美国数学建模论文.docx

1、美国数学建模论文Modeling for Crime BustingAbstract: In the mathematical modeling, we discussed how to solve the problem of crime busting. First, we established a mathematical model to simulate the network of the stuff in the company, by calculating the weight of each edge to calculate the probability of eac

2、h node. This model with a strong ability to adapt, can be easily applied to other network structure. Then we will apply the semantic analysis and text analysis in our model to make the model more accurate. Finally, we apply the model to the cell network relations of infectionAiming at the question o

3、ne, we consider that the network of the company is single-line and the property of each edge is different. So, we classify all the information flow according to the type of the message and the type of the two nodes in each edge. Then, we calculate the weight of each type of information flow. And the

4、n, we get the probability of each node, that is the probability of the stuff.Aiming at the question two it is the same as the model in question one. There are two conditions changed in the question two. Homologous, we change the conditions in question one with the same model, then we get the probabi

5、lity of the stuff in question two.Aiming at the question three, We need to use semantic analysis and text analysis to amend the model established. For text analysis, we adopt the method of TF-IDF. We calculate the frequency of all the words in the topics, then we get the keyword about the conspiracy

6、. Later we classify the topics more meticulously to make the weight of each edge accurate.Aiming at the question four, we need to apply the model into a broader network type. In this problem, we assume that a simple cell infection of network structure. Then we calculate the probability of cell infec

7、tion by using the model and the results prove that the model can be used in other network structure.Key words: Crime Network AHP TF-IDF Content1 Introduction1.1 Background and Analysis of the Problems1.2 Method of the Analysis1.3 Assumption2 Model Approach2.1 How to judge ones suspicion2.2 The Crime

8、 Network Circle2.3 Set Word Network Analysis Model 2.3.1 Define some Parameters2.3.2 The CNC node position suspicious degree model 2.4 The Weight Vector - An AHP Solution 2.4.1 Set up a Structure Model2.4.2 Figure out Judging Matrix and Eigenvector 2.5 Conclusion 2.5.1 The Final Suspicion Order of 8

9、3Nodes 3 Context Analysis3.1 Basic Assumptions3.2 TF-IDF Model 3.3 Conclusion 4.The model in cell infection network 5. Sensitivity Analysis and Improvements5.1 Sensitivity Analysis5.2 Improvements6. Model Evaluation6.1 Strengths6.2 Weaknesses7. References1. Introduction1.1 Background and Analysis of

10、 the ProblemsA conspiracy network is embedded in a network of employees of a company, with edge representing a message sent from one employee (node) to another and categorized by topics. Our organization, ICM, has already known some information. Those investigators think that information will help t

11、hem to find out the most-possible people selected of the ambiguous conspirators and unknown leader. The goal of molding is to find out the most-possible conspirators in the office. According to information, 7 people have already been confirmed to be conspirators, 15 topics (3 of which have been deem

12、ed to be suspicious), and 400 message links ,our goal is to make sure who are conspiracy, and who are the leader, prioritize the 83 nodes by likelihood of being apart of the conspiracy and determine a discriminate line separating conspirators from non-conspirators If some already known information c

13、hanged, we have more information, what changes will happen with the result When dealing with more information or more complicated circumstance, the model must can be applied to any condition1.2 Method of the Analysis As investigators, we have known about 83 nodes, 400 links over 21000 words of messa

14、ge traffic, 15 topics (3 have been deemed to be suspicious), 7 known conspirators and 8 known non-conspirators. To make sure who are the conspirators, there are too many factors to take into consideration, so we formulate a model to account for the importance of every factors, and these factors woul

15、d affect the determination of who are conspirators.1.3 Assumptions Conspirators tend not to talk frequently with each other about irrelevant topics. The leader of the conspiracy tries to minimize risk by restricting direct contacts. People can freely talk to each other, and without the limit of dist

16、ance. Non-conspirators do not have the idea that there are conspirators in their company, and conspirators will not add more people.2. Model Approach2.1 How to judge ones suspicion As a conspirator, he or she must have some words or action make people feel strange and suspicious. As a group of consp

