# Multiple Flat Projections for Cross-manifold Clustering

arXiv: https://arxiv.org/abs/2002.06739 · HTML: https://mlsanity.com/paper/2002.06739/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [Fuzzy Discriminant Clustering with Fuzzy Pairwise Constraints](https://mlsanity.com/paper/2104.08546/) (2021)
- [ACEV: Unsupervised Intersecting Manifold Segmentation using Adaptation to Angular Change of Eigenvectors in Intrinsic Dimension](https://mlsanity.com/paper/2410.00930/) (2024)

## Abstract (arXiv)

Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering problems. In our MFPC, the given samples are projected into multiple subspaces to discover the global structures of the implicit manifolds. Thus, the cross-manifold clusters are distinguished from the various projections. Further, our MFPC is extended to nonlinear manifold clustering via kernel tricks to deal with more complex cross-manifold clustering. A series of non-convex matrix optimization problems in MFPC are solved by a proposed recursive algorithm. The synthetic tests show that our MFPC works on the cross-manifold structures well. Moreover, experimental results on the benchmark datasets show the excellent performance of our MFPC compared with some state-of-the-art clustering methods.