国际数学建模大赛一等奖论文Research on the Location and Time of Serial Criminals.doc

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1、For office use onlyT1_T2_T3_T4_Team Control NumberProblem ChosenBFor office use onlyF1_F2_F3_F4_Research on the Location and Time of Serial CriminalsFebruary 22,2010AbstractTwisted souls and antisocial spirits have resulted in serial murders. In order to prevent such crimes which cause great harm to

2、 public security, the paper has established effective early warning systems and efficient detection programs by using mathematical models so that we can reduce the number of potential victims significantly. Warning preparations: First, the paper makes a statistical analysis of the victims personalit

3、y characterictics (such as physical characteristics, clothing, occupations, etc.), locations and time of the criminal offenses, then the paper has a Principal Factor Analysis of those factors so that we can rule out the obvious or non-intrinsic factors. The principal factors obtained above are the c

4、haracteristics of the crime targets in the serial murders. According to the conclusion, early warnings are given to the vulnerable groups and residents with the same situation, residence and daily schedule so as to strengthen their vigilance. Scheme One: The Establishment of Geographical Profile Bas

5、ed on Time-Series Analysis ModelAccording to the statistics of the locations of serial crimes, the paper predicts the distance between adjacent cases via GPS (Global Positioning System) and establishes a time series analysis model. The paper uses SPSS software to predict the distance between the pos

6、sible locations of the next crime and the past crime scenes. The data of the serial murders committed by Peter Sutcliffe and of the serial robberies in Dallas are used to verify the model: at 95% confidence level, the data obtained tally with the real circumstances.Scheme Two: The Establishment of G

7、eographical Profile Based on the Adaptive Network-Based Fuzzy Inference System (ANFIS) and Fuzzy Matter-Element AnalysisBased on a large number of crime statistics, the paper has established the Adaptive Network-Based Fuzzy Inference System (ANFIS) model and the Subtractive Clustering Initializing F

8、uzzy Inference System (SCIFIS) model. The crime data in Dallas from 1992 to 2007 are taken as the sample to verify the accuracy of the ANFIS model for the prediction of the distribution of the citys high crime areas and the areas where similar criminal cases take place. Then, based on results of neu

9、ral network training, the crime areas obtained are made further screening. The complex element matrix is established by using Fuzzy Matter-Element Analysis. Thus the associated vector is generated through the relationship among the three elements of matter-element. The possible locations of the next

10、 crime are screened through the comparison of correlation. The paper predicts the serial robberies in Dallas and compares the data with the facts using the model reaching 95% confidence level. Therefore, the model is also reasonable and reliable. The prediction of the time of crime: Based on the tim

11、e series formula, the paper predicts the time of the next crime by commensurability of ternary, quaternion and quintuple and the existing time of criminal offenses.The criminal is predicted over time and space based on the geographical Profile generated by the two schemes mentioned and time predicti

12、on method mentioned above. In this way, the case solving rate can be significantly increased, which is also helpful to build a harmonious society. Keywords: Principal Factor Analysis; Time-series Analysis; Adaptive Network- Based Fuzzy Inference System; Fuzzy Matter-Element Analysis; Commensurabilit

13、y;Executive SummaryIn view of the increasing criminal rate in the world, the polices final goal is to increase their case solving rate. Based on this, a model is established under the premise of serial criminal cases, which is used to predict the time and location of the criminal cases. There are tw

14、o schemes in the model, which can be used to predict the geographical Profile and one method to predict the time of the crime. The first scheme can predict the circular region of the next crime by using the Time Series Analysis Model and further reduces the predicted region by using the Principal Fa

15、ctor Analysis method. The second scheme can predict the next possible location of similar cases by using the Adaptive Network-based Fuzzy Inference System. Then a Fuzzy Matter-element Analysis is made of the common characteristics of the victims in the serial crimes so that the prediction region can

16、 be further reduced. While predicting the geographical files, the commensurability of ternary, quaternion and quintuple is used to determine the time of the next criminal offense. In this way, the suspected serial criminal can be determined from the two aspects: time and space. This model has some a

