Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks
Influence public opinion in the network dynamics modeling and analysis of the latest developments
Thesis Section 6, Section 1 introduces the basic dynamic model of public opinion and the results of several recent topics. Section 2 introduces the basic concepts of graph theory, and the basic model and the model Degroot Friedkin-Johnsen model of dynamics of public opinion, as well as the associated mathematical formulas and theorems. Section 3 introduces the concept of self-confidence / social power, and DeGroot Friedkin model comes in the ideological evolution of social rights DeGroot model, and put forward many new results, to discuss the direction of development. Section 4 describes the views expressed divided views and private views of EPO model, and pointed out many interesting phenomena caused because the research model, and once again recorded the direction of future work. It describes the logic associated with dynamic network in Section 5. Finally, the conclusions in Section 6.
1 Introduction
Dynamic opinion (Opinion dynamics) is a dynamic model (dynamical models) the development and analysis, these models describe the social network and exchange views on how individuals interact, there may be individuals in the network by lead their neighbors with the views expressed by learning Over time (k) is changed. Many comments dynamic model (opinion dynamics models) are based on the model of the subject (agent-based models), also is a kind of microscopic model, starting from the individual's point of view to characterize the evolution of ideas, where each individual opinion on a topic all with a true value (real value) indicates that the value changes with time. Graphics can be represented by a network of human interaction network, a node represents a person, and side views of the representatives of the interaction between two people.
For large networks, agent-based model may not be suitable, but to still be useful for small networks, because many small consultative group will make important decisions. In addition to the simple model captures the consensus, some DeGroot model variants in different studies how social phenomena are produced. For example Hegselmann-Krause model using finite homogeneity captured confidence, only one of them interact with other people having a similar view, with the passage of time, these individuals may be divided into discrete clusters, each cluster internal the final of the same opinion, but the final opinion between different clusters and clusters (Category).
Polarization, the network is divided into two opposing points of view. Altafini model uses the concept of a negative edge weights (negative edge weights) introduced oppositional interaction between individuals (antagonistic interactions), resulting in a lot of reasons for this opposition, such as hate or do not trust each other. If the network is a cluster "balanced structure" and to meet the appropriate connection condition, the views will be divided into two opposing polarization. Some proposed model had a negative interaction. Polarization also attributed to personal biases tend to assimilate the information source ( biased assimilation ).
Most of these models capture the weak network diversity, in which there is no difference between the personal views of the same cluster. There is a growing concern model is able to capture the powerful diversity, and these models in the real world are often observed. In this case, the views will eventually merge into a value having a different range of views, which is inconsistent with a durable configuration (and there may be a set of similar but not equal to the value of the views in the cluster). This powerful model of diversity, one is considered a strong social network diversity, these social networks over time to maintain some form of connectivity. But as rare as in the real world eventually completely disconnected clusters in Hegselmann-Krause models that appear in; the other is to consider several questions: If the point of view of social influence is more closely together, so What other processes have a strong diversity in the process of playing a role in the network connected?
Mäs, who considered the two features. The first is the "social alienation" (so? Cial distancing), that individuals applying a negative weight to their views and opinions worth far removed. In Altafini model, the main difference that the weight weight weight opposition considered depending on weight differences of opinion, and it is assumed that the model Altafini a negative weight is constant or time varying (but regardless of the state). The second feature is the personal "desire unique" (desire to be unique), that is, when getting close to the average personal opinions as the views of the network, the noise associated with the state will continue to increase. Amelkin, who assume personal impact on interpersonal sensitivity depends on the individual's current point of view, then there will be a strong diversity, but it appears only in exceptional circumstances model. Friedkin-Johnsen model shows that because of personal stubbornness of the initial comments (stubborn) (varies depending on intensity) may have a strong diversity. In the current opinion dynamics, Friedkin-Johnsen model has been extensively validated through a small network of quasi-experimental field of laboratory experiments and medium-sized networks.
First, DeGroot Friedkin model considers a range of topics discussed in social networks, each time with DeGroot model for discussion. The major problem is the evolution of individual social forces, social forces individuals to give their views during the discussion component of the evolution of social forces occur before the end of the discussion when a topic and start another topic. How does one social force will change depending on his or her time to discuss the results of the impact. A person's social forces typically increase as he or she discussed the impact of the increase, decrease and reduction.
Secondly, we propose a novel dynamic model views EPO (expressed and private opinion), to study the same expression of personal opinions (expressed opinion) and private difference of opinion (private opinion) is how to produce. Individual in the social environment can hold his or her opinions expressed by different private views. So far, almost all the comments of dynamic models assume that each person holds a view for each topic. EPO model assumes that everyone has their own independent expression and personal opinions, they evolved separately. Personal and private opinion is based on a modified Friedkin-Johnsen model evolved, and his or her express their views due to follow an average of expression (average expressed opinion) (on behalf of groups of standards or specifications) pressure and inconsistent with personal opinions. As used herein, the model reviewed two classics of social psychology: Asch conformity experiments and Prentice and Miller ignorance about the diverse fields of experimental data, which involves acceptance of the Princeton University campus drinking culture.
