Unfolding ADMM for Enhanced Subspace Clustering of Hyperspectral Images

TL;DR

The paper addresses hyperspectral image clustering by integrating interpretability with performance through an unfolding of the ADMM-based sparse subspace clustering solver into a neural network. It combines a convolutional auto-encoder for spatial feature extraction, an unfolded ADMM block to compute the self-representation matrix, and a KNN-based structure-preservation module to maintain data geometry, with the objective aligned to the sparse subspace model $min ||X - YC||_F^2 + \lambda ||C||_1$ and diag(C)=0. Key contributions include (i) first application of unfolding to compute the self-representation matrix for subspace clustering, (ii) incorporation of structure priors to preserve data geometry, and (iii) superior empirical results on three standard HSI datasets compared to state-of-the-art methods. The approach enhances interpretability and robustness while delivering competitive clustering performance, indicating practical value for HSIs in applications like land-cover mapping and material identification.

Abstract

Deep subspace clustering methods are now prominent in clustering, typically using fully connected networks and a self-representation loss function. However, these methods often struggle with overfitting and lack interpretability. In this paper, we explore an alternative clustering approach based on deep unfolding. By unfolding iterative optimization methods into neural networks, this approach offers enhanced interpretability and reliability compared to data-driven deep learning methods, and greater adaptability and generalization than model-based approaches. Hence, unfolding has become widely used in inverse imaging problems, such as image restoration, reconstruction, and super-resolution, but has not been sufficiently explored yet in the context of clustering. In this work, we introduce an innovative clustering architecture for hyperspectral images (HSI) by unfolding an iterative solver based on the Alternating Direction Method of Multipliers (ADMM) for sparse subspace clustering. To our knowledge, this is the first attempt to apply unfolding ADMM for computing the self-representation matrix in subspace clustering. Moreover, our approach captures well the structural characteristics of HSI data by employing the K nearest neighbors algorithm as part of a structure preservation module. Experimental evaluation of three established HSI datasets shows clearly the potential of the unfolding approach in HSI clustering and even demonstrates superior performance compared to state-of-the-art techniques.

Figures (2)

• Figure 1: The structure of the proposed method. As shown in the figure, initially, the HSI patches $x_1,x_2,...x_n$ are fed into a deep auto-encoder to extract latent representations $\mathbf{H}$, with a reconstruction loss. This latent representation is then transposed and normalized, resulting in $\Tilde{\mathbf{H}}$, which is fed into an ADMM unfolding network to produce the self-representation matrix $\mathbf{C}$. To improve the quality of $\mathbf{C}$, the loss of self-representation, the loss of structure-preservation, and the sparsity loss are applied.
• Figure 2: Results on PaviaU: (a) Kmeans, (b) FCM, (c) Finch, (d) SC, (e) SpectralNET, (f) DscNet, (g) HyperAE, (h) Ours, (i) Ground truth