1 Network Intelligence and Networked Intelligence 网络智能和网络化智能 Deyi Li ( 李 德 毅 ) Aug. 1, 2006

2 Challenge to AI for Knowledge Representation

3 Study on Knowledge Representation one-dimensional representation: one-dimensional representation: predicate calculus, natural language understanding, etc. predicate calculus, natural language understanding, etc. two-dimensional representation: two-dimensional representation: pattern recognition, neural network learning, etc. pattern recognition, neural network learning, etc. attention on evolutional networks with uncertainty was less paid unfortunately. attention on evolutional networks with uncertainty was less paid unfortunately.

4 Networks are present everywhere. All we need is an eye for them.

5 We are witnessing a revolution in the making as scientists from all different disciplines discover that complexity has a strict architecture. We have come to grasp the important knowledge of networks. We are witnessing a revolution in the making as scientists from all different disciplines discover that complexity has a strict architecture. We have come to grasp the important knowledge of networks.

6 Networks interact with one another and are recursive. Networks interact with one another and are recursive. Getting such a diverse group to agree on a common core of knowledge representation about networks is a significant challenge to both Cognitive Science and Artificial Intelligence. Getting such a diverse group to agree on a common core of knowledge representation about networks is a significant challenge to both Cognitive Science and Artificial Intelligence.

7 Networks Evolution and Growth drive the fundamental issue that forms our view of network representation and network intelligence. Networks Evolution and Growth drive the fundamental issue that forms our view of network representation and network intelligence.

8 Paul.Erdos Albert Barabasi Reka Albert Steven Strogatz Alfred Renyi Duncan Watts ER pure random graph(1960) WS small world model (1998) BA scale-free model(1999)

9 “Small worlds” and “power law distributions” are generic properties of networks in general. “Small worlds” and “power law distributions” are generic properties of networks in general. There is a new knowledge representation out there that is the network representation. There is a new knowledge representation out there that is the network representation.

10 It’s the fact that all of these real world networks can be explained and understood using the same concepts, and the same mathematics, that makes network representation so important in AI research in the information age. It’s the fact that all of these real world networks can be explained and understood using the same concepts, and the same mathematics, that makes network representation so important in AI research in the information age.

11 Mining Typical Topologies from Real Complex Networks

12 typical topologies with randomness

13 An evolutional and growth network may be by and large characterized by an ideal typical model

14 Expectation of topologies at different scales: Small world network Small world network Scale free network Scale free network Hub Network Hub Network Star Network Star Network Mining Typical Topology from Real World Networks at Multi-scale

15 Extend more properties of networks the mass of a node the mass of a node physical distance between two nodes physical distance between two nodes the age of a node the age of a node betweenness of a link betweenness of a link betweenness of a node betweenness of a node

16 With the extended properties of networks, we may map relational data into networked representation and propose a new direction that is networked data mining. With the extended properties of networks, we may map relational data into networked representation and propose a new direction that is networked data mining.

17 A detailed networked data

18 Mining typical topology with a middle granularity

19 Mining typical topology with a large granularity

20 Discover critical links and important communities from a real network

21 Many networks are inhomogeneous, consisting lot of an undifferentiated mass of nodes, but of distinct groups.

22 Mining communities Classification: The typical problem in networked data mining is that of dividing all the nodes of a network into some number of groups, while minimizing the number of links that run between nodes in different groups. Classification: The typical problem in networked data mining is that of dividing all the nodes of a network into some number of groups, while minimizing the number of links that run between nodes in different groups. Clustering: Given a network structure, try to divide into communities in such a way that every node belongs only to one of the communities. Clustering: Given a network structure, try to divide into communities in such a way that every node belongs only to one of the communities.

23  Community model can capture the hierarchical feature of a Network.

24 A link removal method A link removal method based on link betweenness Input ： Initial network topology ， the number of community Output ： network communities Step 1. Calculate the betweenness for all links in the network. Step 2. Remove the link with the highest betweenness. Step 3.Re-calculate betweennesses for all links affected by the removal. Step 4.Repeat from step 2 until generating specified numbers of communities.

