Computational Discovery in
Evolving Complex Networks
Yongqin Gao
Yongqin Gao December 2006 Dissertation Defense
Outline
• Background
• Methodology for Computational Discovery
• Problem Domain – OSS Research
• Process I: Data Mining
• Process II: Network Analysis
• Process III: Computer Simulation
• Process IV: Research Collaboratory
• Contributions
Background
• Network research gains more attentions
– Internet
– Communication network – Social network
– Software developer network – Biological network
• Understanding the evolving complex network
– Goal I: Search
– Goal II: Prediction
Yongqin Gao December 2006 Dissertation Defense
Computational Discovery
Our Methodology
Research Collaboratory Data Mining Network Analysis Computer Simulation Discovery Assessment Revision Feedback Researcher Community Members Contribution Reference InitializationProblem Domain
• Open Source Software Movement
– What is OSS
• Free to use, modify and distribute and source code available and modifiable
• Potential advantages over commercial software: Potentially high quality; Fast development; Low cost
– Why study OSS (Goal)
• Software engineering — new development and coordination methods
• Open content — model for other forms of open, shared collaboration
• Complexity — successful example of self-organization/emergence
Yongqin Gao December 2006 Dissertation Defense
Glory of OSS
Problem Domain
• SourceForge.net community
– The biggest OSS development communities
– 134,751 registered projects
Yongqin Gao December 2006 Dissertation Defense
Problem Domain
• Our Data Set
– 25 monthly dumps since January 2003.
– Totally 460G and growing at 25G/month.
– Every dump has about 100 tables.
– Largest table has up to 30 million records.
• Experiment Environment
– Dual Xeon 3.06GHz, 4G memory, 2T storage
– Linux 2.4.21-40.ELsmp with PostgreSQL 8.1
Related Research
• OSS research
– W. Scacchi, “Free/open source software development practices in the computer game community”, IEEE Software, 2004.
– C. Kevin, A. Hala and H. James, “Defining open source software project success”, 24th International
Conference on Information Systems, Seattle, 2003.
• Complex networks
– L.A. Adamic and B.A. Huberman, “Scaling behavior of the world wide web”, Science, 2000.
– M.E.J. Newman, “Clustering and preferential
attachment in growing networks”, Physics Review, 2001.
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Related Research:
– S. Chawla
,
B
.
Arunasalam and J. Davis,
“Mining open source software (OSS) data using
association rules network”,
PAKDD, 2003
.
– D. Kempe
,
J
.
Kleinberg and E. Tardos,
“Maximizing the spread of influence through a
social network”,
SIGKDD, 2003.
– C. Jensen and W. Scacchi, “Data mining for
software process discovery in open source
software development communities”,
Workshop on Mining Software Repositories,
2004
.
Process I: Data Mining
Raw data Relevant data Data Purging Feature Selection Algorithm Application Data Preparation DatabaseYongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Data Preparation
– Data discovery
• Locating the information
– Data characterization
• Activity features: user categorization • Network features
– Data assembly
• Data Purging
– Treatment about data inconsistency
• Unifying the date presentation by loading into single depository
– Treatment about data pollution
• Removing “inactive” projects
• Feature Selection
– This method is used to remove dependent or insignificant features. – NMF (Non-negative Matrix Factorization)
Process I: Data Mining
• Result I
– Significant features
• By feature selection, we can identify the significant feature set describing the projects.
• Activity features: “file_releases”, “followup_msg”, “support_assigned”, “feature_assigned” and task related features
• Network features: “degrees”, “betweenness” and “closeness”
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Distribution-based clustering
(Christley, 2005)– Clustering according to the distribution of
features instead of values of individual feature
– We assume every entity (project) has an
underlying distribution of the feature set
(activity features)
– Using statistical hypothesis test
• Non-parametric test
• Fisher’s contingency-table test is used
– Joachim Krauth, “Distribution-free statistics: an application-oriented approach”, Elsevier Science Publisher, 1988.
