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Budget Online Learning Algorithm for Least Squares SVM

机译：最小二乘支持向量机的预算在线学习算法

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摘要

Batch-mode least squares support vector machine (LSSVM) is often associated with unbounded number of support vectors (SVs’), making it unsuitable for applications involving large-scale streaming data. Limited-scale LSSVM, which allows efficient updating, seems to be a good solution to tackle this issue. In this paper, to train the limited-scale LSSVM dynamically, we present a budget online LSSVM (BOLSSVM) algorithm. Methodologically, by setting a fixed budget for SVs’, we are able to update the LSSVM model according to the updated SVs’ set dynamically without retraining from scratch. In particular, when a new small chunk of SVs’ substitute for the old ones, the proposed algorithm employs a low rank correction technology and the Sherman–Morrison–Woodbury formula to compute the inverse of saddle point matrix derived from the LSSVM’s Karush-Kuhn-Tucker (KKT) system, which, in turn, updates the LSSVM model efficiently. In this way, the proposed BOLSSVM algorithm is especially useful for online prediction tasks. Another merit of the proposed BOLSSVM is that it can be used for -fold cross validation. Specifically, compared with batch-mode learning methods, the computational complexity of the proposed BOLSSVM method is significantly reduced from to for leave-one-out cross validation with training samples. The experimental results of classification and regression on benchmark data sets and real-world applications show the validity and effectiveness of the proposed BOLSSVM algorithm.
机译：批处理模式最小二乘支持向量机（LSSVM）通常与无穷多个支持向量（SV'）相关联，使其不适用于涉及大规模流数据的应用程序。允许有效更新的有限规模LSSVM似乎是解决此问题的好方法。在本文中，为了动态训练有限规模的LSSVM，我们提出了一种预算在线LSSVM（BOLSSVM）算法。从方法上讲，通过为SV设置固定预算，我们可以根据更新的SV设置动态地更新LSSVM模型，而无需从头开始进行培训。特别是，当新的一小部分SV替代旧SV时，提出的算法采用低秩校正技术和Sherman-Morrison-Woodbury公式来计算从LSSVM的Karush-Kuhn-得出的鞍点矩阵的逆。 Tucker（KKT）系统，进而有效地更新LSSVM模型。这样，提出的BOLSSVM算法对于在线预测任务特别有用。提出的BOLSSVM的另一个优点是它可以用于交叉交叉验证。具体而言，与批处理模式学习方法相比，对于带有训练样本的留一法交叉验证，建议的BOLSSVM方法的计算复杂度从显着降低到。在基准数据集和实际应用中进行分类和回归的实验结果证明了所提出的BOLSSVM算法的有效性和有效性。

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