Identifying Communities on Twitter: Time, Topics & Clusters

Pascal Jürgens (@pascal)Dept. of Communication, U of Mainz, Germany

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Overview

Relevance / Why it’s interesting

The Basic Idea / Why it works

Limitations / When it works

Algorithms / How it works

Evaluations / How to tell whether it works

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Overview

What Science are we in,anyways?“The antireductionist catch-phrase, “the whole is more than the sum of its parts,” takes on increasing significance as new sciences such as chaos, systems biology, evolutionary economics, and network theory move beyond reductionism to explain how complex behavior can arise from large collections of simpler components.”

Mitchell, 2009 — Complexity: A Guided Tour

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What Science are we in, anyways?

Interdisciplinary territory with distinct influences

20th century Sociology — small-scale social network analysis

Econometrics — time-series analysis, predictions & forecasting

Mass Communication — media effects

Theoretical Physics — abstract, high-level descriptions of networks; large-scale network analysis (Why is this even here?)

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What is Community Detection?“Communities are groups of vertices which probably share common properties and/or play similar roles within the graph.”

Fortunato & Castellano 2009 — Community Structure in Graphs in the Encyclopedia of Complexity and Systems Science

An exploratory method for partitioning a network into smaller pieces.In many ways it is comparable to cluster analysis.

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(Caveat Emptor)CD is a complex, fairly new set of statistical methods for exploratively building groups from data

So why not use simpler, better-known methods such as clustering?

By all means, use simple methods!(but they do something different)

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RelevanceNetworks are a fundamental structure of the world

There are global properties of networks (diameter &c.)

There are properties of nodes (centrality &c.)

However — Networks are almost never homogenous!

There is a structure hidden within the whole

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Group A

Group C

Group B

ApplicationsIdentify separate groups within relevant population for further description

Captures “public sphere” better than aggregates such as #hashtags(Users who share a #tag might have nothing in common)

Investigate relationship of communities (mesoscopic graph)

In general: more accurate, delivers more details

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TerminologyGraph: A network, consisting of

nodes (or vertices) such as twitter users- with degree = number of connections

links (or edges) such as relationships via @-messageswith weight = intensity of links

Partition: one way to split a network into a set of communities

(k-) Clique: a set of k completely connected nodes

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The Basic IdeaCommunities: Local structures within a network that differ in their structure from the surroundings

A good starting point: communities are better connected among themselves than with other communities

Opens up two obvious methods:

Add links between close nodes until some condition is met

Remove links between distant nodes until some condition is met

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12possible Partitions

The Edge Betweenness Algorithm (Girvan / Newman)

Edge betweenness: the number of shortest paths between any two nodes that go through one edge

High EB: the link is very important to fast information flow

Low EB: the link can easily be replaced by using another way

The algorithm simply eliminates the links with the highest EB step by step

An optimal cut can be selected from the sequence of partitions

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14small network example

15small network example — edge betweenness cluster

Limitations — TechnicalThe number of potential ways to divide a network grows super-exponentially with the number of nodes (!)

Two critical performance parameters of algorithms: runtime (“Big-O”-notation) and memory

Networks up to 100s of nodes and/or edges — usually OK

Networks up to 10 000s of nodes and/or edges — buy a lot of memory (8GB upwards) and prepare to wait

Bigger networks: Ask a computer scientist

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Limitations — MethodologicalQuality of partitions — algorithms don’t guarantee best results

Instability of partitions — algorithms can be non-deterministic and very sensitive to small changes

Evaluation / Comparison of partitions is near-impossible

Sometimes result is not one best but a whole set of partitions

Nodes can only belong to one community (!)

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18large network example — edge betweenness cluster

Notable AlgorithmsThe Edge Betweenness Algorithm (Girvan / Newman)

Markov Cluster Algorithm (MCL, van Dongen, this one is in gephi)

Clique Percolation (CPM, Palla et al.)

Information theoretical Algorithm (Roswall & Bergstrom, does hierarchies and works with communities of very different sizes)

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A Word about MCLMarked as experimental in gephi and hard to use (clustering panel needs to be open before loading dataset), but the only clustering algorithm available

Based on probability of link use - simulates flow through the network

Often sub-stellar results

Connection probabilities seem an odd predictor for empirical connection habits

DEMO

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Clique PercolationOne among several new algorithms that address shortcomings

Intuitive mechanism

Nodes can be in several communities!

Works rather well for dense networks!

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Clique PercolationIdea: Find k-cliques in the network

Try to “move” the cliques until they reach a bottleneck that they can’t fit through

All the nodes covered by this “trail” are assigned to a community

Rather easy to implement in software (igraph) plus free implementation available (CFinder, cfinder.org)

DEMO

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Clique Percolation by Example

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EvaluationExploratory methods are notoriously difficult to assess (beyond rule-of-thumb judgements).

Two ways allow rigorous examination:

Comparison of two partitions

Comparison of a partition agains a baseline model (zero model)

Effectively unfeasible for non-mathematicians: Pick a good algorithm and treat results with care

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What about user attributes?What happens when we use empirical attributes to group users?

Example of the German General Election 2009: Measured party affiliation (wahlgetwitter hashtag +/- convention)

Turns out, users don’t cluster by party affiliation

But careful: this approach means measuring with two loose ends

Clustering baseline needs to be really, really solid

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TakeawayCommunity detection used to be hard but is pretty usable now

Think about the design and scope of a collected network beforehand! (timeframe, directed, size/scope etc.)

Watch the outliers (Justin Bieber will sink your analysis)

Choose an algorithm that

uses directed & weighted links, is understandable, robust

and one that produces meaningful, simple results!

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Thanks!

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Literature

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Fortunato, Santo and Castellano, Claudio (2009): Community Structure in Graphs. In: Meyers, Robert A. (Ed.): Encyclopedia of Complexity and Systems Science. Springer.

Lancichinetti, Andrea and Fortunato, Santo: Community detection algorithms: a comparative analysis. Phys. Review E.

Mitchell, Melanie (2009): Complexity: A Guided Tour

Palla, Gergely; Barabási, Albert-László and Vicsek, Tamás (): Quantifying social group evolution