# Triangle Lasso for Simultaneous Clustering and Optimization in Graph Datasets

arXiv: https://arxiv.org/abs/1808.06556 · HTML: https://mlsanity.com/paper/1808.06556/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2018.

## Built on by (most cited first, 8 of 8)

- [RayMVSNet++: Learning Ray-based 1D Implicit Fields for Accurate Multi-View Stereo](https://mlsanity.com/paper/2307.10233/) (2023)
- [Towards Target-Driven Visual Navigation in Indoor Scenes via Generative Imitation Learning](https://mlsanity.com/paper/2009.14509/) (2020)
- [Learning Fine-Grained Segmentation of 3D Shapes without Part Labels](https://mlsanity.com/paper/2103.13030/) (2021)
- [ARM3D: Attention-based relation module for indoor 3D object detection](https://mlsanity.com/paper/2202.09715/) (2022)
- [DisARM: Displacement Aware Relation Module for 3D Detection](https://mlsanity.com/paper/2203.01152/) (2022)
- [STEdge: Self-training Edge Detection with Multi-layer Teaching and Regularization](https://mlsanity.com/paper/2201.05121/) (2022)
- [3DRM:Pair-wise relation module for 3D object detection](https://mlsanity.com/paper/2202.09721/) (2022)
- [RayMVSNet: Learning Ray-based 1D Implicit Fields for Accurate Multi-View Stereo](https://mlsanity.com/paper/2204.01320/) (2022)

## Abstract (arXiv)

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.