1. Result of N Categorical Variable Regional Co-location Mining
November 11, 2008
Result of N Categorical Variable Regional Co-location Mining
Dataset, 4 class lattices:
0.3,0.4,A,B ,C ,D
0.2,0.3,A ,B,C,D
AsP
AsFeSe
AsSeFeF
AsF

2. Regional Co-Location Mining Framework for q Binary Variables
Example: Co-location set CS={A,B,C};
CoLoc-interestingness({A,B,C},r)= ((r,A) 1)((r,B) 1)((r,C) 1)
Dataset O
Remark:
Strength is
computed by
comparing r
with the whole
Dataset O. r
Remarks:
Have to iterate over all possible co-location sets
Interestingness of the region is the interestingness of the maximum valued co-location set

3. Region Interestingness
Region interestingness is assessed by computing the most prevalent pattern:
Region interestingness solely depends on the most interesting co-location set for the region.

4. Example of a Result
All experiments: P(B) = (AsB or AsB) and |B|<5.
Experiment 1
 = 1.3, …
Exp. No.
Top 5 Region s
Region Size
Region Reward
Maximum Valued Pattern in theRegion
Average Product for maximum valued pattern
Exp. 1 1 23
AsMoVF- 2 40
AsMoV 3 11
AsMoVSO42- 4 36
AsBCl-TDS 5 7
AsMoCl-TDS

5. Co-Location Mining Framework for q Binary Class Variables Version1
O – dataset
rO – a region
oO – object in the dataset O
CS= {C1,…,Cr} – set of binary class variables that form base patterns; oCo.C=true
th – class multiplier interestingness threshold, default-value 1
  [0, ∞) – form parameter, default value 1
CCS be a single class variable
BCS – a co-location set
P(B) is a predicate over B that restricts the set of co-location sets considered; e.g. P(B)=|B|<5 or P(B)=AsB (“only look for patterns involving high arsenic”)
(r,C)=(|{or|oC}|)/|r|)/(|{oO|oC}|/|O|) – C’s probability multiplier in r; high interestingness is associated with high multipliers
z(C,r)= If (r,C)>th then ((r,C)-th) else 0 – normalized interestingness for C in r
k(B,r)= CBz(C,r) – normalized interestingness of co-location set B in r
i(r)=maxBS & |B|>1 and P(B)k(B,r) – region interestingness; maximum normalized interestingness observed for subsets BCS constrained by P
Reward(r)= i(r)*|r|b

6. Co-Location Mining Framework for q Binary Class Variables Version2
O – dataset
rO – a region
oO – object in the dataset O
CS= {C1,…,Cr} – set of binary class variables that form base patterns; oCo.C=true
th1 – co-location set interestingness threshold
  [0, ∞) – form parameter, default value 1
CCS be a single class variable
BCS – a co-location set
P(B) is a predicate over B that restricts the set of co-location sets considered; e.g. P(B)=|B|<5 or P(B)=AsB (“only look for patterns involving high arsenic”)
(r,C)=(|{or|oC}|)/|r|)/(|{oO|oC}|/|O|) – C’s probability multiplier in r; high interestingness is associated with high multipliers
k(B,r)= CB (r,C) –interestingness of co-location set B in r
i’(r)=maxBS & |B|>1 and P(B)k(B,r) – region interestingness; maximum interestingness observed for subsets BCS constrained by P
i(r)=IF i’(r)> th THEN (i’(r)-th) ELSE 0 –normalized region interestingness (th>=1;  form parameter)
Reward(r)= i(r)*|r|b

7. Datasets and Program Interface
Discretize the z-score normalized variable as follows:
z(A)1: A
-1 z(A) 1: A
Otherwise: A
The transformed dataset therefore have the form: <longitude, latitude, <class-variable>+ )
Limit Co-location sets we are looking for in experiments to “” and “” class variables, to make it comparable to the continuous approach
Limit Co-location Sets to sizes 2-4 in the experiments!
Possibly conduct experiments with large sets using a single seed pattern; e.g. D
Therefore the program inputs of the categorical regional collocation mining versions should include:
k’ ---the maximum set size considered
The seed pattern, e.g. B, if we have a seed pattern; if we do not have a seed pattern is given all sets of sizes 2,…,k’ will be considered
Pattern list considered