF
P. G. Rodriguez
Javier F. Tabima
M. E. Polo
Gilles Celeux
Zihuai He
Willem van Loon
Marie−Laure Martin−Magniette
Cathy Maugis−Rabusseau
rnn
Seunggeun Lee
Parmeet Singh Bhatia
Gerard Goavert
Nick Golding
LGRF
Pallavi Singh
Hanna Jankowski
Grard Goavert
Jonah C. Brooks
Geraldine Henningsen
Stacy A. Krueger−Hadfield
Bastiaan Quast
CPHshape
Canhong Wen
Victor Kmmritz
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poisson.glm.mix
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jvmr
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Tim David
Coelli J. Harris
SelvarMix
BayesComm
Fei Wang
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Anastasios A. Tsiatis
bamboo
SKAT
Larisa Miropolsky
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Victor Kummritz
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convexHaz
Tobias Liboschik
K. Ullas Karanth
J.−P. Baudry
Min Zhang
Wu
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Jim Hines
Michael E. Meredith
Ivy Wang
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Hugh McCague
Yanfei Kang
cdcsis
Devcharan Jathanna
James D. Nichols
Kendon Bell
Andrew J. Royle
Mohammed Sedki
Danijel Belusic
prism
Michael WuMicheal
Sumanta Mukherjee
Arjun M. Gopalaswamy
Jon A. Wellner
TED
robeth
label.switching
rWBclimate
Xueqin Wang
N. Samba Kumar
Dipti Bharadwaj
Edmund Hart
RobustAFT
Mian Huang
Aaron Ellison
EcoSimR
biorxivr
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VarSelLCM
Nick Gotelli
Jean−Luc Muralti
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Wenliang Pan
MvBinary
Bertrand Michel
speff2trial
Cathy Maugis
V. J. Victor
Matthieu Marbac
robustvarComp
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Francisco Herrera Triguero
Jose Manuel Benitez
frbs
Stefan Van Aelst
Peter J. Green
Jean−Patrick Baudry
Sylvain Arlot
Francisco Herrera
Alex Randriamiharisoa
Rmalschains
Lala Septem Riza
José M. Benítez
RoughSets
Javier Otegui
Xiaomin Lu Chris Cornelis
Chaitanya Khadilkar
Fields Development Team
William H. Swanson
Karen Schettlinger
Ella Roelant
Dominik Slezak
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simr
Claudio Agostinelli
LOGICOIL SCORER2
Paul H. Artes
Sebastian Stawicki
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Mitchell W. Dul
Neil O’Leary
visualFields
Catriona MacLeod
Victor E. Malinovsky
wle
circular
Derek N. Woolfson
gimme
Richard Russell
Shiquan Wu
ImageMetrics
Thomas L. Vincent
CircStats
Hallie Pike
localdepth
Craig T. Armstrong
T. E. C. Common Mathematical
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bipartite
Marco Chiarandini
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Michal Juraska
Ulric Lund
David H. Foster
modelfree
Ivan Marin−Franch
Rouven Strauss
Mario Romanazzi
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Aaron Clauset
Sean J. Westwood
NetCluster
NetData
triads
Nimisha Chaturvedi
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robustHD
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Diana Perkins
seqDesign
sparseLTSEigen
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Clark Jeffries
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cvTools
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NEff
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msgl
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Belardinelli
MarkKay
Wunsch
Jordan Killpack
Thomas Schreiber
Sara Lopez−Pintado
Jaakko Jarvi
Garrett Miller
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Casey Kolderup
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RcmdrPlugin.depthTools
Conrad Sanderson
Yoondong Lee
Gianluca Gazzola
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Yuchao Jiang
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Armin Graber
rrdflibs
Matthias Bogaert
depthTools
Ryan Freebern
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Koen W. De Bock
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Mark Sample
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Canopy
SamplingStrata
PPtree
Martin Vincent
GAMens
snpXpert
Daniela Pagliuca
dummy
gSeg
genalg
AUC
asVPC
Taesung Park
MADAM
seqCBS
Hyeong−Seok Lim
PPtreeViz
Yoojin Jung
Nathaniel Mitchell
gCat
Egon Willighagen
AggregateR
Sung Gon Yi
Patrick Rodriguez
Michael Dewberry
Jie Ding
Andrey Volkov
fit4NM
Matthias Wieser
Mueller
Eva Budinska
Hao Chen
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rrdf
kernelFactory
Czech Republic
ORMDR
arrayMissPattern
PKmodelFinder
Eun−Kyung Lee
lift
Michel Ballings
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Dirk Van den Poel
