# Structure Learning with Similarity Preserving

arXiv: https://arxiv.org/abs/1912.01197 · HTML: https://mlsanity.com/paper/1912.01197/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

## Built on by (most cited first, 9 of 9)

- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Pseudo-supervised Deep Subspace Clustering](https://mlsanity.com/paper/2104.03531/) (2021)
- [Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering](https://mlsanity.com/paper/2106.09874/) (2021)
- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)
- [A Local Similarity-Preserving Framework for Nonlinear Dimensionality Reduction with Neural Networks](https://mlsanity.com/paper/2103.06383/) (2021)
- [Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms](https://mlsanity.com/paper/2103.10656/) (2021)
- [One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering](https://mlsanity.com/paper/2305.07386/) (2023)
- [Subspace Clustering in Wavelet Packets Domain](https://mlsanity.com/paper/2406.03819/) (2024)

## Abstract (arXiv)

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply being low-rank or sparse. Fully extracting and exploiting hidden structure information in the data is always desirable and favorable. To reveal more underlying effective manifold structure, in this paper, we explicitly model the data relation. Specifically, we propose a structure learning framework that retains the pairwise similarities between the data points. Rather than just trying to reconstruct the original data based on self-expression, we also manage to reconstruct the kernel matrix, which functions as similarity preserving. Consequently, this technique is particularly suitable for the class of learning problems that are sensitive to sample similarity, e.g., clustering and semisupervised classification. To take advantage of representation power of deep neural network, a deep auto-encoder architecture is further designed to implement our model. Extensive experiments on benchmark data sets demonstrate that our proposed framework can consistently and significantly improve performance on both evaluation tasks. We conclude that the quality of structure learning can be enhanced if similarity information is incorporated.