The document discusses a method called Outskewer for detecting outliers in datasets. It uses skewness, a measure of the asymmetry of a probability distribution, to identify outliers. Outskewer analyzes how the skewness coefficient changes as extreme values are sequentially removed from the dataset. If skewness decreases with removals, the extreme values were outliers that skewed the distribution. The method requires no assumptions about the underlying data distribution. It is not effective on distributions where extreme values are common, like power law distributions.
I will discuss paradigmatic statistical models of inference and learning from high dimensional data, such as sparse PCA and the perceptron neural network, in the sub-linear sparsity regime. In this limit the underlying hidden signal, i.e., the low-rank matrix in PCA or the neural network weights, has a number of non-zero components that scales sub-linearly with the total dimension of the vector. I will provide explicit low-dimensional variational formulas for the asymptotic mutual information between the signal and the data in suitable sparse limits. In the setting of support recovery these formulas imply sharp 0-1 phase transitions for the asymptotic minimum mean-square-error (or generalization error in the neural network setting). A similar phase transition was analyzed recently in the context of sparse high-dimensional linear regression by Reeves et al.
PhD Defense: Analyse exploratoire de flots de liens pour la détection d'événe...Sébastien
Link streams represent traces of complex systems’ activities over time, in which links appear when two system entities interact with each other; the aggregation of entities (i.e. nodes) and links is a graph. These traces have become strategic datasets in the last few years for analyzing the activity of large-scale complex systems, involving millions of entities, e.g. mobile phone networks, social networks, or the Internet.
This thesis deals with the exploratory analysis of link streams, in particular the characterization of their dynamics and the identification of anomalies over time (called events). We propose an exploratory framework involving statistical methods and visualization, with no hypothesis about data. The detected events are statistically significant and we propose a method to validate their relevance. We finally illustrate our methodology on the evolution of Github online social network, on which hundred thousands of developers contribute to open source software projects.
Why contribute? “I did it for teh lulz” R. Stallman
Most of Free/Open Source Software (FOSS) developers are not paid to contribute, so why do they work anyway? In this talk, we’ll investigate the motivations of individual contributors. We’ll put them in perspective with recent studies on motivations and communities of practice. In particular, we’ll see that distinguishing internal vs external incentives is a key to understand why FOSS communities are able to attract and keep contributors around the production of a software…
Presented at http://fossa.inria.fr/fr/program/community
Dec 6, 2012
Tour d'horizon des personnes morales adhérentes à l'APRILSébastien
Ce diaporama présente la position des sites des personnes morales adhérentes à l'APRIL dans un graphe du Web. La totalité de l'étude est consultable sur http://web-mining.fr .
I will discuss paradigmatic statistical models of inference and learning from high dimensional data, such as sparse PCA and the perceptron neural network, in the sub-linear sparsity regime. In this limit the underlying hidden signal, i.e., the low-rank matrix in PCA or the neural network weights, has a number of non-zero components that scales sub-linearly with the total dimension of the vector. I will provide explicit low-dimensional variational formulas for the asymptotic mutual information between the signal and the data in suitable sparse limits. In the setting of support recovery these formulas imply sharp 0-1 phase transitions for the asymptotic minimum mean-square-error (or generalization error in the neural network setting). A similar phase transition was analyzed recently in the context of sparse high-dimensional linear regression by Reeves et al.
PhD Defense: Analyse exploratoire de flots de liens pour la détection d'événe...Sébastien
Link streams represent traces of complex systems’ activities over time, in which links appear when two system entities interact with each other; the aggregation of entities (i.e. nodes) and links is a graph. These traces have become strategic datasets in the last few years for analyzing the activity of large-scale complex systems, involving millions of entities, e.g. mobile phone networks, social networks, or the Internet.
This thesis deals with the exploratory analysis of link streams, in particular the characterization of their dynamics and the identification of anomalies over time (called events). We propose an exploratory framework involving statistical methods and visualization, with no hypothesis about data. The detected events are statistically significant and we propose a method to validate their relevance. We finally illustrate our methodology on the evolution of Github online social network, on which hundred thousands of developers contribute to open source software projects.
