METHODS AND APPARATUS FOR DISTRIBUTED COMMUNITY FINDING

• US 20130046842A1
• Filed: 10/25/2012
• Published: 02/21/2013
• Est. Priority Date: 05/10/2005
• Status: Active Grant

• Current Assignee: NetSeer, Inc. (Inuvo, Inc.)
• Original Assignee: NetSeer, Inc. (Inuvo, Inc.)
• Inventors: Muntz, Alice Hwei-Yuan Meng, Rezaei, Behnam Attaran
• Granted Patent: US 8,825,654 B2
• Time in Patent Office: Days
• US Class Current: 709/206
• CPC Class Codes: G06Q 10/00 Administration; Management
• CPC Class Codes: Y10S 707/93 intellectual property analysis
• CPC Class Codes: Y10S 707/937 intellectual property searching
• CPC Class Codes: Y10S 707/959 Network

Abstract

Methods and apparatus for a new approach to the problem of finding communities in complex networks relating to a social definition of communities and percolation are disclosed. Instead of partitioning the graph into separate subgraphs from top to bottom a local algorithm (communities of each vertex) allows overlapping of communities. The performance of an algorithm on synthetic, randomly-generated graphs and real-world networks is used to benchmark this method against others. An heuristic is provided to generate a list of communities for networks using a local community finding algorithm. Unlike diffusion based algorithms, The provided algorithm finds overlapping communities and provides a means to measure confidence in community structure. It features locality and low complexity for exploring the communities for a subset of network nodes, without the need for exploring the whole graph.

Claims

1. A method comprising:

maintaining a representation of a distributed user community stored in a database, the distributed user community comprising a plurality of overlapping user communities, wherein each user community comprises a contact list and contact addresses corresponding to the contact list; and

analyzing an email addressed to a user from a source by applying a percolation community finding algorithm to the distributed user community.

2. The method of claim 1, further comprising identifying the email as spam.

3. The method of claim 1, further comprising forwarding the email to the user.

4. The method of claim 3, further comprising modifying the header of the email prior to forwarding the email to the user.

5. The method of claim 1, wherein the percolation community finding algorithm comprises:

initiating a percolation message from a source node of the distributed user community, the distributed user community comprising a plurality of nodes and a plurality of edges, each edge connecting at least two of the plurality of nodes, wherein a node is a neighbor if the node is connected to another node in the plurality of nodes by an edge, wherein the percolation message comprises a percolation probability and an identifier of the source node, and wherein initiating a percolation message from the source node comprises transmitting the percolation message to each neighbor of the source node with the percolation probability;

propagating the percolation message through the distributed user community, wherein propagating the percolation message through the distributed user community comprises;

transmitting the percolation message from each node that receives the percolation message to each neighbor of each node that receives the percolation message; and

transmitting a response to the source node from each node that receives the percolation message;

collecting each response to the percolation message at the source node; and

storing a list of nodes that transmitted the response at the source node.

6. The method of claim 1, wherein the percolation community finding algorithm comprises:

initiating a plurality of percolation messages from each of a plurality of source nodes at a plurality of percolation probabilities, wherein the plurality of percolation probabilities are selected from a set of values between 0 and 1;

determining a list of nodes that received the plurality of percolation messages for each of the plurality of source nodes;

aggregating the list of nodes for each of the plurality of source nodes to determine a local neighborhood for each of the plurality of source nodes, wherein each node is weighted based on a number of times each node received the plurality of percolation messages;

plotting the local neighborhood size versus percolation probabilities for each of the local neighborhoods;

locating phase transition points in the plot; and

determining nested local communities for the plurality of source nodes by combining the local neighborhoods at the phase transition points.

7. The method of claim 1, wherein the percolation community finding algorithm comprises:

selecting one of the set of seed nodes as a source node;

computing a set of local communities for the source node;

identifying a set of nodes in the set of local communities having a weight greater than a threshold;

generating a strong local community for the source node including only the set of nodes that have a weight greater than the threshold;

storing the strong local community as one of a plurality of communities of the network;

repeating the selecting, computing, identifying, generating, and storing and removing until a community is generated that comprises only nodes with a degree less than a threshold value; and

labeling the set of stored strong local communities as one of a disjoint community structure of the network or an overlapping community structure of the network.

8. The method of claim 1 further comprising:

specifying a weight for each link; and

determining a weight for each of the plurality of communities.

9. The method of claim 8, further comprising modifying the weight for each link, and determining a modified weight for each of the plurality of communities.

10. The method of claim 1 further comprising:

specifying a weight for each node; and

determining a weight for each of the plurality of communities.

11. The method of claim 10, further comprising modifying the weight for each node, and determining a modified weight for each of the plurality of communities.

12. A program storage device readable by a machine, embodying a program of instructions executable by the machine to perform a method, the method comprising:

maintaining a representation of a distributed user community stored in a database, the distributed user community comprising a plurality of overlapping user communities, wherein each user community comprises a contact list and contact addresses corresponding to the contact list; and

analyzing an email addressed to a user from a source by applying a percolation community finding algorithm to the distributed user community.