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falcon
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hybridEnsemble
Michiel Van Herwegen
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Helmholtz Centre Munich
TERAplusB
rotationForest
leapp
GrammR
Michiel Vanherwegen
Vendula Svendova
Michael G. SchimekEva Budinska
bayesQR
Matthias Dehmer
Laurin A. J. Mueller
Deepak N. Ayyala
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Li Lee
esaBcv
Art B. Owen
Samsun Sung
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Kun Chen
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DIME
Heebal Kim
BOG
Taeyoung Hwang
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Javkhlan−Ochir Ganbat
Shili Lin
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BootCL
imputeMDR
Youyi Fong
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Michael Schutte
interpretR
imputeMissings
Junghyun Namkung
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dblcens
Taeheon Lee
Wonil Chung
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optismixture
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krm
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ELYP
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Hera Y. He
Mai Zhou
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chngpt
Ralf Bundschuh
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Hee−Seok Oh
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Murat Erdogdu
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Jin Zhezhen
Dongik Jang
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gb
sparseSEM
HyunJi Kim
Maria Alvarez
Wim Hordijk
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Nora M. Villanueva
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decon
Lawrence H. Cox
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miRada
Alencar Xavier
Brian Diers
Zhiqiu Hu
distfree.cr
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Carla Moreira
Rosa M. Crujeiras
Pedro Puig
Wilfried Thuiller
Jacques Brisson
Thierry Duchesne
NPCirc
Daniel Fortin
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Jerome P. Reiter
bark
Robert Wolpert
acmeR
Jacob Coleman
Katy Rainey
Radu V. Craiu
DTDA
María Oliveira
radir
p3state.msm
TPmsm
NAM
NPsimex
trust
Ana Moreira
survivalBIV
SoyNAM
Quanli Wang
William Muir
polyapost
Antoine Guisan
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EditImputeCont
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Shizhong Xu
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aster2
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Glen D. Meeden
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biomod2
Alan F. Karr
Zhi Ouyang
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Jun Sheng
gdor
audit
Denis Talbot
Manuel Higueras
hermite
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Loic Pellissier
Tiago Pimenta
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David Moriña
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sROC
BACprior
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rvTDT
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Artur Araujo
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gte
Luís Meira−Machado
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pooh
bWGR
Rongcai Yang
rcdd
genSurv
Jingchen Hu
Yifan Ethan Xu
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BAS
Zhiquan Wang
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Michael Littman
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nice
Sophie Baillargeon
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Daniel Manrique−Vallier
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TP.idm
Susana Faria
aster
TEEReg
BCEE
Geneviève Lefebvre
complex.surv.dat.sim
Julien Pottier
seq2R
discretization
fANCOVA
Andrew S. Allen
Juli Atherton
Centre Tecnològic de Nutrició
Dorothea Pio
Marta Sestelo
Xiaodong Cai
Anhui Huang
Universitat Autònoma de
Barcelona
Ruben Garcia Mateo
Daniel Scherrer
EBglmnet
spt
Bin Wang
mnspc
Chaitanya R. Acharya
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coreTDT
Yu Jiang
accrual
Matthew S. Mayo
Sample.Size
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Beatriz Pateiro−Lopez
rNMF
Leif T. Johnson
Jacobo de Una−Alvarez
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Wei Jiang
alphashape3d
grade
Helene Crepeau Louis−Paul Rivest Serge Couturier
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sgof
Yulei Wang
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Jiayang Sun
