association rule mining to remotely sensed data

8/9/2019 Association rule mining to Remotely sensed data

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Represented By

Madhusmita Sahu

(CSE,950014)

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Contentsy Introductiony Apriori Algorithmy Mining Rules to Imagery data

-Problem definition

-Partitioning quantitative attributes-Finding larger itemsets from imagery data

y New pruning techniques for fast data mining-Technique one-Technique two

y

An example of applying new algorithmy Conclusiony Reference

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REMOTE SENSING

Remote Sensing is the science of acquiring information about the Earth'ssurface without actually being in contact with it.

recording reflected energy

images collected in multiple bands of the electromagnetic spectrum


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Association Rule MiningyAssociations

y Simple rules in categorical data

y

Sample applicationsy Market Basket Analysis

Buys(Milk) Buys(Eggs)

y Transaction Processing

Income(Hi) & Single(Y) Owns(Computer)

y Search for Strong Rulesy Support R(A B) = P(A U B)

y Confidence R(A B) = P(B | A) = P(A B) / P(A)

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The Apriori Algorithm : Pseudo code

y Join Step: Ck is generated by joining Lk-1with itselfy Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a

frequent k-itemsety Pseudo-code:

Ck: Candidate item set of size kLk: frequent item set of size k

L1= { frequent items};For(k= 1; Lk!=; k++ ) do begin

Ck+1= candidates generated from Lk;F

or each transactiont

in dat

abase doIncrement the count of all candidates in Ck+1 that are contained in tLk+1= candidates in Ck+1 with min_support

endReturn kLk;

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MINING ASSOCIATION RULES

FROM IMAGERY DATA

y Problem definition

y Partitioning Quantitative Attributes

y Finding Large Item sets from Imagery Data

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NEW PRUNING TECHNIQUES FOR FAST DATAMINING

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y Technique one

lemma 1: A pixel value can not belong to two differentintervals from the same band.

lemma 2: The combination of k intervals (k>1)from

same band has support zero.


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Ck : Candidate k-item setsLk: Large k-item sets

* : An operation for contactenationCk : Number of itemset in candidate k-item setsRj : Number of intervals in bandj

L k: Number of itemset in large k-item sets

1. According to the apriori algorithm :Apriori use L1*L1 to generate a candidate set ofitemsets C2.

|C2|apriori = |L1 ||L-1| 2

=

2. According to the new algorithm :Assume L 1 = R1 + R2 + ... + Rn.

C2new =R1 (R2 + R3 + ... + Rn) +R2 (R3 + R4 + ... + Rn) + ...+ Rn-2 (Rn-1 + Rn) + Rn-1(Rn)

=

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Contd

The numberof candidate 2-itemsets generated by new algorithm is muchless than by Apriori .

C2prune 1 = C2 apriori - C2 new

=

whe

n n is lar

ge

and Rj is lar

ge,

C2prune 1 be

come

s anex

tre

me

ly lar

ge

number.Forexample : If the imagery data has 8 bands and each band has 16intervals.The numberof pruned candidate 2-itemsets is8 *16(16-1)=960.It sharply reduces the process cost.

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Technique twoy During the process of data mining ,allow user interaction with the

mining engine and use users prior knowledge will help to speed upthe mining algorithms by restricting the search space.

y Consider only one band "bandN" in output. The association rule is the

form: bandl ... band(N-l)bandN.The number of candidate 2-itemset

C2 new =y we are not interested in those itemsets which do not contain bandN.

We will prune those candidate itemset in which none of the interval ischose from bandN.

The number of pruned candidate 2-itemset is

C2 prune 2 =

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contd.

y

Apply new pruning technique described in technique one.

