Method of multivariate estimation analysis and sampling for data mining

1. A computerized data mining method for determining association rules within N transactions stored in transaction records of a client computer, said method comprising:

computing, by the client computer, a minimum sample size n* of said N transactions, each transaction comprising p different items for characterizing each transaction, p being at least 2, wherein said minimum sample size n* is determined based on a multivariate estimation analysis for achieving precision requirements;

receiving, by a server computer, a sample of n transactions that had been transmitted across a communication network from the client computer to the server computer after the client computer had drawn the n transactions from the N transactions based on the computed n*, wherein n is at least n* and less than N;

computing association rules based on the sample of n transactions according to a methodology for mining of association rules, said computed association rules being an estimation of association rules of said N transactions, said computing association rules being performed by the server computer, said computing association rules based on the sample of n transactions of said N transactions resulting in a reduction in processing time for computing the association rules as compared with computing the association rules based on the N transactions; and

sending, by the server computer, the computed association rules across the communication network to a memory of the client computer for subsequent usage by the client computer, wherein said precision requirements comprise:

a confidence level (1−α) for the minimum sample size n*, wherein α is a specified probability of an error for the minimum sample size n*; and

a relative precision ε k for an item k of a sample, said relative precision ε k defining an acceptable deviation of the support value of item k within the sample of n transactions of said N transactions as compared to the support value of item k within said N transactions, said relative precision ε k being measured relative to the standard deviation of the support value of item k.

2. The method of claim 1 , wherein

n

*

=

χ

(

1

-

α

)

⁢

:

⁢

p

2

⁢

4

⁢

(

∏

k

=

1

p

⁢

1

ɛ

k

2

)

1

p

with χ 1−α:p 2 being the percentile of the χ 2 -distribution with p degrees of freedom.

3. The method of claim 2 , wherein said relative precision ε k =ε is identical for all items k, and wherein

n

*

=

χ

(

1

-

α

)

⁢

:

⁢

p

2

⁢

4

⁢

⁢

1

ɛ

2

.

4. A computerized data mining method for determining association rules within N transactions stored in transaction records of a client computer, said method comprising:

computing, by the client computer, a minimum sample size n* of said N transactions, each transaction comprising different items for characterizing each transaction, wherein said minimum sample size n* is determined based on a univariate estimation analysis for achieving precision requirements for association rules,

wherein said precision requirements comprise a confidence level (1−α) for said minimum sample size n*, wherein α is a specified probability of an error for the minimum sample size n*,

wherein said precision requirements comprise a relative precision δ defining an acceptable deviation of the support value of a certain rule within a sample of n transactions of said N transactions as compared to the support value of said certain rule within said N transactions, said relative precision δ measured relative to the support value of said certain rule, and

wherein said precision requirements comprise a lower boundary p for an expected support value of said certain rule;

receiving, by a server computer, a sample of n transactions that had been transmitted across a communication network from the client computer to the server computer after the client computer had drawn the n transactions from the N transactions based on the computed n*, wherein n is at least n* and less than N;

computing association rules based on the sample of n transactions according to a methodology for mining of association rules, said computed association rules being an estimation of association rules of said N transactions, said computing association rules being performed by the server computer, said computing association rules based on the sample of n transactions of said N transactions resulting in a reduction in processing time for computing the association rules as compared with computing the association rules based on the N transactions; and

sending, by the server computer, the computed association rules across a communication network to a memory of a client computer for subsequent usage by the client computer.

5. The method of claim 4 ,

wherein

n

*

=

u

1

-

α

2

⁢

Np

⁡

(

1

-

p

)

(

N

-

1

)

⁢

δ

2

⁢

p

2

+

u

1

-

α

2

⁢

p

⁡

(

1

-

p

)

 with u 1−α being a percentile of the standard normal distribution.

6. The method of claim 4 , wherein p is a minimum support value (Minsup) used by said methodology for mining of association rules.

7. The method of claim 4 , wherein

n

*

=

u

1

-

α

2

2

⁢

Np

⁡

(

1

-

p

)

(

N

-

1

)

⁢

δ

2

⁢

p

2

+

u

1

-

α

2

2

⁢

p

⁡

(

1

-

p

)

with

u

1

-

α

2

 being a percentile of the standard normal distribution.

8. A computerized data mining method for determining association rules within N transactions stored in transaction records of a client computer, said method comprising:

computing, by the client computer, a minimum sample size n* of said N transactions based on a univariate estimation analysis for achieving precision requirements for association rules, each transaction comprising different items for characterizing each transaction,

wherein said precision requirements comprise a confidence (1−α) for said minimum sample size n*, wherein α is a specified probability of an error for the minimum sample size n*,

wherein said precision requirements comprise an absolute precision d defining an acceptable deviation of the support value of a certain rule within a sample of n transactions of said N transactions as compared to the support value of said certain rule within said N transactions, and

wherein said precision requirements comprise an upper boundary p for an expected support value of said certain rule;

receiving, by a server computer, a sample of n transactions that had been transmitted across a communication network from the client computer to the server computer after the client computer had drawn the n transactions from the N transactions based on the computed n*, wherein n is at least n* and less than N;

computing association rules based on the sample of n transactions according to a methodology for mining of association rules, said computed association rules being an estimation of association rules of said N transactions, said computing association rules being performed by the server computer, said computing association rules based on the sample of n transactions of said N transactions resulting in a reduction in processing time for computing the association rules as compared with computing the association rules based on the N transactions; and

sending, by the server computer, the computed association rules across a communication network to a memory of a client computer for subsequent usage by the client computer.

9. The method of claim 8 ,

wherein

n

*

=

u

1

-

α

2

⁢

p

⁡

(

1

-

p

)

d

2

1

+

1

N

⁢

(

u

1

-

α

2

⁢

p

⁡

(

1

-

p

)

d

2

-

1

)

 with u 1−α being a percentile of the standard normal distribution.

10. The method of claim 8 , wherein p=0.5.

11. The method of claim 8 , wherein

n

*

=

u

1

-

α

2

2

⁢

p

⁡

(

1

-

p

)

d

2

1

+

1

N

⁢

(

u

1

-

α

2

2

⁢

p

⁡

(

1

-

p

)

d

2

-

1

)

with

u

1

-

α

2

 being a percentile of the standard normal distribution.