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Stratified Sampling for Data
Mining on the Deep Web
Tantan Liu, Fan Wang, Gagan Agrawal
{liut, wangfa ,agrawal}@cse.ohio-state.edu
Dec. 16, 2010
Outline
• Introduction
• Background Knowledge
– Association Rule Mining
– Differential Rule Mining
• Basic Formulation
• Main Technical Approach
– A Greedy Stratification Method
• Experiment Result
• Conclusion
Introduction
• Deep Web
– Query interface vs. backend database
– Input attribute vs. Output attribute
• Data mining on the deep web
– High level summary of the data
– Challenge
• Databases cannot be accessed directly
– Sampling
• Deep web querying is time consuming
– Efficient Sampling Method
Background Knowledge-Association
Rule Mining
• Aim: co-occurrence patterns for items
• Frequent Itemset: Support of the itemset
is larger than a threshold
• Rule:
–
is a frequent itemset
– Confidence
is larger than threshold
Background Knowledge-Differential
Rule Mining
• Aim: differences between two deep web data sources
– E.g. Price of the same hotels on two web sites
• Identical attributes vs. Differential attributes
– Same vs. different values
• Rule:
– X: Frequent itemset composed of identical attributes
– t: differential or target attribute
– D1, D2: data sources
Basic Formulation-Problem
Formulation
• Two step sampling procedure
– A pilot sample
– Randomly drawn from the deep web
– Interesting rules are identified
– Additional sample
‒ Verify identified rules
• Association rules X   Y and differential rules
– Sampling more data records satisfying X
– X only contains input attributes – easy
– X contains output attributes
– Randomly sampling ? not efficient!
– how?
Basic Formulation-Problem
Formulation in Detail
• Considering rules with X  { A  a}
– A single output attribute
A
in the left hand
• Association Rule
– Estimate
or,
p(Y | A  a)
• Differential Rule
– Estimate mean of
• Goal – sampling
– High estimation accuracy
– Low sampling cost
given A=a
Basic Formulation-Stratified Sampling
• Sampling separately from strata
– Heterogeneous across strata & homogenous within
stratum
• Estimating mean value of
–
:
: size, and sampled mean value
• Association Rule Mining
‒ y : whether an itemset is contained in a transaction
‒ If an itemset is contained in a transaction, y  1
• Differential Rule Mining
‒ y :the value of target attribute
Background-Neymann Allocation
• Sample Allocation
– Determining sample size for each stratum
– Fixed sum of sample size
• Neymann Allocation
– Minimizing variance of the stratified sampling
• Problem of application in Deep Web
– The probability of A = a in each stratum is not considered
– Possible large sampling cost
• Sampling cost: number of queries submitted to the deep web
Sampling Cost
• Sampling Cost on the Deep web
– Aim: obtain
data records with
– Sampling Cost:
•
•
: number of data records with
: probability of finding a data record with
• Integrated Cost
– Combing sampling cost and estimation variance
– Two adjustable weights
Main technical Approach –
Stratification Process
• Stratification by a tree on the query space
– A top-down construction manner
– Best split to create child nodes
• Input attribute with the smallest integrated cost
– The splitting process stops
• Integrated cost at each leaf node is small
– Leaf nodes: final strata for sampling
Experiment Result
• Data Set: US census
– The income of US households from 2008 US
Census
– 40,000 data records
– 7 categorical and 2 numerical attributes
• Two Metrics
– Variance of Estimation
– Sampling Cost
Experiment Result-Settings
• Five sampling procedures
– Four different weights for variance and sampling
cost
•
•
•
•
Full_Var:
Var7 :
Var5 :
Var3 :
– Rand : simple random sampling
Experiment Result – Variance of
Estimation
• Association Rule Mining
• Increase of variance of estimation by decreasing
• Random Sampling has higher estimation of variance
Experiment Result – Sampling Cost
• Association Rule Mining
• Decrease of sampling cost by decreasing
• Random Sampling has higher sampling cost
Conclusion
• Stratified sampling for data mining on the deep web
• Considering estimation accuracy and sampling cost
• A tree model for the relation between input attributes
and output attributes
• A greedy stratification to maximally reduce an
integrated cost metric
• Our experiments show that
– Higher sampling accuracy and lower sampling cost
compared with simple random sampling
– Reducing sampling costs by trading-off a fraction of
estimation error
Questions & Comments?