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## Ratio Rule Mining from Multiple Data Sources

### Citations

3417 | Principal Component Analysis. - Jolliffe - 2002 |

2803 |
Matrix Computations
- Golub, Loan
- 1982
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Citation Context .... 2000; Jolliffe 2002). It aims at findingsthe geometrical structure of data set by finding out the directions along which the data have maximal variances. Through Singular Value Decomposition (SVD) (=-=Golub and Van 1996-=-), the eigen-system analysis can find an optimal set of directions in the sense 3 of least square reconstruction error. Its computational complexity is O( m ) , where m is the minor value between the ... |

707 |
Foundations of modern probability,
- Kallenberg
- 1997
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Citation Context ...× n data matrix Value at row i, column j of data matrix X The th i item (a column vector) The mean of i leading items 1 i x = j 1x i ∑ = The transpose of x i Inner product of two vectors Expectation (=-=Kallenberg 2002-=-) Identity matrix of order k i j Euclidean norm (Golub and Van 1996) Linear space spanned by φ1, ⋯ , φk (Hamilton 1990) Diagonal matrix whose diagonal elements are λ1, ⋯ , λd Number of data sources 3.... |

463 | Discovery of multiple-level association rules from large databases.
- Han, Fu
- 1995
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Citation Context ...h is one of the most important approaches in data mining (Agrawal, Imielinski et al. 1993; Aumann and Lindell 1999), is one of the major representations for knowledge discovered from large databases (=-=Han and Fu 1995-=-). Association-rule mining from multiple databases has attracted more and more attention of researchers nowadays. To mining the association rules, most prevalent approaches assume that the database tr... |

367 |
Stochastic approximation methods for constrained and unconstrained systems.
- Kushner, Clark
- 1978
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Citation Context ...edure greatly and are not suitable to streaming data problems. Some other works have addressed the problems of robust eigen-system analysis (Liano 1996; Huber 2003) or adaptive eigen-system analysis (=-=Kushner and Clark 1978-=-; Weng, Zhang et al. 2003). However, few of them have considered the robust and adaptive eigen-system at the same time (Li 2004). Moreover, to the best of our knowledge, none of the existing algorithm... |

224 | Evaluating evaluation measure stability.
- Buckley, Voorhees
- 2000
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Citation Context ... the significance of difference between RR and RARR on data generated with noise. It is a method of examining the accuracy measures commonly used in data mining and information retrieval experiments (=-=Buckley and Voorhees 2000-=-). The T-test gives the probability that the difference between the two approaches is caused by chance. It is customary to say that if this probability is less than 0.05 that the difference is 'signif... |

193 | Robust and efficient fuzzy match for online data cleaning. - Chaudhary, Ganjam, et al. - 2003 |

160 | Mining Association Rules between - Agrawal, Imielinski, et al. |

139 | C.P.: A framework for analysis of data quality research. - Wang, Storey, et al. - 1995 |

125 |
On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix.
- Oja
- 1985
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Citation Context ... function Je ( M ) = E{ ρe( d( X , M ))} , the problem that remains is to optimize this function adaptively. We propose to use a stochastic approximation approach (Ljung 1977; Kushner and Clark 1978; =-=Oja and Karhunen 1985-=-) to obtain this solution. Stochastic approximation was proposed by Robbins and Monro (H. and S. 1951). It is often used to optimize an unknown formed objective function. For better comprehension, we ... |

106 | A statistical theory for quantitative association rules.
- Aumann, Lindell
- 2003
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Citation Context ...a-stream mining problems have attracted much attention of researchers recently. Association rule mining, which is one of the most important approaches in data mining (Agrawal, Imielinski et al. 1993; =-=Aumann and Lindell 1999-=-), is one of the major representations for knowledge discovered from large databases (Han and Fu 1995). Association-rule mining from multiple databases has attracted more and more attention of researc... |

83 | Candid covariance-free incremental principal component analysis,” Pattern Analysis and Machine Intelligence, - Weng, Zhang, et al. - 2003 |