Process I: Data Mining
• Procedure:
While (still unclustered entities)
Put all unclustered entities into one cluster
While (some entities not yet pairwise compared) A = Pick entity from cluster
For each other entity, B, in cluster not yet compared to A
Run statistical test on A and B If significant result
Remove B from cluster
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Result II
• Unsupervised learning
– Distribution-based method used to cluster the project history using the activity distribution
– We named the clusters using ID and the results are shown in the table
– High support and confidence in evaluation 100960 Total 2060 3 9191 2 89709 1 Size Cluster ID
Process I: Data Mining
• Two sample
distributions from
different categories
• Unbalanced feature
distribution
→
could
be “unpopular”
• Balanced feature
distribution
→
could
be “popular”
20 1641 3488 22 0 312 736 229 1510 534 82 121 28 0 4 0 500 1000 1500 2000 2500 3000 3500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Activity Category Cluster 1 134 3781 8435 431 0 21792537 667 9169 7134 601 2411 1651 0 399 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Activity Category Cluster 3Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Discoveries in Process I
– Significant feature set selection
• Network features are important • Further inspection in next process
– Distribution based predictor
• Based on the activity feature distribution
• Prediction of the “popularity” based on the balance of the activity feature distribution
• Benefit of these discoveries
– For collaboration based communities, these discoveries can help in resource allocation optimization.
Process II: Network Analysis
• Why network analysis
– Assess the importance of the network measures
to the whole network and to individual entity in
the network
– Inspect the developing patterns of these
network measures
• Network analysis
– Structure analysis
– Centrality analysis
– Path analysis
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Related research:
– P. Erdös and A. Rényi, “On random graphs”,
Publicationes Mathematicae, 1959
.
– D.J. Watts and S. H. Strogatz, “Collective
dynamics of small-world networks”,
Nature,
1998.
– R. Albert and A.L. Barab
ά
si, “Emergence of
scaling in random networks”,
Science, 1999
.
– Y. Gao, “Topology and evolution of the open
source software community”,
Master Thesis,
2003
.
Process II: Network Analysis
• Structure Analysis
– Understanding the influence of the network structure to individual entities in the network
– Inspected measures
• Approximate diameter
• Approximate clustering coefficient
• Component distribution 1 ) / log( ) / log( 1 2 1 + = z z z N D ) 3 2 ( ) )( ( 1 1 3 2 1 1 1 2 1 2 1 2 ! ! ! ! µ ! ! µ µ + " " " + = C
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Conversion among C-NET, P-NET and
D-NET
Process II: Network Analysis
• Result I
– Approximate Diameters
• D-NET: between (5,7) while network size ranged from 151,803 to 195,744.
• P-NET: between (6,8) while network size ranged from 123,192 to 161,798.
– Approximate Clustering Coefficient
• D-NET: between (0.85, 0.95) • P-NET: between (0.65, 0.75)
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
Process II: Network Analysis
• Centrality Analysis
– Understanding the importance of individual entities to the global network structure
– Inspected measures: • Average Degrees • Degree Distributions • Betweenness • Closeness
!
" # # = V t v s st st v v B $ $ ( ) ) (!
" = V t dG v t v C ) , ( 1 ) (Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Result II
– Average Degrees
• Developer degree in C-NET: 1.4525 • Project degree in C-NET: 1.7572
• Developer degree in D-NET: 12.3100 • Project degree in P-NET: 3.8059
Process II: Network Analysis
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Result II (Degree distributions in D-NET
and P-NET)
Process II: Network Analysis
• Result II
– Average Betweenness
• P-NET: 0.2669e-003– Average Closeness
• P-NET: 0.4143e-005– Normally these two measures yield very small
value in large networks (N>10,000).