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Junheng Ma
Irene Castro Conde
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Guo−Qiang Zhang
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Justin J. Wilkins
Martin J. Lercher
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Ron Keizer
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granova
Joan Guàrdia
Armin Biere
saws
Giambattista Toller
rateratio.test
Rajen Piernikarczyk
Johann M. Kraus
Brian A. Danielak
ssanv
GiANT
Dao Zhou
Han de Vries
SCVA
Antonio Solanas
Florian Schmid
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NADA
interval
Blum Michael
Michael G. B. Blum
PairTrading
pcadapt
Francis Nguyen
Michael Blum
Amit G. Deshwar
abc
Jean−Michel Becu
Csillery Katalin
Syed Haider
Paul C. Boutros
Shinichi Takayanagi
Derek Beaton
Herve Abdi
Francois Olivier
KsPlot
Kyle Leckett
bedr
NanoStringNorm
apTreeshape
Louisiane Lemaire
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RFinanceYJ
bios2mds
Marie Chabbert
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ExPositionMExPosition
Nicolas Bortolussi
Nobuaki Oshiro
EasyUpliftTree
Cherise R. Chin Fatt
TInPosition
Olivier François
Daryl M. Waggott
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Zuojing Li
blockmatrix
Julien Pele
Jenny Rieck
Ye Yang
RClimMAWGEN
Emilie Lalonde
Michal Grzadkowski
Clement Fung
Eric Durand
rHadoopClient
RSearchYJ
sqlutils
DistatisR
prettyGraphs
FRBData
Marta Padilla
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Interpol.T
RMAWGEN
RGENERATE
glpk
Lopaka Lee
Marco Foracchia
InPosition
abc.data
Lemaire Louisiane
LTR
Statomica
Alaa Ali
PsiHat
Corey M. Yanofsky
Jenn Kirk
SCRT
Stefan Mundus
Zhenyu Yang
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Joseph Dunlop
Quaid D. Morris
Katalin Csillery
HighProbability
David R. Bickel
Shrinkage
geotopbricks
Emanuele Eccel
Emanuele Cordano
RMRAINGEN
choplump
nivm
Rumen Manolov
SCMA
Tamara J. Blätte
Ludwig Lausser
TriMatch
ISOpureR
RGENERATEPREC
hbim
asht
RcmdrPlugin.SLC
Binarize
TunePareto
makeR
Jason Bryer
timeline
Daniele Andreis
soilwater
Mike Fay
steepness
SLC
Isis Bulte Patrick Onghena
BiTrinA
multilevelPSA
Deya Alzoubi
RSeed
Louis Luangkesorn
boussinesq
Michael P. Fay
MChtest
RcmdrPlugin.SCDA
Martin Hopfensitz
Christoph Müssel
Hans A. Kestler
PSAboot
sybilSBML
glpkAPI
Eric Stroemberg
Combine
ClimClass
David Leiva
BoolNet
William E. J. Doane
granovaGG
Claus Jonathan Fritzemeier
PopED
Keurcien Luu
Zahra Montazeri
Fabio Zottele
perm
RcmdrPlugin.EACSPIR
Robert M. Pruzek
clpAPI
Gabriel Gelius−Dietrich
cplexAPI
Joakim Nyberg
Andrew C. Hooker
Gerald Quon
Catalina V. Anghel
exactci
RcmdrPlugin.steepness
James E. Helmreich
sybil
Abdelmoneim Desouki
xpose4classic
E. Niclas Jonsson
Mats O. Karlsson
xpose4genericxpose4specific
Kohta Ishikawa
bpcp
exact2x2
Troy D. Hanson
PSAgraphics
Marc Andre Daxer
xpose4
xpose4data
ncappc
empiricalBayes
Maribel Peró
Yohei Sato
likert
Annalisa Di Piazza
ChangeAnomalyDetection
RWebMA
Kimberly Speerschneider
Terrence Brooks
skewtools
Marco Tamburini
EasyHTMLReport
YjdnJlp
Lehrkamp Matthias
ic.infer
Margret C. FuchsManfred Fischer
Peter J. Galante
Mario Samigli
Fentaw Abegaz
Abdolreza Mohammadi
James J. Yang
Guido Raos
Minjeong Jeon
Roger Guimera
Rlinkedin
Maria Uriarte
FrF2.catlg128
FrF2
Patricio S. La Rosa
F gure 1
Sophia Rabe−Hesketh
Riccardo Inchingolo
Authorsh p graph (subset)
Christoph Schmidt
Michael Piccirilli
Mariano Soley−Guardia
Rachel K. Smedley
Berkley Shands
Anne Buu
relaimpo
Skye Buckner−Petty
DoE.wrapper
Lenth Russ
Matteo Quartagno
Luminescence
Matthias Lehrkamp
Ulrike Groemping
Stefano Spada
Javier Contreras−Reyes
HMP
SparseTSCGM
BDgraph
DiscreteInverseWeibull
orcutt
Javier E. Contreras−Reyes
bingat
HMPTrees
L. Keoki Williams
ChargeTransport
Guilhem Doulcier
rnetcarto
Rpdb
Benjamin Lauderdale
StressStrength
Robert P. Anderson
Sebastian Kreutzer
mcll
EILA
ENMeval
Markus Fuchs
Rfacebook
DiscreteLaplace
Jamie M. Kass
Aleksandar Radosavljevic
Ernst C. Wit
DiscreteWeibull
RcmdrPlugin.DoE
jomo
afmtools
William D. Shannon
Elena Deych
Julien Idé
Alessandro Barbiero
spThin
Tina Zhuo
Jia Li
glassomix
bio3d
Bruno Vilela
streamR
bigGP
Rollin Thomas
Timothee Poisot
MetaDE
Jan Odvarko
Xingbin Wang
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paco
Fernando Cagua
Kohei Watanabe
Benjamin Lipshitz
Christina Ludwig
GenForImp
instaR
Barry Grant
Veronica Vinciotti
meta
Christopher Paciorek
tightClust
DWreg
Tiago Dantas
Juan Antonio Balbuena
digitize
aLFQ
Wing H. Wong
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letsR