Why contribute? “I did it for teh lulz” R. Stallman
Most of Free/Open Source Software (FOSS) developers are not paid to contribute, so why do they work anyway? In this talk, we’ll investigate the motivations of individual contributors. We’ll put them in perspective with recent studies on motivations and communities of practice. In particular, we’ll see that distinguishing internal vs external incentives is a key to understand why FOSS communities are able to attract and keep contributors around the production of a software…
Presented at http://fossa.inria.fr/fr/program/community
Dec 6, 2012
Tour d'horizon des personnes morales adhérentes à l'APRILSébastien
Ce diaporama présente la position des sites des personnes morales adhérentes à l'APRIL dans un graphe du Web. La totalité de l'étude est consultable sur http://web-mining.fr .
Inference for stochastic differential equations via approximate Bayesian comp...Umberto Picchini
Despite the title the methods are appropriate for more general dynamical models (including state-space models). Presentation given at Nordstat 2012, Umeå. Relevant research paper at http://arxiv.org/abs/1204.5459 and software code at https://sourceforge.net/projects/abc-sde/
Average case acceleration through spectral density estimationFabian Pedregosa
We develop a framework for designing optimal quadratic optimization methods in terms of their average-case runtime. This yields a new class of methods that achieve acceleration through a model of the Hessian's expected spectral density. We develop explicit algorithms for the uniform, Marchenko-Pastur, and exponential distributions. These methods are momentum-based gradient algorithms whose hyper-parameters can be estimated without knowledge of the Hessian's smallest singular value, in contrast with classical accelerated methods like Nesterov acceleration and Polyak momentum. Empirical results on quadratic, logistic regression and neural networks show the proposed methods always match and in many cases significantly improve over classical accelerated methods.
Statistical Analysis of Imaging Trials: Multivariate Methods and Prediction, Probing Cancer with MR II: From Animal Models to Clinical Assessment, 17th Annual Conference of the International Society for Magnetic Resonance in Medicine, Honolulu, Hawai\'i, April 19-24
Inference for stochastic differential equations via approximate Bayesian comp...Umberto Picchini
Despite the title the methods are appropriate for more general dynamical models (including state-space models). Presentation given at Nordstat 2012, Umeå. Relevant research paper at http://arxiv.org/abs/1204.5459 and software code at https://sourceforge.net/projects/abc-sde/
Average case acceleration through spectral density estimationFabian Pedregosa
We develop a framework for designing optimal quadratic optimization methods in terms of their average-case runtime. This yields a new class of methods that achieve acceleration through a model of the Hessian's expected spectral density. We develop explicit algorithms for the uniform, Marchenko-Pastur, and exponential distributions. These methods are momentum-based gradient algorithms whose hyper-parameters can be estimated without knowledge of the Hessian's smallest singular value, in contrast with classical accelerated methods like Nesterov acceleration and Polyak momentum. Empirical results on quadratic, logistic regression and neural networks show the proposed methods always match and in many cases significantly improve over classical accelerated methods.
Statistical Analysis of Imaging Trials: Multivariate Methods and Prediction, Probing Cancer with MR II: From Animal Models to Clinical Assessment, 17th Annual Conference of the International Society for Magnetic Resonance in Medicine, Honolulu, Hawai\'i, April 19-24
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!SOFTTECHHUB
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
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The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
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End to end testing is a critical piece to ensure quality and avoid regressions. In this session, we share our journey building an E2E testing pipeline for GridMate components (LWC and Aura) using Cypress, JSForce, FakerJS…
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Outskewer: Using Skewness to Spot Outliers in Samples and Time Series
1. cnrs - upmc laboratoire d’informatique de paris 6
Outskewer:
Using Skewness to Spot Outliers
in Samples and Time Series
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien
e e
ASONAM 2012
2. Did you know?
Outlier detection is an important problem to data mining:
source: https://xkcd.com/539/
3. cnrs - upmc laboratoire d’informatique de paris 6
How to detect outliers?
