By dividing the original data set into several sub-sets, Multiple Partial Empirical Kernel Learning (MPEKL) constructs multiple kernel matrixes corresponding to the sub-sets, and these kernel matrixes are decomposed to provide the explicit kernel functions. Then, the instances in the original data set are mapped into multiple kernel spaces, which provide better performance than single kernel space. It is known that the instances in different locations and distributions behave differently. Therefore, this paper defines the weight of instance in accordance with the location and distribution of the instances. According to the location, the instances can be categorized into intrinsic instances, boundary instances and noise instances. Generally, the boundary instances, as well as the minority instances in the imbalanced data set, are assigned high weight. Meanwhile, a regularization term, which regulates the classification hyperplane to fit the distribution trend of the class boundary, is constructed by the boundary instances. Then, the weight of instance and the regularization term are introduced into MPEKL to form an algorithm named Multiple Partial Empirical Kernel Learning with Instance Weighting and Boundary Fitting (IBMPEKL). Experiments demonstrate the good performance of IBMPEKL and validate the effectiveness of the instance weighting and boundary fitting.

中文翻译：

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具有实例加权和边界拟合的多部分经验内核学习。

通过将原始数据集划分为几个子集，多部分经验内核学习（MPEKL）构造了与子集相对应的多个内核矩阵，并对这些内核矩阵进行分解以提供显式的内核功能。然后，将原始数据集中的实例映射到多个内核空间，这比单个内核空间提供了更好的性能。众所周知，不同位置和分布的实例的行为不同。因此，本文根据实例的位置和分布来定义实例的权重。根据位置，可以将实例分为固有实例，边界实例和噪声实例。通常，边界实例以及不平衡数据集中的少数实例，被分配高权重。同时，由边界实例构造一个正则化项，该正则化项调节分类超平面以适应类边界的分布趋势。然后，将实例的权重和正则化项引入MPEKL，以形成一种名为带有实例加权和边界拟合的多部分经验核学习的算法（IBMPEKL）。实验证明了IBMPEKL的良好性能，并验证了实例加权和边界拟合的有效性。将实例的权重和正则化项引入MPEKL，以形成名为带有实例加权和边界拟合的多部分经验内核学习（IBMPEKL）的算法。实验证明了IBMPEKL的良好性能，并验证了实例加权和边界拟合的有效性。将实例的权重和正则化项引入MPEKL，以形成名为带有实例加权和边界拟合的多部分经验内核学习（IBMPEKL）的算法。实验证明了IBMPEKL的良好性能，并验证了实例加权和边界拟合的有效性。