13. The program storage device of claim 12, further comprising identifying the email as spam.

14. The program storage device of claim 12, further comprising forwarding the email to the user.

15. The program storage device of claim 14, further comprising modifying the header of the email prior to forwarding the email to the user.

16. The program storage device of claim 12, wherein determining the community structure comprises:

initiating a percolation message from a source node of the distributed user community, the distributed user community comprising a plurality of nodes and a plurality of edges, each edge connecting at least two of the plurality of nodes, wherein a node is a neighbor if the node is connected to another node in the plurality of nodes by an edge, wherein the percolation message comprises a percolation probability and an identifier of the source node, and wherein initiating a percolation message from the source node comprises transmitting the percolation message to each neighbor of the source node with the percolation probability;

propagating the percolation message through the distributed user community, wherein propagating the percolation message through the distributed user community comprises;

transmitting the percolation message from each node that receives the percolation message to each neighbor of each node that receives the percolation message; and

transmitting a response to the source node from each node that receives the percolation message;

collecting each response to the percolation message at the source node; and

storing a list of nodes that transmitted the response at the source node.

17. The program storage device of claim 12, wherein determining the community structure comprises:

initiating a plurality of percolation messages from each of source nodes at a plurality of percolation probabilities, wherein the plurality of percolation probabilities are selected from a set of values between 0 and 1;

determining a list of nodes that received the plurality of percolation messages for each of the plurality of source nodes;

aggregating the list of nodes for each of the plurality of source nodes to determine a local neighborhood for each of the plurality of source nodes, wherein each node is weighted based on a number of times each node received the plurality of percolation messages;

plotting the local neighborhood size versus percolation probabilities for each of the local neighborhoods;

locating phase transition points in the plot; and

determining nested local communities for the plurality of source nodes by combining the local neighborhoods at the phase transition points.

18. The program storage device of claim 12, wherein determining the community structure comprises:

selecting one of the set of seed nodes as a source node;

computing a set of local communities for the source node;

identifying a set of nodes in the set of local communities having a weight greater than a threshold;

generating a strong local community for the source node including only the set of nodes that have a weight greater than the threshold;

storing the strong local community as one of a plurality of communities of the network;

repeating the selecting, computing, identifying, generating, and storing and removing until a community is generated that comprises only nodes with a degree less than a threshold value; and

labeling the set of stored strong local communities as one of a disjoint community structure of the network or an overlapping community structure of the network.

19. The program storage device of claim 12 further comprising:

specifying a weight for each link; and

determining a weight for each of the plurality of communities.

20. The program storage device of claim 19, further comprising modifying the weight for each link, and determining a modified weight for each of the plurality of communities.

21. The program storage device of claim 12 further comprising:

specifying a weight for each node; and

determining a weight for each of the plurality of communities.

22. The program storage device of claim 21, further comprising modifying the weight for each node, and determining a modified weight for each of the plurality of communities.

23. An apparatus comprising:

memory;

one or more computers configured to;

maintain a representation of a distributed user community stored in a database, the distributed user community comprising a plurality of overlapping user communities, wherein each user community comprises a contact list and contact addresses corresponding to the contact list; and

analyze an email addressed to a user from a source by applying a percolation community finding algorithm to the distributed user community.

24. The apparatus of claim 23, wherein the one or more computers are further configured to identify the email as spam.

25. The apparatus of claim 23, wherein the one or more computers are further configured to forward the email to the user.

26. The apparatus of claim 23, wherein the one or more computers are further configured to modify the header of the email prior to forwarding the email to the user.

27. The apparatus of claim 23, wherein determining the community structure comprises:

initiating a percolation message from a source node of the distributed user community, the distributed user community comprising a plurality of nodes and a plurality of edges, each edge connecting at least two of the plurality of nodes, wherein a node is a neighbor if the node is connected to another node in the plurality of nodes by an edge, wherein the percolation message comprises a percolation probability and an identifier of the source node, and wherein initiating a percolation message from the source node comprises transmitting the percolation message to each neighbor of the source node with the percolation probability;

propagating the percolation message through the distributed user community, wherein propagating the percolation message through the distributed user community comprises;

transmitting the percolation message from each node that receives the percolation message to each neighbor of each node that receives the percolation message; and

transmitting a response to the source node from each node that receives the percolation message;

collecting each response to the percolation message at the source node; and

storing a list of nodes that transmitted the response at the source node.

