# A Dimension Reduction Technique for Large-scale Structured Sparse Optimization Problems with Application to Convex Clustering

arXiv: https://arxiv.org/abs/2108.07462 · HTML: https://mlsanity.com/paper/2108.07462/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2021.

## Built on by (most cited first, 3 of 3)

- [Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees](https://mlsanity.com/paper/2303.16841/) (2023)
- [Adaptive Self-supervised Robust Clustering for Unstructured Data with Unknown Cluster Number](https://mlsanity.com/paper/2407.20119/) (2024)
- [Bilevel Models for Adversarial Learning and A Case Study](https://mlsanity.com/paper/2510.25121/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with intrinsic structured sparsity. We establish the finite convergence property of the AS technique and the EAS technique with inexact solutions of the reduced subproblems. As an important application, we apply the AS technique and the EAS technique on the convex clustering model, which could accelerate the state-of-the-art algorithm SSNAL by more than 7 times and the algorithm ADMM by more than 14 times.