• No formal definition, it is a subjective concept.
• Depends on cases and hypotheses on data.
• Intuitively: to identify values which deviate remarkably from
the remainder of values (Grubbs, 1969).
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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Usual approaches in literature
Hypothesis: data ∼ normal
Distance data points /
distribution.
theoretical values.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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Problem statement
Most of the time, we can’t make strong assumptions on:
• the theoretical distribution of values.
• how the data should evolve over time (time series).
Thus we want a method which makes no hypothesis on data.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
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Skewness coefficient
n x−mean 3
γ= (n−1)(n−2) x∈X standard deviation
density
density
x x
γ<0 γ>0
Example of skewed distributions.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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7/27
8. cnrs - upmc laboratoire d’informatique de paris 6
Skewness coefficient
n x−mean 3
γ= (n−1)(n−2) x∈X standard deviation
density
density
x x
γ<0 γ>0
Example of skewed distributions.
It is sensitive to extremal values (min/max) far from the mean !
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
7/27
9. cnrs - upmc laboratoire d’informatique de paris 6
Skewness signature
Definition
Evolution of skewness coefficient γ when extremal values are
removed one by one from the sample.
Algorithm
If γ > 0 then remove max(X ),
1.5
skewness
Else remove min(X ). 1.0
0.5
0.0
Example
1 2 3 4 5 6 7
X = {-3, -2, -1, -1, 0, 1, 2, 3, 7} # extremal values removed
γ: 1.09, 0.22, 0.17, 0, 0.4, 0, 1.73
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
8/27
10. cnrs - upmc laboratoire d’informatique de paris 6
Our method: Outskewer
Our definition
Outlier = extremal value which skews a distribution of values.
Implication
The removal of these extremal values one by one should reduce
the skewness of the distribution.
Implication
Otherwise, there is no outlier as we define it.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
9/27
11. cnrs - upmc laboratoire d’informatique de paris 6
Outskewer : non-relevant cases
Where extremal values far from the mean are common.
e.g. Power law distributions
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
10/27
12. cnrs - upmc laboratoire d’informatique de paris 6
Outskewer : p-stability
Is the signature p-stable?
p: fraction of extremal values removed.
p-stable ⇔ |γ| ≤ 0.5 − p, for each p from p to 0.5
1.0 q 0.5 t T
cumulative distribution
q q
q
q
qq
q
0.8
q
q
q
q
q
0.4
q
q
q
|skewness|
q
q
q
0.6 q
q 0.3
|g|
qq
qq
qq
q
q
0.4 q
q
q
q
q
0.2
qq
q
q
qq
0.2 qq
q q
q
0.1
q q q
q
q
0.0 0.0
−8 −6 −4 −2 0 2 0 0.14 0.30
0.16 0.5
x p
Example: 0.16-stable but not 0.30-stable
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
11/27
13. cnrs - upmc laboratoire d’informatique de paris 6
Outskewer : p-stability
Is the signature p-stable?
p: fraction of extremal values removed.
p-stable ⇔ |γ| ≤ 0.5 − p, for each p from p to 0.5
If yes: there may be outliers.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
12/27
14. cnrs - upmc laboratoire d’informatique de paris 6
Outskewer : p-stability
Is the signature p-stable?
p: fraction of extremal values removed.
p-stable ⇔ |γ| ≤ 0.5 − p, for each p from p to 0.5
If yes: there may be outliers.
