# Modified online Newton step based on element wise multiplication

## TL;DR

This paper introduces a modified online Newton step method that uses element-wise multiplication to efficiently handle large multi-class datasets, maintaining performance while reducing computational complexity.

## Contribution

It proposes a novel online Newton step variant that stores smaller matrices using element-wise operations, enabling faster computation on large datasets.

## Key findings

- Faster computation due to reduced matrix size
- Mistake rate comparable to existing methods
- Effective on large multi-class datasets

## Abstract

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.