1,053 research outputs found
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
Dual Information Enhanced Multi-view Attributed Graph Clustering
Multi-view attributed graph clustering is an important approach to partition
multi-view data based on the attribute feature and adjacent matrices from
different views. Some attempts have been made in utilizing Graph Neural Network
(GNN), which have achieved promising clustering performance. Despite this, few
of them pay attention to the inherent specific information embedded in multiple
views. Meanwhile, they are incapable of recovering the latent high-level
representation from the low-level ones, greatly limiting the downstream
clustering performance. To fill these gaps, a novel Dual Information enhanced
multi-view Attributed Graph Clustering (DIAGC) method is proposed in this
paper. Specifically, the proposed method introduces the Specific Information
Reconstruction (SIR) module to disentangle the explorations of the consensus
and specific information from multiple views, which enables GCN to capture the
more essential low-level representations. Besides, the Mutual Information
Maximization (MIM) module maximizes the agreement between the latent high-level
representation and low-level ones, and enables the high-level representation to
satisfy the desired clustering structure with the help of the Self-supervised
Clustering (SC) module. Extensive experiments on several real-world benchmarks
demonstrate the effectiveness of the proposed DIAGC method compared with the
state-of-the-art baselines.Comment: 11 pages, 4 figure
Sketch-based subspace clustering of hyperspectral images
Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images
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