If no for all p: the skewness coefficient is always too large, thus no
outlier as we define it can lie in the sample.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
12/27
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Outskewer : outlier detection
|g| area of
outliers
area of
potential
area with no outlier
2.0 outliers
1.5
1.0 q not outlier q
|skewness|
q q
cumulative frequency
qq
qq
0.8 potential outlier q
q
q
q
1.0
q
q
qq
outlier q
q
q
q
q
0.6 q
q
q
q
qq
qq
q
0.5
q
0.4 q
q
q
q
t’
q
q
q
q
0.2
T’
0.0 0.0
−8 −6 −4 −2 0 2 t T
x 0 0.14 0.5 1
p
t smallest t-stable value , t smallest value so that |γ| ≤ 0.5 − t
T largest T -stable value , T smallest value so that |γ| ≤ 0.5 − T
Example: 50 values, including 7 outliers and 5 potential outliers
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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Outskewer : outcome
Each value of the sample is classified as follows:
qqqqqqqqqqqqqq
qqqqqqqqqq status
q not outlier
potential outlier
outlier
2000
or unknown when the method is not applicable (skewness
signature never p-stable).
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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14/27
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Extension to time series
On a sliding window of size w , each value of X is classified w
times.
The final class of a value is the one that appears the most.
time
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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False positive rate
• Normal distribution: 3% for n = 10, 0.01% for n = 100
• Pareto distribution: 5% for n = 100, 0.01% for n = 1000
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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21. Experimental Results
French population during the 20th century.
Logs of a P2P search engine.
22. cnrs - upmc laboratoire d’informatique de paris 6
French population
during the 20th century
Number of inhabitants per year
qqq
qqq
60M qqq
qqq
qqqqq
qqqq
qqqq
population
qqqq
qqq qqqq
q qqq
50M qqq
qqq
qq
qq
qqq
qq
qqq
q qqq
qqqqqqqqqqqqq qqqqq qqqqqqqqqq
qqq
q
40M qqq
qq qqqq qqqqq
q
1900 1920 1940 1960 1980 2000
Year
Difference over years
1000000
q q q q
500000 q q
qqq qqqqqqq qqq qqqqqqqqqqq status
∆population
q qqqqqqqqqq
qq qq q
q qqqqqqqqqqqqqqqqqqqqqqqqqq
q
qqqqqqqqqqqqq q qqq qq
0 q qq
q not outlier
−500000
potential outlier
−1000000
−1500000 outlier
1900 1920 1940 1960 1980 2000
Year
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
20/27
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Harry Potter on eDonkey
Number of outliers per day
75
# outliers / day
in theatre unknown event pirate release outliers
0
50 potential outliers
15 Jul 24 Aug 12 Oct 1 Dec
Date
Data:
• search logs on P2P network eDonkey.
• # queries containing “half blood prince” per hour, computed
every 10 minutes.
• during 28 weeks.
• over 205 millions of queries.
• for 24.4 millions of IP addresses.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
21/27
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Contributions
Our method:
• is non-parametric but for the size of the time window.
• classifies values only when the statistical conditions are met.
• is naturally generalized to on-line analysis.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
22/27
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Conclusion
• Motivation: outlier detection with no hypothesis on data.
• Method based on the skewness of distributions.
• Excellent experimental results.
• Relevant on various data sets.
• Open source code in R on
http://outskewer.sebastien.pro
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
e e
23/27
27. cnrs - upmc laboratoire d’informatique de paris 6
Homogeneous / heterogeneous data
Outlier = unexpected extremal value?
Extremal values far from the mean?
• heterogeneous (Pareto, Zipf...): common
• homogeneous (normal, Laplace...): uncommon
100
10−5
density
10−10
10−15
10−20
−10 −5 0 5 10
x
Probability density function of normal and Pareto laws.
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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Skewness signature
Normal
2
1 median
0 min
s(p)
max
−1
q1
−2
q3
0.0 0.2 0.4 0.6 0.8 1.0
p
Pareto
8
6 median
4 min
s(p)
2 max
0 q1
−2 q3
0.0 0.2 0.4 0.6 0.8 1.0
p
S´bastien Heymann, Matthieu Latapy, Cl´mence Magnien — Outskewer — ASONAM 2012
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Local view of the internet topology
13000
Nb nodes
12000
11000 outlier potential outlier q not outlier unknown
0 1000 2000 3000 4000 5000
Nb rounds
M. Latapy, C. Magnien and F. Ou´draogo, A Radar for the Internet, in Complex Systems, 20 (1), 23-30, 2011.
e
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