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Path Analysis
– Understanding the developing patterns of the
network structure and individual entities in the
network
– Inspected measures:
• Active Developer Percentage • Average Degrees
• Diameters
• Clustering coefficients • Betweenness
Process II: Network Analysis
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
Process II: Network Analysis
• Result III (Average degrees in D-NET and
P-NET)
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Result III (Diameters in D-NET and
P-NET)
Process II: Network Analysis
• Result III (Clustering coefficients for
D-NET and P-D-NET)
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Result III (Average betweenness and
closeness for P-NET)
Process II: Network Analysis
N/A Yes N/A Component Distribution N/A Yes Yes Average Closeness DevelopmentN/A Yes
Yes Average Betweenness Development
N/A Yes
Yes Clustering Coefficient Development
N/A Yes Yes Diameter Development Yes Yes Yes Average Degree Development
Yes Yes
Yes Active Entity Size Development
N/A Yes Yes Average Closeness N/A Yes Yes Average Betweenness N/A Yes N/A Major Component Yes Yes Yes Degree Distribution N/A Yes Yes Clustering Coefficient N/A Yes Yes Diameter Yes Yes Yes Average Degree C-NET P-NET D-NET Measures
Yongqin Gao December 2006 Dissertation Defense
Process II: Network Analysis
• Discoveries in Process II:
– Measures of structure analysis and centrality analysis all indicate very high connectivity of the network. – Measures of path analysis reveal the developing
patterns of these measures (life cycle behavior).
• Benefits of these discoveries
– High connectivity in a network is an important feature for information propagation, failure proof.
Understanding this discovery can help us improve our practices in collaboration networks and communication networks.
– Understanding the developing patterns of these network measures provides us a method to monitor network
Process III: Computer Simulation
• Related Research:
– P.J. Kiviat, “Simulation, technology, and the decision process”, ACM Transactions on Modeling and
Computer Simulation,1991.
– R. Albert and A.L. Barabási, “Emergence of scaling in random networks”, Science, 1999.
– J. Epstein R. Axtell, R. Axelrod and M. Cohen, “Aligning simulation models: A case study and results”, Computational and Mathematical
Organization Theory, 1996.
– Y. Gao, “Topology and evolution of the open source software community”, Master Thesis, 2003.
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
• Iterative simulation
method
– Empirical dataset – Model – Simulation• Verification and
validation
– More measures – More methods Model Simulation Empirical Data Collection Des crip tion Char acte rizat ion G en er ation Adju stm ent Verification ValidationProcess III: Computer Simulation
• Previous iterated models (master thesis):
– Adapted ER Model
– BA Model
– BA Model with fitness
– BA Model with dynamic fitness
• Iterated models in this study
– Improved Model Four (Model I)
– Constant user energy (Model II)
– Dynamic user energy (Model III)
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
• Model I
– Realistic stochastic procedures.
• New developer every time step based on Poisson distribution
• Initial fitness based on log-normal distribution
– Updated procedure for the weighted project
pool (for preferential selection of projects).
Process III: Computer Simulation
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
Process III: Computer Simulation
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
Process III: Computer Simulation
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
• Model II
– New addition: user energy.
– User energy
• the “fitness” parameter for the user
• Every time a new user is created, a energy level is randomly generated for the user
• Energy level will be used to decide whether a user will take a action or not during every time step.
Process III: Computer Simulation
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
Process III: Computer Simulation
• Model III
– New addition: dynamic user energy.
– Dynamic user energy
• Decaying with respect to time
• Self-adjustable according to the roles the user is taking in various projects.
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
Process III: Computer Simulation
Decreasing Decreasing Average Closeness Decreasing Decreasing Average Betweenness Decreasing Decreasing Diameter Decreasing Decreasing Clustering Coefficient Increasing Increasing Average DegreesPower Law (small tail) Power Law (small tail)
Project Distribution
Power Law (large tail) Power Law (large tail)
Developer Distribution
Model III (dynamic user energy)
Decreasing Decreasing Average Closeness Decreasing Decreasing Average Betweenness Decreasing Decreasing Diameter Decreasing Decreasing Clustering Coefficient Increasing Increasing Average Degrees
Power Law (reasonable tail)
Power Law (small tail)
Project Distribution
Power Law (large tail) Power Law (large tail)
Developer Distribution
Model II
(constant user energy)
Decreasing Decreasing Average Closeness Decreasing Decreasing Average Betweenness Decreasing Decreasing Diameter Decreasing Decreasing Clustering Coefficient Increasing Increasing Average Degrees
Power Law (large tail) Power Law (small tail)
Project Distribution
Power Law (small tail) Power Law (large tail)
Developer Distribution Model I (more realistic distributions) Simulated Patterns Patterns in Data Measures Models
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
• Discoveries in Process III
– Expanding the network models for modeling
evolving complex networks (more parameters)
– Providing a validated model to simulate the
community network at SourceForge.net
• Benefits of these discoveries
– Expanded network models can benefit other
researchers in complex networks.
