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Sequential pattern mining is a crucial but challenging task in many applications, e.g., analyzing the behaviors of data in transactions and discovering frequent patterns in time series data. This task becomes difficult when valuable patterns are locally or implicitly involved in noisy data. In this paper, we propose a method for mining such local patterns from sequences. Using rough set theory, we describe an algorithm for generating decision rules that take into account local patterns for arriving at a particular decision. To apply sequential data to rough set theory, the size of local patterns is specified, allowing a set of sequences to be transformed into a sequential information system. We use the discernibility of decision classes to establish evaluation criteria for the decision rules in the sequential information system.  相似文献
2.
Consider an optimization problem arising from the generalized eigenvalue problem $Ax = \lambda Bx$, where $A,B \in \mathbb{C}^{m \times n}$ and $m > n$. Ito et al. showed that the optimization problem can be solved by utilizing right singular vectors of $C := [B,A]$. In this paper, we focus on computing intervals containing the solution. When some singular values of $C$ are multiple or nearly multiple, we can enclose bases of corresponding invariant subspaces of $C^HC$, where $C^H$ denotes the conjugate transpose of $C$, but cannot enclose the corresponding right singular vectors. The purpose of this paper is to prove that the solution can be obtained even when we utilize the bases instead of the right singular vectors. Based on the proved result, we propose an algorithm for computing the intervals. Numerical results show property of the algorithm.  相似文献
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