17、dvantages as follows:1. The Simplicity of its Applying Method Scheme One：This paper primarily confirms each accurate location where the crimes have emerged, following that step, it calculates the distance between neighboring places, then puts the figures into statistical software of SPSS, by adoptin

18、g its predicted function of time series to predict the distance between the address of this crime and next one. Meanwhile, it can be identified that the predicted distance will move within a domain, predicting it as an annular region on the map, which can be defined as the potential place where next

19、 crime may happen. By analyzing the environment of the criminal places and each accurately characters of criminals to ensure the mainly attacking targets of the criminals. Furthermore, by carrying out the experienced analysis to the annular region, it can reduce the criminal regions where the next c

20、rime may happen.Scheme Two：Firstly, the researchers compile the ANFIS fuzzy systematic procedure into the Matlab software, and input the times of criminals of its completely criminal category which belong to the studied city, subsequently, it can produce the list of possible happened criminal region

21、s of all kinds of crimes in each cities. Moreover, the researchers compile the subtractive clustering initialization fuzzy deducing ANFIS model into the Matlab software, and input the data of serial crimes and the potential criminal regions got from the above procedure into this software, then it ca

22、n produce the possible happened regions of the criminal rate of the definitely criminals. Therefore, it is necessary to do the checking in the regions where there is highly criminal rates. Assurance of Time Prediction Sorting out the cases happened time according to the months sequence, taking “The

23、Yorkshire Ripper” for example, for the first time, it happens on July 5, 1975, and the number is 7. Adopting it as a standard, it can deduce a figure of each happened region. Once again, the researchers compile the procedures of commensurability of ternary, quaternion and quintuple in the Matlab sof

24、tware, and then to input these date, it can produce the predicted criminal time. (Limited to the month accurately, take January, 1975 as the standard of the model).2. The Highly Reliability The predictive domain in the geographic files of scheme one is made under the circumstance of its SIGNIFICANT

25、TEST level to be 5%, thats to say, the reliability of scheme one is 95%. The scheme two carries out the error testament by using the data of Dallas, thus ,it can obtain the permitting errors difference to be 0.0683, in another word, the reliability is 93.2%. Because it is impossible to enlarge the e

26、rrors difference by combining of the two methods, therefore, the least value of reliability is 93.2%. The time prediction adopts the method of commensurability of ternary, quaternion and quintuple; the acquired predictive time is the largest figure among all of possible criminal time, which proves t

27、o be the possible criminal time.3. The Wide Range of its Application Scheme One testifies the possibility of the model by adopting two kinds of psychological criminal types (the murder is identified as emotional crime, while, the robber is identified as profitable crime). It proves that scheme one i

28、s accurately right to most of the cases.Scheme Two primarily calculates the regions where the similar crimes happened, it can be applied into the prediction of non-serial criminals instead of selection which does not take advantage of serial crimes, and therefore, its application turns to be more wi

29、dely. Because the two methods take applications into consideration from difference aspects and the repeating factors can be neglected, then it is impossible to add the errors difference by combining of the two methods, on the contrary, it may be reduce the difference. When the researchers do the pre

30、dictions, it can take advantage of the commensurability method to increase the probability of arresting criminals, and decrease the losing of property and the labor. This method effectively reduces the waiting time of policemen in the predictive regions.ContentsIntroduction6Analysis6Model Preparatio

31、n:7Assumption8Modeling and Solution81.Appropriate Warning8(1) Theory of the Principle Factor Analysis8(2) Analysis of Yorkshire Ripper Case92. Building a Model to Generate the Geographic Profile10Scheme One: to Establish a Time Series Model10(1) Introduction to Time Series Analysis10(2) Random Time

32、Series Theory11(3) Solving the Cases of the Yorkshire Ripper15(4) The Analysis of the Continuous Robbery in Dallas18Scheme Two: Constructing the Predicting Model of ANFIS19(1)T-S (Takagi-Sugeno) Fuzzy Model19(2) Systematic Structure of ANFIS20(3) The Systematic Algorithm of ANFIS21(4) Analysis of th

