special topics in educational data mining hudk5199 spring 2013 march 25, 2012
TRANSCRIPT
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Special Topics in Educational Data Mining
HUDK5199Spring 2013
March 25, 2012
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Today’s Class
• Social Network Analysis
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General Principles of Social Network Analysis
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General Principles of Social Network Analysis
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General Postulates of Social Network Analysis
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General Postulates of Social Network Analysis
• There are many entities, referred to as nodes or vertices
• Nodes have connections to other notes, referred to as ties or links
• Nodes can have different types or identities• Links can have different types or identities• Links can have different strengths
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Example(Student work groups – Kay et al., 2006)
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Example(Student work groups – Kay et al., 2006)
nodes
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Example(Student work groups – Kay et al., 2006)
ties
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Example(Student work groups – Kay et al., 2006)
Strong ties
Weak ties
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Which student group works together better?
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Which is the most collaborative pair?
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Who is the most collaborative student?
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Types
• In a graph of classroom interactions, what different types of nodes could there be?
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Types
• In a graph of classroom interactions, what different types of nodes could there be?– Teacher– TA– Student– Project Leader– Project Scribe
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Types
• In a graph of classroom interactions, what different types of links could there be?
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Types
• In a graph of classroom interactions, what different types of links could there be?– Leadership role (X leads Y)– Working on same learning resource– Helping act– Criticism act– Insult
– Note that links can be directed or undirected
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Strength
• In a graph of classroom interactions, what would make links stronger or weaker?
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Strength
• In a graph of classroom interactions, what would make links stronger or weaker?– Intensity of act (Examples?)– Frequency of act (Examples?)
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Examples
• What might be some types of social networks that would be studied in the learning sciences?
• What might be some relevant research questions?
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Social Network Analysis
• Use social network graphs to study the patterns and regularities of the relationships between the nodes
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Density
• Proportion of possible lines that are actually present in graph
• What is the density of these graphs?
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Reachability
• A node is “reachable” if a path goes from any other node to it
• Which nodes are reachable and unreachable?
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Geodesic Distance
• The number of nodes between one node N and another node M
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Example(Dawson, 2008)
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What is the geodesic distance?
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What is the geodesic distance?
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What is the geodesic distance?
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Geodesic Distance
• What might be a use for geodesic distance in educational research?
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Flow
• How many possible paths are there between node N and node M?
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What is the flow?
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Flow
• What might be a use for flow in educational research?
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Centrality
• How important is a node within the graph?
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Centrality
• Four common measures– Degree centrality– Closeness centrality– Betweeness centrality– Eigenvector centrality
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Nodal Degree
• Number of lines that connect to a node
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Which node has the highest nodal degree?
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Nodal Degree
• Indegree: number of lines that come into a node– How might this be interpreted for some link types
you might see in educational data?
• Outdegree: number of lines that come out of a node– How might this be interpreted for some link types
you might see in educational data?
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Closeness
• A node N’s closeness is defined as the sum of its distance to other nodes
• The most central node in terms of closeness is the node with the lowest value for this metric
• Note that strengths can be used as a distance measure for calculating closeness– Higher strength = closer nodes
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Which node has highest closeness? (looking solely at number of steps)
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Which node has highest closeness? (looking at link strengths)
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Betweenness
• Betweeness centrality for node N is computed as:
• The percent of cases where• For each pair of nodes M and P (which are not N)– The shortest path from M to P passes through N
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What is this node’s betweenness
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What is this node’s betweenness
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What is this node’s betweenness
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Betweenness
• How might this be interpreted for some link types you might see in educational data?
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Eigenvector Centrality
• Complex math, but assigns centrality to nodes through recursive process where
• More and stronger connections are positive• Connections to nodes with higher eigenvector
centrality contribute more than connections to nodes with lower eigenvector centrality
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Eigenvector Centrality
• What type of applications might this have?
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How do these measures differ in meaning?
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Reciprocity
• What percentage of ties are bi-directional?– Can be computed as number of bi-directional ties
over total number of connected pairs
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What is the reciprocity?
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What could reciprocity tell you?
• For educational data
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Clique
• Sub-set of a network for which all nodes are connected to each other– If there is any node which is connected to all
nodes in the clique– Then it is also part of the clique
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What are the cliques?
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Clique
• What could cliques tell you in educational research problems?
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N-Clique
• Sub-set of a network for which all nodes are connected to each other with a path of geodesic distance of N or less
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What are the 2-cliques?
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K-plex
• Sub-set of a network, of size N, for which all nodes are connected to at least N-K other members of the K-plex
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What are the 1-plexes?
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Connections between cliques
• Can represent key conduits for information
• Example from Haythornthwaite (1998)
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Communication in a class (letters indicate groups)
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Comments? Questions?
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Case Studies in Uses of Social Network Analysis
• (Haythornthwaite, 2001)• (Dawson, 2008)
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How?
• How did Haythornthwaite and Dawson use social network analysis to learn about collaborative learning?
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Haythornthwaite• Analyzed data from four groups from same class over time• Analyzed students’ communication behaviors
– Collaborative Work– Exchanging Advice– Socializing– Emotional Support
• Analyzing students’ use of communication technologies– Webboard– IRC– Email– NetMeeting– Telephone– Face-to-Face
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Dawson
• Analyzed student perception of being part of a social community and a learning community, in relation to their centrality (multiple measures)
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Other uses?
• What are some other uses of social network analysis for learning beyond those we’ve discussed today?
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Comments? Questions?
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Assignment 6
• Solutions
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Assignment 7
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Next Class• Wednesday, March 27
• Correlation Mining and Causal Mining
• Readings• Arroyo, I., Woolf, B. (2005) Inferring learning and attitudes from a Bayesian
Network of log file data. Proceedings of the 12th International Conference on Artificial Intelligence in Education, 33-40.
• Rai, D., Beck, J.E. (2011) Exploring user data from a game-like math tutor: a case study in causal modeling. Proceedings of the 4th International Conference on Educational Data Mining, 307-313.
• Rau, M. A., & Scheines, R. (2012) Searching for Variables and Models to Investigate Mediators of Learning from Multiple Representations. Proceedings of the 5th International Conference on Educational Data Mining, 110-117.
• Assignments Due: None
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The End