# Simultaneous Clustering and Optimization for Evolving Datasets

## TL;DR

This paper introduces a new approach for simultaneous clustering and optimization tailored for evolving datasets, utilizing a variant of ADMM to maintain model accuracy efficiently over time.

## Contribution

It proposes a novel formulation of SCO for dynamic data and develops an ADMM-based method with theoretical guarantees for specific tasks.

## Key findings

- Effective in handling evolving datasets
- Theoretical guarantees for ridge regression and convex clustering
- Empirical results confirm efficiency and accuracy

## Abstract

Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a dataset evolves over time, those existing methods have to update the model frequently to guarantee accuracy; such updating is computationally infeasible. In this paper, we propose a new formulation of SCO to handle evolving datasets. Specifically, we propose a new variant of the alternating direction method of multipliers (ADMM) to solve this problem efficiently. The guarantee of model accuracy is analyzed theoretically for two specific tasks: ridge regression and convex clustering. Extensive empirical studies confirm the effectiveness of our method.