C2 prune 1 =

y The total number of pruned candidate 2-itemset

C2 prune = C2prune 1 + C2 prune 2

=

y

And the remaining steps are the same as Apriori algorithm,

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Contd.

y If there are (N-M) bands in output in the form:

bandl ... bandM band(mM+l ) .... bandN

The total number of pruned candidate 2-itemset

C2prune = C2 prune l+ C 2 prune2

= +

And the remaining steps are the same as Apriori algorithm

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Steps

y Step 1: Choose one of the partition method (equaldepth,uneven depth and discontinous partition) to

determine the intervals.

y Step 2: From large l-item set, apply new pruningtechnique (technique one and technique two) to

generate candidate 2-itemset.

y Step 3: Applying remaining steps of Apriori algorithm

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An example for applying new algorithm (Assume user select equal depth

partitioning.Diameter two for band1 and band4 , Diameter three for band2 and band3

Pixel Band1 Band2 Band3 Band4

1 40 140 200 240

2 50 130 210 250

3 45 135 210 190

4 100 180 50 1005 110 170 40 120

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[0,63] [64,127] [128,191] [192,255]

band1 b11 b12 b13 B14

band4 b41 b42 b43 b44

[0,31] [32,63] [64,95] [96,127

]

[128,

159]

[160,

191]

[192,

225]

[226,

255]

band2 b21 b22 b23 b24 b25 b26 b27 B28

band3 b31 b32 b33 b34 b35 b36 b37 b38


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An example ofpartition the value into intervals.

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Pixel

b11

b12

b13

b14

b21

b25

b26

b28

b31

b32

b37

b38

b41

b42

b43

b44

1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

2 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

3 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0

4 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0

5 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0

y After selecting partition method.Map each value in thistable into intervals.


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Contd.y Apply new pruning techniques forcandidate 2-itemset

generation.Assume the minsup=40% and minconf=60%y Candidate 1-itemset:

{b11,b12,b13,b14,b21,b22,b23,b24,b25,b26,b27,b28,b31,b32,

b33,b34,b35,b36,b37,b38,b41,b42,b43,b44} Large 1-itemset:

{b11(3),b12(2),b25(3),b26(2),b32(2),b37(3),b42(2),b44(2)}Candidate 2-itemsets:

{{b42,b11},{b42,b12},{b42,b25},{b42,b32},{b42,b37},{b44,b11},{b44,b12},{b44,b25},{b44,b26},{b44,b32},{b44,b37}}

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An example contd.

Applying pruning technique one,C2 prune 1 =1+1+1+1=4

Applying pruning technique two,

C2 prune 2 =2 X (2+2)+2 X2 = 12 Total pruned no. of candidate 2-itemsets is =12+4=16 Applying apriori algorithm,the no. of candidate 2-itemset

C2 apriori =(8 X 7)/2 = 28

The percentage of pruning is 57%.so,theexecutionefficiency of mining process is improved. Remaining steps are the same as Apriori algorithm.

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Conclusion

y In this seminar,we defined a new data mining problem ---mining association rules from imagery data and its applicationin precision agriculture.

y Since theefficiency of a mining algorithm is a very importantissue of data mining,we proposed two simple and effectivepruning techniques forcandidate 2-itemset generation.

y by exploiting the nature of the problem and characteristics of

imagery data,we can prune significant numberof unnecessarycandidate itemsets during thevery early phase of miningprocess.

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References

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Jianning Dong,william Perrizo,Qin Ding and Jingkai Zhou,Associationrule mining to Remotely sensed data North Dakota StateUniversity,Fargo,ND 581105

Data Mining: Concepts and Techniques(Hardcover - Mar 2006)

byJiawei han,Micheline kamber. J. Zhang, H. Wynne, M. L. Lee, Image mining: issues, frameworks, and

techniques, inProceedings of 2nd International Workshop on MultimediaData Mining, San Francisco, Aug 2001, pp. 13 20.

J. Li and R. M. Narayanan, "Integrated spectral and spatial information

mining in remote sensing,"IEEE Transactions on Geoscience and RemoteSensing,vol. 42, no. 3, pp. 673 685, March 2004.


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Thank You!!

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association rule mining to remotely sensed data

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