Crime Forecasting Using Boosted

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Nov 20, 2013 (3 years and 7 months ago)

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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.


T
raining 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

A
ggregated
Data

4

3

1

1

1

Crime Forecasting Using Boosted Ensemble Classifiers Chung
-
Hsien

Yu

Monthly
Data

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

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1

1

0

5

0

0

2

6

0

3

3

1

0

0

0

0

0

1

0

4

3

3

2

8

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1

2

2

2

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4

3

0

2

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1

2

3

0

0

0

0

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1

1

0

5

0

0

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6

0

3

3

1

0

0

0

0

0

1

0

4

3

3

2

8

9

4

0

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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

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3

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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
𝒁
𝒕
=


𝒕

𝒆𝒑

𝜶
𝒕



𝒕




Let
𝐶
𝑅
=
𝛼ℎ


and ignore the boosting round

.


=


𝑖
exp
(

𝐶
𝑅
𝑖

𝑖
)


𝐶
𝑅

is defined as the
confidence value
for the rule
𝑅

and
𝐶
𝑅
=
0

if


𝑅
.

Crime Forecasting Using Boosted Ensemble Classifiers Chung
-
Hsien

Yu

Objective Function

12

Therefore,

=


𝑖
𝑖

𝑖

𝑅
+


𝑖
exp
(

𝐶
𝑅
𝑖

𝑖

𝑅

𝑖
)



=

0
+

+
exp

𝐶
𝑅
+


exp
+
𝐶
𝑅



0
=


𝑖
𝑖

𝑖

𝑅


+
=


𝑖
𝑖

𝑖

𝑅

𝑎𝑛𝑑


=
1



=


𝑖
𝑖

𝑖

𝑅

𝑎𝑛𝑑


=

1


0
+

+
+


=
1

Crime Forecasting Using Boosted Ensemble Classifiers Chung
-
Hsien

Yu

Minimum Z Value

13



𝐶
𝑅
=


+
exp

𝐶
𝑅
+


exp
𝐶
𝑅
=
0




exp
𝐶
𝑅
=

+
exp

𝐶
𝑅


ln


exp
𝐶
𝑅
=
ln

+
exp

𝐶
𝑅


ln


+
𝐶
𝑅
=
ln

+

𝐶
𝑅


2
𝐶
𝑅
=
ln

+

ln




𝐶
𝑅
=
1
2
ln

+






has the minimum value

0
+
2

+



when
𝐶
𝑅
=
1
2
ln
(
𝑊
+
𝑊

)



𝐶
𝑅
2
=

+
exp

𝐶
𝑅
+


exp
𝐶
𝑅
>
0

Crime Forecasting Using Boosted Ensemble Classifiers Chung
-
Hsien

Yu

BuildChain

Function

14





=

0
+
2

+



=
1


+

2

+


+



=
1

(

+



)
2


0
+

+
+


=
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



=
1


+



+

+
exp
(

𝐶

𝑅
)
+


exp
(
+
𝐶

𝑅
)

Loss Function:

Minimize



by removing the last classifier from R.

𝐶

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
𝐶

𝑅

with
ensemble classifier
R
on
the entire data set.


𝑡
+
1
𝑖
=

𝑡
𝑖
exp

𝐶

𝑅

 𝑙

ℎ


𝑖

𝑅



where

=


1

𝑖

𝑖

𝑖



ℎ



1

𝑖

𝑖

𝑖



𝑙



Crime Forecasting Using Boosted Ensemble Classifiers Chung
-
Hsien

Yu


Strong Hypothesis

17

𝐻

=
𝑖
(

𝐶

𝑅
𝑡
𝑇
𝑡
=
1
)


At the end of
boosting,
there are
𝑇

chains,
𝑅
1
,
𝑅
2
,

,
𝑅
𝑇


𝐶

𝑅
𝑡
=
0

𝑖




𝑅
𝑡

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