Nadia Solaro
betalink
Xin−Qiu Yao
George C. Tseng
AnalytixWare
Gerta Rücker
Jonne Guyt
AAindex
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Subharup Guha
Yanchun Bao
Pilar Rubio
Pablo Barberá
Paul Nulty
Lars Skjaerven
Pier Alda Ferrari SunterSampling
RLumShiny
Elisabeth Dietze
Guido Schwarzer
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quanteda
Matthew Hutchinson
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Hongquan Xu
Boyko Amarov
metasens
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log10
Mirko Signorelli
Anani Lotsi
ForImp
Matthew E. Aiello−Lammens
copas
Jia Wang
Kenneth Benoit
Cari Kaufman
Robert Muscarella
Michael Dietze
Christoph Burow
DoE.base
James Carpenter
ForeCA
Georg M. Goerg
Wilfredo Palma
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Daniel B. Stouffer
Robert A. Boria
Fox John
LICORS
George M. Goerg
Actigraphy
glmmGS
George Rosenberger
MetaPCA
netmeta
Hannes Roest
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Don Kang
Michele Morara
Louise Ryan
Ulrike Krahn
Douglas Galagate
Jochem König
mxkssd
Jose Manuel Soria
pan
pcg
Irina Mahlstein
Luitgard A. M. Veraart
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Helena Brunel
chillR
fpc
FactMixtAnalysis
F. Din−Houn Lau
Mark Liniger
tawny
Qiong Ding
futile.paradigm
Zhouwen Liu
Rebecca Hiller
systemicrisk
Bedia Jimenez
Jun Ma
survivalMPL
Alfonso Buil
ifa
Asun Lubiano
lambda.tools
spaa
Sari Acra
PhysicalActivity
Igor Sieradzki
introgress
Charles E. Matthews
nonlinearTseries
Maciej S. Buchowski
gmum.r
futile.options
Maciej Zgliczynski
D. Olivieri
Axel Gandy
smoothmest
decisionSupport
Jonas Bhend
Andreas Weigel
Andrey Ziyatdinov
Dominique−Laurent Couturier
Jinlong Zhang
tawny.types
Marcin Data
Michal Pletty
Zachariah Gompert
Karol Jurek
Wojciech Czarnecki
RHRV
ProfileLikelihood
Zhiyi Xu
Lutz Göhring
phylotools
Elisabetta Bonafede
A. Mendez
Kong Y. Chen
Robert R. Junker
dynRB
M. Lado
bayespref
Kristin Tolksdorf
Samir Kanaan−Izquierdo
cpca
L. Rodriguez−Linares
Leena Choi
PhyActBedRest
HK80
futile.any
Jan Terje Kvaloy
simctest
afc
chemosensors
Wolfgang Trutschnig
Constantino A. Garcia
J. Dustin Tracy
dcv
Jonas Kuppler
futile.logger
spcadjust
Zongshan Li
futile
trimcluster
mixtNB
Claudia Mignani
Fernando Tusell
Stanislaw Jastrzebski
SAFD
seqRFLP
Brian Lee Yung Rowe
lambda.r
Christoph Spirig
ibd
cat
Baidya Nath Mandal
Mateusz Bruno−Kaminski
Konrad Talik
Piotr Kowenzowski
Gunther Sawitzki
futile.matrix
Christian Hennig
quantileDA
Cinzia Viroli
easyVerification
Matteo De Felice
Alexandre Perera
extlasso
Bernhard Hausdorf
prabclus
chopthin
Eike Luedeling
solarius
Stephane Heritier
norm
lshorth
Jihong Huang
Angel Martinez−Perez
nnlasso
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strap
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Ladislav Kasparek
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Pavel V. Moskalev
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Martin Hanel
T. G. Masaryk Water Research
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clustrd
Angelos Markos
Daniel−Corneliu Leucuta
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fanc
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Michio Yamamoto
Maria Xose Rodriguez−Alvarez
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Anna L. Tyler
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Paul Fischer
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Diane Bailleul
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Laurent Gatto
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Paul W. Eslinger
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Juan Manuel Truppia
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Ricardo Jorge de Almeida
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Juan David Velasquez
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Michaela Dvorzak
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Manuel Fontenla
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Pavel Khomski
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paramlink
Thorsten Pohlert
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Roberto Gatta
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Majid Sarmad−
Imperial College London
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bride
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Pieter Vermeesch
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Tobias Kley
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10000
10000
100
Num Users
1000
1000
5
50
100
10
1
Figure 3.