28. The apparatus of claim 23, wherein determining the community structure comprises:

initiating a plurality of percolation messages from each of source nodes at a plurality of percolation probabilities, wherein the plurality of percolation probabilities are selected from a set of values between 0 and 1;

determining a list of nodes that received the plurality of percolation messages for each of the plurality of source nodes;

aggregating the list of nodes for each of the plurality of source nodes to determine a local neighborhood for each of the plurality of source nodes, wherein each node is weighted based on a number of times each node received the plurality of percolation messages;

plotting the local neighborhood size versus percolation probabilities for each of the local neighborhoods;

locating phase transition points in the plot; and

determining nested local communities for the plurality of source nodes by combining the local neighborhoods at the phase transition points.

29. The apparatus of claim 23, wherein determining the community structure comprises:

selecting one of the set of seed nodes as a source node;

computing a set of local communities for the source node;

identifying a set of nodes in the set of local communities having a weight greater than a threshold;

generating a strong local community for the source node including only the set of nodes that have a weight greater than the threshold;

storing the strong local community as one of a plurality of communities of the network;

repeating the selecting, computing, identifying, generating, and storing and removing until a community is generated that comprises only nodes with a degree less than a threshold value; and

labeling the set of stored strong local communities as one of a disjoint community structure of the network or an overlapping community structure of the network.

30. The apparatus of claim 23 wherein the one or more computers are further configured to:

specify a weight for each link; and

determine a weight for each of the plurality of communities.

31. The apparatus of claim 23, wherein the one or more computers are further configured to modify the weight for each link, and determine a modified weight for each of the plurality of communities.

32. The apparatus of claim 23 wherein the one or more computers are further configured to:

specify a weight for each node; and

determine a weight for each of the plurality of communities.

33. The apparatus of claim 32, wherein the one or more computers are further configured to modify the weight for each node, and determine a modified weight for each of the plurality of communities.

34. An apparatus comprising:

means for maintaining a representation of a distributed user community stored in a database, the distributed user community comprising a plurality of overlapping user communities, wherein each user community comprises a contact list and contact addresses corresponding to the contact list; and

means for analyzing an email addressed to a user from a source by applying a percolation community finding algorithm to the distributed user community.

35. The apparatus of claim 34, further comprising identifying the email as spam.

36. The apparatus of claim 34, further comprising forwarding the email to the user.

37. The apparatus of claim 36, further comprising modifying the header of the email prior to forwarding the email to the user.

38. The apparatus of claim 34, wherein the means for determining the community structure comprises:

means for initiating a percolation message from a source node of the distributed user community, the distributed user community comprising a plurality of nodes and a plurality of edges, each edge connecting at least two of the plurality of nodes, wherein a node is a neighbor if the node is connected to another node in the plurality of nodes by an edge, wherein the percolation message comprises a percolation probability and an identifier of the source node, and wherein initiating a percolation message from the source node comprises transmitting the percolation message to each neighbor of the source node with the percolation probability;

means for propagating the percolation message through the distributed user community, wherein the means for propagating the percolation message through the distributed user community comprises;

means for transmitting the percolation message from each node that receives the percolation message to each neighbor of each node that receives the percolation message; and

means for transmitting a response to the source node from each node that receives the percolation message;

means for collecting each response to the percolation message at the source node; and

means for storing a list of nodes that transmitted the response at the source node.

39. The apparatus of claim 34, wherein the means for determining the community structure comprises:

means for initiating a plurality of percolation messages from each of source nodes at a plurality of percolation probabilities, wherein the plurality of percolation probabilities are selected from a set of values between 0 and 1;

means for determining a list of nodes that received the plurality of percolation messages for each of the plurality of source nodes;

means for aggregating the list of nodes for each of the plurality of source nodes to determine a local neighborhood for each of the plurality of source nodes, wherein each node is weighted based on a number of times each node received the plurality of percolation messages;

means for plotting the local neighborhood size versus percolation probabilities for each of the local neighborhoods;

means for locating phase transition points in the plot; and

means for determining nested local communities for the plurality of source nodes by combining the local neighborhoods at the phase transition points.

40. The apparatus of claim 34, wherein the means for determining the community structure comprises:

means for selecting one of the set of seed nodes as a source node;

means for computing a set of local communities for the source node;

means for identifying a set of nodes in the set of local communities having a weight greater than a threshold;

means for generating a strong local community for the source node including only the set of nodes that have a weight greater than the threshold;

means for storing the strong local community as one of a plurality of communities of the network;

means for repeating the selecting, computing, identifying, generating, and storing and removing until a community is generated that comprises only nodes with a degree less than a threshold value; and

means for labeling the set of stored strong local communities as one of a disjoint community structure of the network or an overlapping community structure of the network.

41. The apparatus of claim 34 further comprising:

means for specifying a weight for each link; and

means for determining a weight for each of the plurality of communities.

42. The apparatus of claim 41, further comprising means for modifying the weight for each link, and means for determining a modified weight for each of the plurality of communities.

43. The method of claim 34 further comprising:

means for specifying a weight for each node; and

means for determining a weight for each of the plurality of communities.

44. The apparatus of claim 43, further comprising means for modifying the weight for each node, and means for determining a modified weight for each of the plurality of communities.