– Validated model for SourceForge.net can be
used to study other OSS communities or similar
collaboration networks.
Process IV: Research
Collaboratory
• Related Research:
– G. Chin Jr. and C. Lansing, “The biological
sciences collaboratory”,
Mathematics and
Engineering Techniques in Medicine and
Biological Sciences, 2004
.
– L. Koukianakis, “A system for hybrid learning
and hybrid psychology”,
Cybernetics and
Information Technologies, Systems and
Applications, 2003.
Yongqin Gao December 2006 Dissertation Defense
Process IV: Research
Collaboratory
• What is Collaboratory?
– An elaborate collection of data, information,
analytical toolkits and communication
technologies
– A new networked organizational form that also
includes social processes, collaboration
techniques and agreements on norms,
principles, value, and rules
Process IV: Research
Collaboratory
Yongqin Gao December 2006 Dissertation Defense
Process IV: Research
Collaboratory
• Data tier - schema design
SF0205 SF0103 SF0405 SF0305 SF0605 SF0705 SF0805 SF0505 Every schema is a database dump from the SourceForge.net Timeline
Process IV: Research
Collaboratory
• Data tier - connection pool
Timeline Connection Pool Connection Assigner Logic Tier Connection Request Persistent Link Persistent Link Persistent Link
Yongqin Gao December 2006 Dissertation Defense
Process IV: Research
Collaboratory
• Presentation Tier
– Various access methods – Documentation and references – Community support – Wiki interfaceProcess IV: Research
Collaboratory
• Logic Tier
– Interactive web query system
• Authorized user can submit query to the back end repository through the web query
• Results are provided by files with various formats
– Dynamic web schema browser
• Authorized user can access the dynamic schema of the repository through the schema browser
Yongqin Gao December 2006 Dissertation Defense
Process IV: Research
Collaboratory
• Utilization reports
– Monthly statistics (June 2006)
• Total queries submitted: 16,947
• Total data files retrieved: 13,343
• Total bytes of query data downloaded: 26,684,556,278
• Programmable access method
– Programmable access method should be provided
for complicated access
Process IV: Research
Collaboratory
• Results in Process IV
– Designing, implementing and maintaining a
research collaboratory for OSS related research.
• Benefits of these results
– OSS researchers can access one of the most
complete data sets for a OSS community
development.
– By providing the community service to OSS
researchers, the collaboratory can help in
sparkling, improving and promoting research
ideas about OSS.
Yongqin Gao December 2006 Dissertation Defense
Contributions
• Designed and demonstrated a computational discovery methodology to study evolving complex networks using research on OSS as a
representative problem domain
• Understanding the OSS movement by applying the methods.
– Process I: data mining
• Identifying significant features to describe a project
• Using distribution based clustering to generate a distribution based predictor to predict the “popularity” of a project
– Process II: network analysis
• Introducing more complete analysis to inspect more complete data set from SourceForge.net.
• Discovering high connectivity and possible life cycle behaviors in both the network structure and individuals in the network
– Process III: computer simulation
• Introducing more parameters in modeling evolving complex networks • Generating a “fit” model to replicate the evolution of the SourceForge.net
community.
– Process IV: research collaboratory
• Designing, implementing and maintaining a research collaboratory to host the SourceForge.net data set and provide community support for OSS related researches.
Publications to-date
• Y. Gao; G. Madey and V. Freeh. “Modeling and simulation of the open source software community”, ADSC, San Diego, 2005.
• Y. Gao and G. Madey. “Project development analysis of the oss community using st mining”, NAACSOS, Notre Dame, 2005.
• S. Christley; Y. Gao; J: Xu and G. Madey. “Public goods theory of the open source software development community”, Agent, Chicago, 2004. • Y. Gao, Y. Huang and G. Madey, “Data Mining Project History in Open
Source Software Communities”, NAACSOS, Pittsburgh, 2004. • J. Xu, Y. Gao, J. Goett and G. Madey, “A Multi-model Docking
Experiment of Dynamic Social Network Simulations”, Agent, Chicago, 2003.