72 |
Least mean square error reconstruction principle for self-organizing neural-nets
- Xu
- 1993
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Citation Context ...generates the ratio rules incrementally. We transform the traditional single source ratiorule mining problem into an optimization problem of a non-negative energy function under the square criterion (=-=Xu 1993-=-; Jolliffe 2002). In other words, the ratio rules of a database are the minimal points of a non-negative energy function from our point of view. To make the minimization procedure robust, we use a cla... |

64 |
Agrawal,“Mining Quantitative Association Rules
- Srikant, R
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Citation Context ...nt in the quantities of the items. To capture the quantitative association knowledge, several effective and efficient algorithms for mining quantitative association rules have been proposed recently (=-=Srikant and Agrawal 1996-=-; Korn, Labrinidis et al. 1998). Among them, a new knowledge representation known as ratio rules is presented and proven to be effective (Korn, Labrinidis et al. 1998). A classical example contrasting... |

41 | On incremental and robust subspace learning.
- Li
- 2004
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Citation Context ...iano 1996; Huber 2003) or adaptive eigen-system analysis (Kushner and Clark 1978; Weng, Zhang et al. 2003). However, few of them have considered the robust and adaptive eigen-system at the same time (=-=Li 2004-=-). Moreover, to the best of our knowledge, none of the existing algorithms that address both the robust and adaptive issues provide any in-depth theoretical analysis to verify the robustness and conve... |

19 |
Robust error measure for supervised neural network learning with outliers.
- Liano
- 1996
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Citation Context ...ever, the cleaning procedures can slow down the mining procedure greatly and are not suitable to streaming data problems. Some other works have addressed the problems of robust eigen-system analysis (=-=Liano 1996-=-; Huber 2003) or adaptive eigen-system analysis (Kushner and Clark 1978; Weng, Zhang et al. 2003). However, few of them have considered the robust and adaptive eigen-system at the same time (Li 2004).... |

15 | Database classification for multi-database mining. - Wu, Zhang, et al. - 2005 |

13 | Immc: incremental maximum margin criterion - Yan, Zhang, et al. - 2004 |

5 | Quantifiable Data Mining Using Principal Component Analysis - Faloutsos, Korn, et al. - 1997 |

4 | A stochastic approximation method - H, Monro - 1951 |

3 |
Linear Algebra
- Hamilton
- 1992
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Citation Context ...i x = j 1x i ∑ = The transpose of x i Inner product of two vectors Expectation (Kallenberg 2002) Identity matrix of order k i j Euclidean norm (Golub and Van 1996) Linear space spanned by φ1, ⋯ , φk (=-=Hamilton 1990-=-) Diagonal matrix whose diagonal elements are λ1, ⋯ , λd Number of data sources 3.1 Mining Ratio Rules from Static Single Data Source In general, the problem of ratio-rule mining is as follows. Given ... |

2 |
Analysis of Recusive Stochasitic Algorithms
- Ljung
- 1977
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Citation Context ...gy function under SCF can find similar solutions as the square criterion but it has the additional advantage that it is not sensitive to outliers. We propose to use stochastic approximation approach (=-=Ljung 1977-=-; Kushner and Clark 1978) to minimize the new energy function under the SCF adaptively. We also give the convergence and robustness proofs of this incremental computation procedure. To solve the secon... |

2 |
Robust Principal Analysis by Self-Organizing Rules Based on Statistical Phsics Approach
- Xu
- 1995
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Citation Context ...( i, m , θ ( i)) , i i−1 i i−1 iswhere θ ( i) A( mi−1) θ ( i 1) B( mi −1) ξi = − + , A( ⋅ ) = 0 , B( ⋅ ) = Id , ξi = xi −1 . It can be easily proved that (*1) satisfies A1~A9. From Theorem 1 of work (=-=Xu 1995-=-) we can draw the conclusion that (*1) can converge to the primary eigenvector of c = lim c( i) . Due to the same reason, it is easy to be extended to the case of (*2), i.e. (*2) can converge to the l... |

1 | Ratio Rules: A New Paradigm for Fast - Korn, Labrinidis - 1998 |