Doubly Stochastic Subspace Clustering

11/30/2020
by   Derek Lim, et al.
0

Many state-of-the-art subspace clustering methods follow a two-step process by first constructing an affinity matrix between data points and then applying spectral clustering to this affinity. Most of the research into these methods focuses on the first step of generating the affinity matrix, which often exploits the self-expressive property of linear subspaces, with little consideration typically given to the spectral clustering step that produces the final clustering. Moreover, existing methods obtain the affinity by applying ad-hoc postprocessing steps to the self-expressive representation of the data, and this postprocessing can have a significant impact on the subsequent spectral clustering step. In this work, we propose to unify these two steps by jointly learning both a self-expressive representation of the data and an affinity matrix that is well-normalized for spectral clustering. In the proposed model, we constrain the affinity matrix to be doubly stochastic, which results in a principled method for affinity matrix normalization while also exploiting the known benefits of doubly stochastic normalization in spectral clustering. While our proposed model is non-convex, we give a convex relaxation that is provably equivalent in many regimes; we also develop an efficient approximation to the full model that works well in practice. Experiments show that our method achieves state-of-the-art subspace clustering performance on many common datasets in computer vision.

READ FULL TEXT
research
07/26/2018

Simplex Representation for Subspace Clustering

Spectral clustering based methods have achieved leading performance on s...
research
11/13/2015

Adaptive Affinity Matrix for Unsupervised Metric Learning

Spectral clustering is one of the most popular clustering approaches wit...
research
09/17/2019

Conformal Prediction based Spectral Clustering

Spectral Clustering(SC) is a prominent data clustering technique of rece...
research
03/05/2019

A Novel Efficient Approach with Data-Adaptive Capability for OMP-based Sparse Subspace Clustering

Orthogonal Matching Pursuit (OMP) plays an important role in data scienc...
research
09/09/2009

Kernel Spectral Curvature Clustering (KSCC)

Multi-manifold modeling is increasingly used in segmentation and data re...
research
06/02/2023

Affinity Clustering Framework for Data Debiasing Using Pairwise Distribution Discrepancy

Group imbalance, resulting from inadequate or unrepresentative data coll...
research
07/23/2021

EGGS: Eigen-Gap Guided Search Making Subspace Clustering Easy

The performance of spectral clustering heavily relies on the quality of ...

Please sign up or login with your details

Forgot password? Click here to reset