Triangle Lasso for Simultaneous Clustering and Optimization in Graph Datasets

TL;DR

This paper introduces triangle lasso, a robust clustering and optimization method that leverages neighborhood information to improve accuracy in noisy and incomplete graph datasets, outperforming existing methods.

Contribution

It proposes a novel triangle lasso approach that uses common neighbors for similarity, along with efficient algorithms for accurate solutions, enhancing robustness against imperfect data.

Findings

Triangle lasso outperforms state-of-the-art methods in noisy data scenarios.

The dual method achieves high accuracy with low additional computational cost.

The approach demonstrates robustness and improved performance in practical data analysis tasks.

Abstract

Recently, network lasso has drawn many attentions due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values etc), and yields sub-optimal solutions. The reason is that it finds the similar instances according to their features directly, which is usually impacted by the imperfect data, and thus returns sub-optimal results. In this paper, we propose triangle lasso to avoid its disadvantage. Triangle lasso finds the similar instances according to their neighbours. If two instances have many common neighbours, they tend to become similar. Although some instances are profiled by the imperfect data, it is still able to find the similar counterparts. Furthermore, we develop an efficient algorithm based on Alternating Direction Method of Multipliers (ADMM) to obtain a moderately accurate solution. In addition, we present a dual method to obtain the accurate solution with the low additional time consumption. We demonstrate through extensive numerical experiments that triangle lasso is robust to the imperfect data. It usually yields a better performance than the state-of-the-art method when performing data analysis tasks in practical scenarios.