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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
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Original Data
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Residential Burglary
911 Calls
Arrest
Foreclosure
Street Robbery
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Aggregated Data
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Data3
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Clusters (k=3)
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Monthly Clusters (k=4)
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Flow Chart
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Algorithm (Part I)
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Algorithm (Part II)
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Confidence Value
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From AdaBoosting (Schapire & Singer 1998) we have
Let and ignore the boosting round .
𝑍=∑𝑖
𝑤 (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
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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
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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=12ln ¿¿
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
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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
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�́�=¿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
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Calculate with ensemble classifier R on the entire data set.
where
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Strong Hypothesis
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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
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Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Q & A
THANK YOU!!
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