33、e Series Criminals Cases in Dallas22(5) Fuzzy Matter-Element Analysis Scheme25(6)Analysis of the Series Criminals Cases in Dallas273. Commensurability Prediction of Real Time Crime29(1) Commensurability Prediction29(2) Model Checking30The Merit and Demerit of the Model33The Direction of Improvement

34、of the Model34References35IntroductionNowadays, because many people have certain distorted spirits in their subconscious minds, thus, it causes many serial crimes in the world. Taking the notorious “Yorkshire Ripper” case for example, it is necessary to construct a kind of quickly and effective Sche

35、me to help the policemen to arrest the criminals. According to the requirements of the local police agency, a Scheme should be developed to aid their investigations of those suspected serial criminals. The solution should make use of at least two different schemes to generate a geographical profile.

36、 It also should develop a technique to combine the results of the different schemes and generate a useful prediction for law enforcement officers. The prediction must provide some kind of estimate or guidance about possible locations of the next crime based on the time and locations of the past crim

37、e scenes. If there are any other evidence in the estimate, the researchers must provide specific details about how the researchers incorporate the extra information. Finally, the researchers will provide an additional executive summary to increase the efficiency of capturing the criminals indeed. An

38、alysisCurrently, the crimes rate is increasing in the world, under the social pressure, family violence and unequal treatment and so on, lead to a phenomenon that some people suffer mental deformities, and take a revenge on others. So they pursue their inner satisfaction by killing, robbery and othe

39、r unlawful criminal acts to release their hatred. In view of this social phenomenon, in order to arrest criminal suspects as soon as possible, the regular criminal psychology analysis only can assist to investigate the criminal means, the crime characteristics and the psychological changes of the cr

40、iminal suspect. The Scheme of, however, generating geographic file can effectively predict the next crime location of the suspect and the crime cycle can be predicted based on time series, this can help the local police arrest the criminals quickly. Two schemes to generate geographic Profile:Scheme

41、One:(1) Based on the respective characteristics of various victims, using the principle factor analysis Scheme to extract the principle factor.(2) Based on the principal factor analysis Scheme, to the extracted principle factor, using time series analysis Scheme to get the distance between the locat

42、ions of this crime and the next one.Scheme Two:Based on the subtractive clustering fuzzy inference system initialization model and the ANFIS-based model of adaptive neural-fuzzy inference system, according to the 18 years of crime data in Dallas, Texas, we can make a reasonable and effective predict

43、ion to its high incidence of crime.Further screening the region received through the previous neural network training and using fuzzy matter-element analysis to sift out the crime location of the next time.Prediction of the Crime Time: Based on the determination of the geography Profile, we can pred

44、ict the crime time of the criminal in order to improve the case solving rate. According to the prediction function of the surability of ternary to the time series, this model predicts the crime time of Peter Sutcliffe.Model Preparation:Peter SucliffePeter Sutcliffe is the son of John and Kathleen Su

45、tcliffe. He was born in the small town of Bingley, just six miles north of Bradford. He is inward-looking, and performed poor at school. At the age of 15, he left school. He once made a living as a grave-digger. His personality and work had a great effect on him as one of the worlds top ten serial k

46、illers. In the 5 years from October 30, 1975 to November 17, 1980 , Peter Sutcliffe killed a total of 13 people, and 10 of them subjected to his malicious attacks. He was arrested until May 22, 1981. Peter Sutcliffe was very cruel when killing. He first pounded the victim in the head with a hammer,

47、and then stabbed a sharp screwdriver into the victims head and abdomen, then conducted fierce beating and kicking. The victim and the persons suffered his malicious attacks are all over the five Central United Kingdom cities: Leeds, Bradford, Huddersfield, Manchester, and Keighley, which involves in

48、 23 cases. Victims Most victims lived in Yorkshire in northern England, near the residence of Peter Sutcliffe. The locations of the crimes are relatively near to each other. All the victims were women, and most of them were prostitutes, rangeing in age from 16 to 47.Status quo of Dallas:According to the data published by the U.S. police authorities, in the cities which the population of more than 1 million lived in, Dallas enjoys the highest crime rate in 2004. It made Dallas the first malicious city in a row of seve