The median is used to separate the higher half of the user population from the lower half.
5
10
20
1
2
5
Num Views
Degree GS .
In Fig. 1, only a subset is shown due to space limits. There
are many more small clusters as those at the bottom of the
figure. The community has one large cluster, the largest connected component (LCC) of the graph, containing 8985 nodes
which are either users or packages. There are many smaller
clusters with few users contributing to packages and also
many users that contribute only to one single package.
Figure 2 shows the number of clusters versus the number
of nodes in it (log-log scale). The LCC is depicted by the dot
at the very bottom right corner of the figure. The majority of
clusters has only few or just a single user package tuple. This
also means that only users within the single largest connected
component will be relevant for our analysis. Since we heavily
rely on user degree in the social graph GS , many users in the
small clusters will have very low importance.
Figure 3 shows the degree distribution of the user graph GS .
Low degree of many users is explained by the large number
of small clusters, which are mainly individual contributors
of single packages. The graph GS consists of 11189 users. A
fraction of 14% has a degree of 0 and 60% of users have a
degree smaller or equal 3. The median4 degree is 85. A fraction
of 0.7% of users (74 users) have a degree larger than 85. Such
degree distributions are typical in online communities.
The next Fig. 4 shows the relationship between CRAN task
views and users. These views are interpreted as skills and expertise ranking is performed within the context of individual
task views. In total, 33 views exist. 7316 users are not associated with any view (because their packages are not listed in
any view). Thus, those users will not be considered in the formation algorithm. 3873 users are associated with one or more
views. The median value for the number of views within this
user segment is 11. This provides already a good diversity in
terms of users having different skills.
The next step is to analyse the relationship between users
and software packages. Figure 5 shows the number of users
over packages. The median value for the number of software
packages is 20. The dependencies of packages are visualized
by Fig. 6. 4550 packages have exactly one dependency (the R
environment). The median value is 10.
Finally, Fig. 7 shows the average number of dependencies
by the number of users. The median value for the average
number of dependencies is clearly 2.
2
Figure 4.
10
20
50
Num Packages
Views.
Figure 5.
Packages.
5000
Clusters.
20
Degree
Num Packages
Figure 2.
10
500
2
50
1
5
5000
1
500
1
1
5
1
50
Num Nodes
4
100
Num Users
10
50
Num Users
500
500
50
Num Clusters
5 10
1
5 10
1
2
5
10
20
Num Dependencies
Figure 6.
Figure 7.
4.2
Dependencies.
User dependencies.
Experiments Setup
In our experiments, we sampled a random set of CRAN task
views representing the demanded team skills. The crossover
probability is set to 0.7 and the mutation probability to
0.05. The metric weights for fitness calculation are set to
wscore = wcost = wdistance = 31 . In each experiment run,
a population of 200 individuals plus 5 individuals for elitism
has been created. We evaluate the quality of the expertise
mining approach by checking key metrics such as degree of a
user, number of packages in a given view (where the user is
top-ranked), and number of all packages.
4.3
Qualitative Evidence
A team with the highest fitness for 5 skills is depicted by Fig. 8
and detailed in Table 1. The team has an average expertise
score of 0.8, a cost of 0.6, and distance 1.0. These are excellent
values. A perfect fitness of 1.0 is not attainable because there
is a tradeoff between expertise and cost. Indeed, the maximum
achievable fitness depends on the selected skills.