• Y. Gao, V. Freeh, and G. Madey, “Analysis and Modeling of the Open Source Software Community”, NAACSOS, Pittsburgh, 2003.
• Y. Gao, V. Freeh, and G. Madey, “Conceptual Framework for Agent-based Modeling and Simulation”, NAACSOS, Pittsburgh, 2003.
• G. Madey; V. Freeh; R: Tynan and Y. Gao. “Agent-based modeling and simulation of collaborative social networks”, AMCIS, Tampa, 2003.
• Y. Gao; V. Freeh and G. Madey. “Topology and evolution of the open source software community”, SwarmFest, Notre Dame, 2003.
Yongqin Gao December 2006 Dissertation Defense
Publication Plan
• Chapter III (data mining)
– Journal of Machine Learning Research – Journal of Systems and Software
• Chapter IV (network analysis)
– Journal of Network and Systems Management – Journal of Social Structure
• Chapter V (computer simulation)
– Spring Simulation Conference 2007 (under review) – IEEE Computing in Science and Engineering
• Chapter VI (research collaboratory)
– CITSA 2007
Conclusion and Future Work
• Cyclic computational discovery method for
studying evolving complex networks
• Study of Open Source Software by applying this
method
• Future works:
– Maintaining and expanding the collaboratory – Verifying the discoveries in the SourceForge.net
against further accumulated database dump from SourceForge.net
– Applying our simulation model on other software development communities
– Extending our methodology to other evolving complex networks like Internet, communication network and various social networks
Yongqin Gao December 2006 Dissertation Defense
Acknowledgement
• My advisor: Dr. Madey • My committee members: – Dr. Flynn – Dr. Striegel – Dr. Wood • My Colleagues:– Scott Christley, Yingping Huang, Tim Schoenharl, Matt Van Antwerp, Ryan Kennedy, Alec Pawling and Jin Xu
• SourceForge.net managers:
– Jeff Bates, VP of OSTG Inc.
– Jay Seirmarco, GM of SourceForge.net.
• US NSF CISE/IIS-Digital Society & Technology, under Grant No. 0222829.
Yongqin Gao December 2006 Dissertation Defense
Case Study II
15850 dev[46] dev[83] 15850 dev[46] dev[48] 15850 dev[46] dev[56] 15850 dev[46] dev[58] 6882 dev[58] dev[47] 6882 dev[47] dev[79] 6882 dev[47] dev[52] 6882 dev[47] dev[55] 7028 dev[46] dev[99] 7028 dev[46] dev[51] 7028 dev[46]dev[57] 7597 dev[46]dev[45] 7597 dev[46] dev[72] 7597 dev[46] dev[55] 7597 dev[46] dev[58] 7597 dev[46] dev[61] 7597 dev[46] dev[64]7597 dev[46] dev[67] 7597 dev[46] dev[70] 9859 dev[46] dev[49] 9859 dev[46] dev[53] 9859 dev[46] dev[54] 9859 dev[46] dev[59] dev[46] dev[83] dev[56] dev[48] dev[52] dev[79] dev[72] dev[51] dev[57] dev[55] dev[99] dev[47] dev[58] dev[53] dev[58] dev[65] dev[45] dev[70] dev[67] dev[59] dev[54] dev[49] dev[64] dev[61] Project 6882 Project 9859 Project 7597 Project 7028 Project 15850
OSS Developer Network (Part)
Developers are nodes / Projects are links 24 Developers
5 Projects 2 hub Developers
Process I: Data Mining
• Characteristics of data set
– Massive
– Incomplete, noisy, redundant
– Complex structures, unstructured
• Classic analysis tools are often inadequate and
inefficient for analyzing these data, especially in
exploratory research
• What is DM (Data mining)
– Nontrivial extraction of implicit, previously unknown and potentially useful information from data.
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Feature Selection
– Given a non-negative n x
m
matrix
V
, find
factors
W
(
n, r
) and
H
(
r, m
) , such that
V
≈
W *H
– This is called the non-negative matrix
factorization (NMF) of the matrix
V
– NMF can be used on multivariate data to
reduce the dimension of the data set
– By using NMF, we can reduce dimension from
Why NMF?