25 Mining Communities

26 Mining clusters in a complex network using data field method and finding virtual kernels Given a traffic network, find virtual traffic centers Given a traffic network, find virtual traffic centers

27 Node mass may represent its degree from data field point of view

28 Node mass may also represent its betweenness from data field point of view

29 Emergence Computation

30 A subtle urge to synchronize is pervasive in nature indeed synchronized clapping synchronized clapping fireflies flashing fireflies flashing menstrual cycles of women menstrual cycles of women adaptive path minimization by ants adaptive path minimization by ants wasp and termite nest building wasp and termite nest building army ant raiding army ant raiding fish schooling and bird flocking fish schooling and bird flocking pattern formation in animal coats pattern formation in animal coats coordinated cooperation in slime molds coordinated cooperation in slime molds

31 Nature Vol. 403, 24 Feb.2000

32 The emergence of synchronized clapping is a delightful expression of self-organization on a human scale The emergence of synchronized clapping is a delightful expression of self-organization on a human scale

33 emergence mechanism For everybody in the audience there are 3 measurements: For everybody in the audience there are 3 measurements: 1.time difference at the beginning of the applause (TDB) 2.interval time of a clap to the next one (IT, represented by △ t) 3.the clapping strength (CS)

34 If there is no any interaction among audience, the distributions of everybody’s TDB, IT and CS, even the number of clap times all follow a kind of poisson curve like. If there is no any interaction among audience, the distributions of everybody’s TDB, IT and CS, even the number of clap times all follow a kind of poisson curve like. If there are interactions among audience, the influence to each other depends on the distance (say r ij ) between them. If there are interactions among audience, the influence to each other depends on the distance (say r ij ) between them.

35 Assume: all the clap strengths are the same. all the clap strengths are the same. “following the many” is fundamental mechanism and pervasive applicable. “following the many” is fundamental mechanism and pervasive applicable. Therefore the relationship of persons in the audience, that is the structure of the network, encoding how people influence each other is set up in formula 1 Therefore the relationship of persons in the audience, that is the structure of the network, encoding how people influence each other is set up in formula 1

36 somebody’s just-happened clap moment is t i and the next IT (say △ t i ’) is based on his current IT (say △ t i ) and influenced by the distanced person who’s just-happened clap is measured by △ t j and clapped moment t j somebody’s just-happened clap moment is t i and the next IT (say △ t i ’) is based on his current IT (say △ t i ) and influenced by the distanced person who’s just-happened clap is measured by △ t j and clapped moment t j σ represents distance influence factor σ represents distance influence factor c 1 and c 2 are coupling factors c 1 and c 2 are coupling factors

37 The formula shows the fact that there is no an invisible control to all the audience, every body affects others and affected by others equally.

38 Single Clapping Single clappingSingle continuous clapping

39 general applause in a theatre

40 all the palms in the theatre came together after a long time applause

41 The ‘up here down there’ applause in the square

42 An experimental platform of emergence computation Visualization of courtesy applause and synchronized applause

43 It is difficult to distinguish the virtual general applause from the real one. It is also difficult to distinguish the virtual synchronous applause from the real one.

44 Network is the key to representing the complex world around us. Small changes in the topology, affecting only a few of the nodes, can open up hidden doors, allowing new possibilities to emerge.

45 Sum up Challenge to AI for Knowledge Representation Challenge to AI for Knowledge Representation Mining Typical Topologies from Real Complex Networks Mining Typical Topologies from Real Complex Networks Discover Critical Links and Important Communities from a Real Network Discover Critical Links and Important Communities from a Real Network Emergence Computation Emergence Computation

46 To be studied in the future: 1.better measurements of network structure in network representation 2.better understanding of the relationship between the architecture of a network and its function 3. better modeling of very large networks 4.mining common concepts of a network across different scales 5.robustness and security of networks 6.networked data mining 7.virtual reality of emergence.

47 Thanks 李 德 毅李 德 毅李 德 毅李 德 毅