2 research outputs found
Graph Convolutional Subspace Clustering: A Robust Subspace Clustering Framework for Hyperspectral Image
Hyperspectral image (HSI) clustering is a challenging task due to the high
complexity of HSI data. Subspace clustering has been proven to be powerful for
exploiting the intrinsic relationship between data points. Despite the
impressive performance in the HSI clustering, traditional subspace clustering
methods often ignore the inherent structural information among data. In this
paper, we revisit the subspace clustering with graph convolution and present a
novel subspace clustering framework called Graph Convolutional Subspace
Clustering (GCSC) for robust HSI clustering. Specifically, the framework
recasts the self-expressiveness property of the data into the non-Euclidean
domain, which results in a more robust graph embedding dictionary. We show that
traditional subspace clustering models are the special forms of our framework
with the Euclidean data. Basing on the framework, we further propose two novel
subspace clustering models by using the Frobenius norm, namely Efficient GCSC
(EGCSC) and Efficient Kernel GCSC (EKGCSC). Both models have a globally optimal
closed-form solution, which makes them easier to implement, train, and apply in
practice. Extensive experiments on three popular HSI datasets demonstrate that
EGCSC and EKGCSC can achieve state-of-the-art clustering performance and
dramatically outperforms many existing methods with significant margins.Comment: This paper is submitted to IEEE TGR
A Critique of Self-Expressive Deep Subspace Clustering
Subspace clustering is an unsupervised clustering technique designed to
cluster data that is supported on a union of linear subspaces, with each
subspace defining a cluster with dimension lower than the ambient space. Many
existing formulations for this problem are based on exploiting the
self-expressive property of linear subspaces, where any point within a subspace
can be represented as linear combination of other points within the subspace.
To extend this approach to data supported on a union of non-linear manifolds,
numerous studies have proposed learning an embedding of the original data using
a neural network which is regularized by a self-expressive loss function on the
data in the embedded space to encourage a union of linear subspaces prior on
the data in the embedded space. Here we show that there are a number of
potential flaws with this approach which have not been adequately addressed in
prior work. In particular, we show the model formulation is often ill-posed in
that it can lead to a degenerate embedding of the data, which need not
correspond to a union of subspaces at all and is poorly suited for clustering.
We validate our theoretical results experimentally and also repeat prior
experiments reported in the literature, where we conclude that a significant
portion of the previously claimed performance benefits can be attributed to an
ad-hoc post processing step rather than the deep subspace clustering model.Comment: Published as a conference paper at the International Conference on
Learning Representations (ICLR) 202