Crime Forecasting Using Boosted Ensemble Classifiers
19
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu Crime Forecasting Using Boosted Ensemble Classifiers Department of Computer Science University of Massachusetts Boston 2012 GRADUATE STUDENTS SYMPOSIUM Present by: Chung-Hsien Yu Advisor: Prof. Wei Ding
description
Crime Forecasting Using Boosted Ensemble Classifiers. Present by: Chung- Hsien Yu. Advisor: Prof. Wei Ding. Department of Computer Science University of Massachusetts Boston . 2012 GRADUATE STUDENTS SYMPOSIUM. Abstract. - PowerPoint PPT Presentation
Transcript of Crime Forecasting Using Boosted Ensemble Classifiers
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Crime Forecasting Using Boosted Ensemble Classifiers
Department of Computer Science University of Massachusetts Boston
2012 GRADUATE STUDENTS SYMPOSIUM
Present by: Chung-Hsien Yu
Advisor: Prof. Wei Ding
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
• Retaining spatiotemporal knowledge by applying multi-clustering to monthly aggregated crime data.
• Training baseline learners on these clusters obtained from clustering.
• Adapting a greedy algorithm to find a rule-based ensemble classifier during each boosting round.
• Pruning the ensemble classifier to prevent it from overfitting. • Constructing a strong hypothesis based on these ensemble
classifiers obtained from each round.
Abstract
2
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Original Data
3
Residential Burglary
911 Calls
Arrest
Foreclosure
Street Robbery
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Aggregated Data
4
3
1
1
1
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Data3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
3
1
1
0
5
0
0
2
6
0
3
3
1
0
0
0
0
0
1
0
4
3
3
2
8
9
4
0
6
4
5
1
2
2
2
5
4
3
0
2
3
1
2
3
0
0
0
0
2
6
1
0
5
6
6
2
7
5
3
3
1
3
4
4
3
1
4
0
4
3
3
2
8
9
4
0
6
4
5
1
2
3
2
3
0
3
0
2
0
1
2
5
0
0
0
0
5
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Clusters (k=3)
6
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Clusters (k=4)
7
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Flow Chart
8
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Algorithm (Part I)
9
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Algorithm (Part II)
10
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Confidence Value
11
From AdaBoosting (Schapire & Singer 1998) we have
Let and ignore the boosting round .
𝑍=∑𝑖𝑤 (𝑖 ) exp (−𝐶𝑅¿ 𝑦 𝑖)¿
is defined as the confidence value for the rule and if .
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Objective Function
12
Therefore,
𝑊 0= ∑{ 𝑖|𝑥 𝑖∉𝑅 }
𝑤 (𝑖 )𝑊+¿= ∑{𝑖|𝑥𝑖∈𝑅 𝑎𝑛𝑑 𝑦=1 }
𝑤 ( 𝑖 ) ¿𝑊−= ∑{𝑖|𝑥 𝑖∈𝑅𝑎𝑛𝑑 𝑦=− 1}
𝑤 (𝑖 )
𝑊 0+𝑊+¿+𝑊 −=1¿
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Minimum Z Value
13
𝑑𝑍𝑑𝐶𝑅
=−𝑊+¿exp (−𝐶 𝑅 )+𝑊 −exp (𝐶𝑅 )=0¿
→𝑊−exp (𝐶𝑅 )=𝑊+¿ exp (−𝐶𝑅 ) ¿
→ ln (𝑊 −exp (𝐶𝑅 ))=ln ¿¿→ ln (𝑊 −)+𝐶𝑅= ln ¿¿→2𝐶𝑅= ln¿ ¿
→𝐶𝑅=12 ln ¿¿
has the minimum value when
𝑑𝑍𝑑𝐶𝑅
2=𝑊+¿ exp (−𝐶𝑅 )+𝑊 −exp (𝐶𝑅 )>0¿
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
BuildChain Function
14
𝑊 0+𝑊+¿+𝑊 −=1¿
Repeatedly adding a classifier to R until it maximizes . This will minimize as well.
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
PruneChain Function
15
�́�=¿Loss Function:
Minimize by removing the last classifier from R.
is obtained from GrowSet. are obtained from applying R to PruneSet
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Update Weights
16
Calculate with ensemble classifier R on the entire data set.
where
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Strong Hypothesis
17
At the end of boosting, there are chains,
�̂�𝑅𝑡=0 𝑖𝑓 𝑥 ∉𝑅𝑡
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
1. The grid cells with the similar crime counts clustered together also are close to each other on the map geographically. Besides, the high-crime-rate area and low-crime-rate area are separated with cluster.
2. The original data set is randomly divided into two subsets each round. The greedy weak-learn algorithm adapts confidence-rate evaluation to “chain” the base-line classifiers using one data set. And then, “trim” the chain using the other data set.
3. The strong hypothesis is easy to calculate.
SUMMARY
18
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Q & A
THANK YOU!!
19
![Chapter 45 ENSEMBLE METHODS FOR CLASSIFIERSLior-Rokach].pdf · Chapter 45 ENSEMBLE METHODS FOR CLASSIFIERS Lior Rokach Department of Industrial Engineering Tel-Aviv University liorr@eng.tau.ac.il](https://static.fdocuments.us/doc/165x107/5e125350bb05d1280c25fffd/chapter-45-ensemble-methods-for-classifiers-lior-rokachpdf-chapter-45-ensemble.jpg)
![Ensemble Boosted Trees with Synthetic Features Generation ...tomczak/PDF/[MZSTJT].pdf · Ensemble Boosted Trees with Synthetic Features Generation in Application to Bankruptcy Prediction](https://static.fdocuments.us/doc/165x107/5ec229441ed38d58ed33ab70/ensemble-boosted-trees-with-synthetic-features-generation-tomczakpdfmzstjtpdf.jpg)