# Learning Sign-Constrained Support Vector Machines

arXiv: https://arxiv.org/abs/2101.01473 · HTML: https://mlsanity.com/paper/2101.01473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 44 references that are in the map.
- First posted on arXiv 5 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)

## Built on by (most cited first, 1 of 1)

- [Linearly Convergent Mixup Learning](https://mlsanity.com/paper/2501.07794/) (2025)

## Abstract (arXiv)

Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of the weight coefficients in learning the linear support vector machine, and develop two optimization algorithms for minimizing the empirical risk under the sign constraints. One of the two algorithms is based on the projected gradient method, in which each iteration of the projected gradient method takes O(nd) computational cost and the sublinear convergence of the objective error is guaranteed. The second algorithm is based on the Frank-Wolfe method that also converges sublinearly and possesses a clear termination criterion. We show that each iteration of the Frank-Wolfe also requires O(nd) cost. Furthermore, we derive the explicit expression for the minimal iteration number to ensure an ε-accurate solution by analyzing the curvature of the objective function. Finally, we empirically demonstrate that the sign constraints are a promising technique when similarities to the training examples compose the feature vector.