Score (GS )
0.00027
0.00150
0.00060
0.00021
0.00113
Overall Fitness
Martin Mächler (Bayesian)
All Pkg
11
57
34
10
71
0.60
80
2
4
6
8
10
2
4
Iteration
Figure 9.
Albrecht Gebhardt
(NumericalMathematics)
6
8
10
Iteration
P -fitness.
Figure 10.
I-fitness.
William N. Venables
(SocialSciences)
Kurt Hornik (Psychometrics)
In the following we answer the question whether an increasing number of skills results in more disconnected teams.
Fig. 11 compares different populations with an increasing
number of skills (from 5 to 9 skills depicted by S5 to S9).
Example team spanning 5 skills.
S5
0
40 80
Figure 8.
Deg. (T)
4
4
4
4
4
0.85
Pkg
2
1
4
5
3
90
Brian D. Ripley (<Coordinator>)
Deg. (GS )
36
276
86
50
318
0.80
Thomas Lumley (MetaAnalysis)
Ch.
201
0
21
509
4
0.75
Score
0.07681
0.87039
0.36787
0.19568
0.85807
0.70
Rank
9
1
2
8
1
Best Individual Fitness
User
A. Gebhardt
M. Mächler
T. Lumley
W. N. Venables
K. Hornik
0.65
Skill
Num. Math.
Bayesian
Meta Analysis
Social Sciences
Psychometrics
Example of team recommendation for 5 skills.
100 110 120 130 140 150
Table 1.
2
6
8
10
6
8
10
6
8
10
6
8
10
6
8
10
S6
0
30
Index
2
4
S7
0
30
Index
2
4
0
30
S8
Index
2
4
S9
30
Index
2
Figure 11.
4.4
4
0
Table 1 shows further team member details. Rank is the
user rank within the specific task view (community rank for
the given skill). Score is the numeric ranking score based on
our advanced expertise mining model and Score (GS ) is the
ranking score computed in GS using a standard PageRank.
This comparison essentially demonstrates the impact of our
advanced context-based ranking model (see [27, 28]). Ch. is
the ranking change (context-based vs. standard PageRank).
One can see that context has a high impact in terms of ranking
position. We positively validated these results by checking the
online profiles of the top-ranked users because most users have
public Web sites. Deg. (GS ) depicts the degree (number of
co-authors) in GS . High degree typically means high community standing. Pkg depicts the number of packages in a given
view and All Pkg all packages of the given user. Deg. (T)
is the team degree. Here we see a perfectly connected team
where each member is connected to all other members. The
user ‘Brian D. Ripley’ is selected as the coordinator.
4
Skills vs. number of disconnected team.
Performance Evaluation
We show the convergence of fitness values for both entire populations (depicted as P -fitness in Fig. 9) and for the best individuals in each population (depicted as I-fitness in Fig. 10).
Convergence means that no major changes between one iteration to the next iteration are observed. 5 skills have been
selected randomly. Different color codes depict 5 runs of GA
formation algorithm. The best teams were identified after 7
iterations. Population fitness started to settle at 10.
The x-axis shows the number of disconnected team members and the y-axis the number of teams within the population
(total number of populations is 205). The figures show that
by increasing the number of skills the number of teams where
only few members are disconnected decreases. More skills to
be satisfied by individual users increases the chance that team
members are disconnected from the rest of the team.
5
Conclusions
This work introduced team formation mechanisms for software ecosystems. We apply a genetic algorithm including a
novel extension called relationship-driven mutation. In development teams, performance and quality are affected by the
programming skills and domain experiences of the project’s
team members. We apply an advanced expertise mining approach to address this problem. Empirical results confirm the
applicability of our presented methods.
Future work includes the following aspects. Estimating collaboration cost is not trivial and may depend on many factors, such as physical co-location, geographical distribution
(including issues related to time difference), or cultural factors. We will analyse and model cost of collaboration. We
will perform further evaluations of the approach in two directions. First, we want to validate results by engaging community members of the R ecosystem to get direct feedback
on formation and expertise ranking results. Second, we will
broaden team formation experiments for other types of software ecosystems including industrial and company internal
software ecosystems. An additional area of investigation is
the consideration of formal skill frameworks such as SFIA5 .
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