crime forecasting using boosted ensemble classifiers chung-hsien yu crime forecasting using boosted...
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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
โข Retaining spatiotemporal knowledge by applying multi-clustering to monthly aggregated crime data.
โข Training baseline learners on these clusters obtained from clustering.
โข Adapting a greedy algorithm to find a rule-based ensemble classifier during each boosting round.
โข Pruning the ensemble classifier to prevent it from overfitting. โข 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 .
๐=โ๐
๐ค (๐ ) exp (โ๐ถ๐ ยฟ ๐ฆ ๐)ยฟ
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,
๐ 0= โ{ ๐|๐ฅ ๐โ๐ }
๐ค (๐ )๐+ยฟ= โ{๐|๐ฅ๐โ๐ ๐๐๐ ๐ฆ=1 }
๐ค ( ๐ ) ยฟ๐โ= โ{๐|๐ฅ ๐โ๐ ๐๐๐ ๐ฆ=โ 1}
๐ค (๐ )
๐ 0+๐+ยฟ+๐ โ=1ยฟ
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
Minimum Z Value
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๐๐๐๐ถ๐
=โ๐+ยฟexp (โ๐ถ ๐ )+๐ โexp (๐ถ๐ )=0ยฟ
โ๐โexp (๐ถ๐ )=๐+ยฟ exp (โ๐ถ๐ ) ยฟ
โ ln (๐ โexp (๐ถ๐ ))=ln ยฟยฟโ ln (๐ โ)+๐ถ๐ =ln ยฟยฟโ2๐ถ๐ =lnยฟ ยฟ
โ๐ถ๐ =12ln ยฟยฟ
has the minimum value when
๐๐๐๐ถ๐
2=๐+ยฟ exp (โ๐ถ๐ )+๐โexp (๐ถ๐ )>0ยฟ
Crime Forecasting Using Boosted Ensemble Classifiers Chung-Hsien Yu
BuildChain Function
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๐ 0+๐+ยฟ+๐ โ=1ยฟ
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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๏ฟฝฬ๏ฟฝ=ยฟLoss 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,
๏ฟฝฬ๏ฟฝ๐ ๐ก=0 ๐๐ ๐ฅ โ๐ ๐ก
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 โchainโ the base-line classifiers using one data set. And then, โtrimโ 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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