基于CUR矩阵分解的多核学习正则化路径近似算法
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东北石油大学计算机与信息技术学院, 大庆, 163318

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国家自然科学基金(51774090, 51574085)资助项目;黑龙江省自然科学基金(E2016008, F2016002)资助项目。


Multiple Kernel Learning Regularization Path Approximation Algorithm Based on CUR Matrix Decomposition
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School of Computer and Information Technology, Northeast Petroleum University, Daqing, 163318, China

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    摘要:

    多核学习在解决不规则、大规模数据问题时表现出良好的优越性。正则化路径是一种多次求解多核学习,选择最优模型的措施。针对多核学习正则化路径算法处理大规模数据时,核矩阵规模较大,计算代价高,影响优化模型效率的问题,提出一种基于CUR矩阵分解的多核学习正则化路径近似算法(Multiple kernel learning regularization path approximation algorithm with CUR, MKLRPCUR)。该算法首先采用CUR算法获得核矩阵的低秩近似矩阵的多个分解矩阵,然后在求解过程中利用低维的分解矩阵相乘替代核矩阵,调整相关矩阵计算的顺序,从而简化算法中核矩阵和拉格朗日乘子向量乘积的计算。 MKLRPCUR算法降低了矩阵的计算规模,优化了矩阵计算,提高了精确算法的计算效率。 从理论上分析低秩近似矩阵的相对误差和算法的时间复杂度,验证了近似算法的合理性。同时,在UCI数据集、ORL和COIL图像数据库上的实验结果表明,本文提出的近似算法不仅保证了学习的准确率,并且降低了算法的运行时间,提高了模型的效率。

    Abstract:

    Multiple kernel learning shows good superiority in solving irregular and large-scale data problems. Regularization path is a method to select the optimal model by solving the multiple kernel learning multiple times.Aiming at the problems that the kernel matrix size is large, the computational cost is high and the efficiency of the optimization model is affected when multiple kernel learning regularization path processes large-scale data, a multiple kernel learning regularization path approximation algorithm based on CUR matrix decomposition is proposed, which is named MKLRPCUR.This algorithm firstly adopts CUR algorithm to obtain multiple decomposition matrices of low-rank opproximation matrix of kernel matrix.Then, in the solution process, the low-dimensional decomposition matrices are used to replace the kernel matrix, and the order of the correlation matrix calculation is adjusted, thereby simplifying the calculation of the kernel matrix and the Lagrange multiplier vector product.MKLRPCUR algorithm reduces the calculation scale of matrix, optimizes matrix calculation, and improves the calculation efficiency of exact algorithm.The relative error of the low-rank approximation matrix and the time complexity of the algorithm are theoretically analyzed to verify the rationality of the approximation algorithm.At the same time, the experimental results on the UCI dataset, ORL and COIL image databases show that the proposed approximate algorithm not only ensures the accuracy of learning, but also reduces the running time of the algorithm and improves the efficiency of the model.

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王梅,李董,薛成龙.基于CUR矩阵分解的多核学习正则化路径近似算法[J].数据采集与处理,2020,35(3):381-391

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  • 收稿日期:2019-10-28
  • 最后修改日期:2019-12-12
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  • 在线发布日期: 2020-05-25