• Feature extraction methods
– linear methods are simpler and more completely understood.
– nonlinear methods are more general and more difficult to analyze.
• Linear methods:
– ICA: Independent Component Analysis – Matrix decomposition: PCA, SVD, NMF
• In practice, NMF is most popular and simple.
• Dimensionality reduction is effective if the loss of
information due to mapping to a
lower-dimensional space is less than the gain due
simplifying the problem.
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
• Feature-based Clustering
– Grouping data into K number of clusters based on features.
– The distance metrics used is Euclidean distance like
– Hierarchical K-Means is used.
• The result is a binary tree.
• The root is the whole data set and the leaf clusters are
the fine-grained clusters, which are the resulting K
Process I: Data Mining
• Case Study Result II
• Unsupervised learning
– K-Means method used to cluster the project history using the features we
selected
– We named the clusters using ID and the results are shown in the table
– The result is not acceptable by evaluation 2 4 4 5 29724 6 4 7 10 8 9 9 84 10 100960 Total 64824 3 98 2 6201 1 Size Cluster ID
Yongqin Gao December 2006 Dissertation Defense
Process I: Data Mining
Admin_flags?
Administrator Core developer Co-developer Active user lurker Grantcvs? Yes No Yes User_group table artifact
table Forumtable People_jobtable Project_tasktable
Doc_data table UNION Other tables User_project_act table Assigned? Activities? Yes No No Yes No
Yongqin Gao December 2006 Dissertation Defense
Clustering Result Evaluation
• Evaluation test set generation
– Popular/unpopular projects
– Stratified sampling to make 500 projects
• Feature sets used
– Popular feature set
– Activity Feature set (Page 34, Table 3.2) – Network Feature set (Page35, Table 3.3)
• Generating rules for the test sets
Popularity Definition
Number of views of the pages Number of views of the subdomain
Number of views of the website Number of downloads
Number of core developers
Description Page_views Subdomain_views Site_views Downloads Developers Feature
Yongqin Gao December 2006 Dissertation Defense
Why K-MEAN?
• The algorithm has remained extremely popular because it converges extremely quickly in practice. In fact, many have observed that the number of iterations is typically much less than the number of points.
• K-Means is most successful algorithm in large data set (size>1000, dimension > 2) than GA and Evolution • CLIQUE is sensitive to noise
• CURE is not scalable O(n2logn)
• CLARANS & BIRCH are not good for high dimension data
• D. Arthur, S. Vassilvitskii (2006): "How Slow is the k-means Method?," Proceedings of the 2006 Symposium on Computational Geometry (SoCG).
K-MEAN
• It maximizes inter-cluster (or minimizes
intra-cluster) variance, but does not ensure
that the result has a global minimum of
variance. Multiple run is needed.
• Elbow criterion
Yongqin Gao December 2006 Dissertation Defense
Distribution Categories
Artifact assigned 15 Todo assigned 14 Support assigned 13 Feature assigned 12 Patch assigned 11 Bug assigned 10 Bug reports 9 Patch request 8 Feature request 7 New message 2 Support request 6 Todo request 5 Artifact request 4 Followup message 3 File release 1 Feature CategoryProcess III: Computer Simulation
Start Stop End of Simu? Weighted Project Pool User Action No Yes Project List User List Project Pool Update Join Create Idle Drop User_Project Links New Users Simulation model procedureYongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
• Poisson Process:
– It expresses the probability of a number of events occurring in a fixed period of time if these events
occur with a known average rate, and are independent of the time since the last event.
– PDF:
!
)
;
(
k
e
k
F
k!
!
! "=
Process III: Computer Simulation
Yongqin Gao December 2006 Dissertation Defense
Process III: Computer Simulation
•
Kolmogorov-Smirnov test
– Used to determine whether two underlying one-dimensional distributions differ.
– Two one-sided K-S test statistics are given by
))
(
)
(
max(
))
(
)
(
max(
x
F
x
F
D
x
F
x
F
D
n n n n!
=
!
=
! +Yongqin Gao December 2006 Dissertation Defense
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• Chapter III (data mining)
– JMLR: G. Hamerly, E. Perelman..Using machine learning to guide simulation (Feb. 2006)
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