17、irators, they connect each other through words, so if someone refers to much information about suspicious topics, the possibility that he is a conspirator is high. In addition to this condition, talking too much with conspirators is also making someone more suspicious. In all, we conclude some point

18、s below to discriminate who are more likely to be conspirator: The frequency of sending and receiving suspicious topics The frequency of contacting with conspirators The frequency of talking with the same people and about the same topic(because between conspirators ,they maybe contact with secret wo

19、rds) 2.2 The Crime Network Circle We create a model called the crime network circle (CNC), the model is created on the base of analysis about network, the CNC model has three areas: A (the outside ring), B (the middle ring) and C (the inside ring), A is the area that represents people who are innoce

20、nt, B is the area that represents people who are suspects, and C is the area that represents people who are conspirators. To be frank, we draw a 10-people social network CNC picture.2.3 Set Word Network Analysis Model 2.3.1 Define some Parameters In the CNC model, we use a dot to represent a person,

21、 we define every dot is a node. The words between two people is a line in the picture, we define the line is a degree, one person talks to another one, the degree is an out-degree; likely, if someone receive a message from others, the degree is an in-degree. Whats more, another important factor is t

22、hat whether the topic is a suspicious topic. So a degree can be represented in the form of a matrix (x, y, z). The meaning of x y and z is in the table below:Table 2xThe identity of speaker, and the position of node in the CNC picture, x=a, b, cyThe identity of listener, and the position of node in

23、the CAN picture, y=a, b, czThe topic. If the topic is a suspicious one, z=1; otherwise, z=0According to what we have defined, we can give two weight vector matrix: and . is the case that topics are not suspicious, and is the case that topics are suspicious. 2.3.2 The CNC node position suspicious deg

24、ree model According to the assumptions, at every junction we have Where is the weight vector of out-degree, is the weight vector of in-degree. We define =0.7, =0.3. is the out-degree of node from area x to area y in CNC picture; familiarly, means the in-degree of node from area y to area x in CNC pi

25、cture. In the equation, represents product of the out-degree of dote i and the weight vector of out-degree area, it reflects the degree of contribution that node s out-degree give suspect to node .At the same way, represents product of the in-degree of node and the weight vector of in-degree area, i

26、t reflects the degree of contribution that node s in-degree give suspect to node . These two indexes comprehensively consider the suspect degree by in-degree and out-degree of node , which makes the model more reasonable. If we calculate someones is very high, then this person has a higher possibili

27、ty to be a conspirator.2.4 The Weight Vector - An AHP Solution 2.4.1 Set up a Structure Model We use AHP mainly because this question does not have clear and specific data that we cant do some quantification analysis, in order to having more accurate answer, we convert quantification judgment into c

28、omparing the importance of every factor, avoiding having subjective and wrong judgments. The first stage is to set up a structure model .The model are below: Structure 3The judgment of a conspirator ATarget layer Case 18 C 18Case 3 C 3 Case 2 C 2Case 1 C 1Criterion Layer . The Suspicion of Each Indi

29、vidual P Program layer To demonstrate better the different cases, we present in Table 4 below:Table 4SpeakerListenerTopicsInnocentInnocentSuspiciousInnocentInnocentNot SuspiciousInnocentSuspectSuspiciousInnocentSuspectNot SuspiciousInnocentConspiratorSuspiciousInnocentConspiratorNot SuspiciousSuspec

30、tInnocentSuspiciousSuspectInnocentNot SuspiciousSuspectSuspectSuspiciousSuspectSuspectNot SuspiciousSuspectConspiratorSuspiciousSuspectConspiratorNot SuspiciousConspiratorInnocentSuspiciousConspiratorInnocentNot SuspiciousConspiratorSuspectSuspiciousConspiratorSuspectNot SuspiciousConspiratorConspir

31、atorSuspiciousConspiratorConspiratorNot Suspicious2.4.2 Figure out Judging Matrix and EigenvectorTo give judging matrix A-C, we first define the meaning of the value of A about this question: A=1: A is as important as A(suspicious); A=3: A is a little important than A; A=5: A is much important than A; A=7: A is extremely important than A; A=2,4,6,8: the importance of A and A is between adjacent two number above. We consider that people refer more suspicious topics and talk frequently with c