The second order method as Newton Step is a suitable technique in Online Learning to guarantee regret bound. The large data is a challenge in Newton method to store second order matrices as hessian. In this paper, we have proposed an modified online Newton step that store first and second order matrices of dimension m (classes) by d (features). we have used element wise arithmetic operation to retain matrices size same. The modified second order matrix size results in faster computations. Also, the mistake rate is at par with respect to popular methods in literature. The experiments outcome indicate that proposed method could be helpful to handle large multi class datasets in common desktop machines using second order method as Newton step.

中文翻译：

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基于元素乘法的修改在线牛顿步骤

二阶方法作为牛顿步骤是在线学习中的一种合适的技术，以保证后悔边界。大数据是牛顿方法中将二阶矩阵存储为 Hessian 的挑战。在本文中，我们提出了一种改进的在线牛顿步骤，用于存储维度为 m（类）乘以 d（特征）的一阶和二阶矩阵。我们使用了逐元素算术运算来保持矩阵大小相同。修改后的二阶矩阵大小导致更快的计算。此外，错误率与文献中的流行方法相当。实验结果表明，所提出的方法可以帮助使用二阶方法作为牛顿步骤处理普通台式机中的大型多类数据集。