Finally, the discussion focuses on the direction of the third plurality of logic networks interdependent subject matter. A person is likely to think that the two issues are logically related, therefore because of the belief system of a person's point of view may not be independent of his or her views on another point of the development. The term belief system (belief system) for representing a logical connection between the respective set of themes and topics connected. When a group of people would logically interdependent themes to express their views, a person may be consistent with the internal belief systems group members, or may be inconsistent. Roughly speaking, it is more likely to reach a consensus agreed upon.
2 comments Dynamic Modeling
$ 1_ {n} $: represents an n-dimensional column vectors are all 1
0_ {n} $ $ : represents a n-dimensional column vector are all 0
$ I_ {n} $: represents an n × n unit matrix
$ E_ {i} $: group represented by unit vector, vector addition of the i-th position on the outer rest are 1 0
A non-negative matrix of the matrix, which means that all of the elements $ a_ {ij} \ geq0 $
N matrix A is a matrix, which means that all of the elements $ a_ {ij}> 0 $
For nonnegative matrix A, if $ \ sum_ {j = 1} ^ {n} a_ {ij} \ leq 1 $, i.e. each row elements and less than or equal 1, then A is a random matrix row times; if $ \ sum_ {j = 1} ^ {n } a_ {ij} = 1 $, then A is a random matrix row; if $ \ sum_ {j = 1} ^ {n} a_ {ij} = 1 $ and $ \ sum_ { j = 1} ^ {n} a_ {ji} = 1 $, then A is a doubly stochastic matrix.
Spectral radius: only the matrix have spectral radius, is the spectral radius of the largest absolute eigenvalue of the matrix A. $ \ Rho (A) = max \ left | \ _ {I} the lambda \ right | $
Primitive matrix: if $ \ exists k \ in N $, such that $ A ^ {k}> 0 $, nonnegative matrix A is said to present the original matrix.
2.1 Graph Theory
Graph Theory (Graph Theory) is a branch of mathematics. It Pictured study. FIG graph theory is given by a number of graphic points and the line connecting the two points is constituted such commonly used to describe a specific pattern relationship between certain things, things with point represents, by connecting the two points between the two lines represent the respective object having such a relationship. In this paper by FIG simulated interactive network between a group of individuals.
Related definitions map
$ G \ left [A \ right] = (V, \ varepsilon \ left [A \ right], A) $, where $ V = \ left \ {v_ {1}, v_ {2}, ..., v_ {n} \ right \} $ vertices in the graph is, represents a single individual in the text;
Side $ e_ {ij} = \ left (v_ {i}, v_ {j} \ right) $ at $ A_ ij of {}> 0 $$ time, an ordered set $$ \ varepsilon \ left [A \ right ] $ elements;
If $ \ varepsilon \ left [A \ right] the presence of elemental $ e_ {ii} $, the nodes representing $ v_ {i} $ a loop (Loop) $ in;
$ E_ {ij} $ a $ v_ {j} $ input is $ v_ {i} $ output means $ v_ {j} $ will learn information about $ v_ {i} $ (usually a opinion score);
Typically $ A \ neq A ^ {T} $, it is assumed here that $ g \ left [A \ right] $ is a directed graph;
$v_{i}$的邻居节点为$N_{i}= \left \{ v_{j}\in V:\left ( v_{j}, v_{i}\in \epsilon \left [ A \right ] \right ) \right \}$
If a direct path exists, so that from $ v_ {j} $ reach $ v_ {i} $, called $ v_ {i} $ is reached, the direct path is the set of edges.
Strong communication: In a directed graph $ \ varepsilon \ left [A \ right] $, for all paths between any two nodes is strongly connected FIG.
Digraph: starting point and end point are the same, and in addition to the starting point on the path / repeat no end point is the number of path length in FIG side.
Aperiodic: Any self-loop diagrams are non-periodic.
Lemma 1: If and only if the original matrix A when present, $ \ varepsilon \ left [A \ right] $ is strongly connected, aperiodic.
Lemma 2 (dominant eigenvectors):
For strongly connected graph $ \ varepsilon \ left [A \ right] $ and the random matrix row A, there are strictly positive left and right eigenvector $ u ^ {T} $ and $ 1_ {n} $
A feature value thereof with the $ \ lambda _ {1} = \ rho \ left (A \ right) = 1 $ related, and so orthogonalized U ^ {T} $ 1_ {} =. 1 n- $, $ U ^ and {T} $ $ 1_ {n} $ referred a leading left and right eigenvector.
2.2 DeGroot 和 Friedkin-Johnsen models