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A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
Graph property detection aims to determine whether a graph exhibits certain structural properties, such as being Hamiltonian. Recently, learning-based approaches have shown great promise by leveraging data-driven models to detect graph…
This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak,…
The analysis of the modular structure of networks is a major challenge in complex networks theory. The validity of the modular structure obtained is essential to confront the problem of the topology-functionality relationship. Recently,…
We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
We analyse uniformly random proper $k$-colourings of sparse graphs with maximum degree $\Delta$ in the regime $\Delta < k\ln k $. This regime corresponds to the lower side of the shattering threshold for random graph colouring, a…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
We show that unitary representations of simply connected, semisimple algebraic groups over local fields of characteristic zero obey a spectral gap absorption principle: that is, that spectral gap is preserved under tensor products. We do…
This paper investigates a general framework to discover categories of unlabeled scene images according to their appearances (i.e., textures and structures). We jointly solve the two coupled tasks in an unsupervised manner: (i) classifying…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…
This work presents an unsupervised and semi-automatic image segmentation approach where we formulate the segmentation as a inference problem based on unary and pairwise assignment probabilities computed using low-level image cues. The…
For graphs $G$ and $H$, let $G\to (H,H)$ signify that any red/blue edge coloring of $G$ contains a monochromatic $H$ as a subgraph, and $\mathcal{H}(\Delta,n)=\{H:|V(H)|=n,\Delta(H)\le \Delta\}$. For fixed $\Delta$ and $n$, we say that $G$…
Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…
Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…