Related papers: Finite-sample confidence regions for spectral clus…

Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…

We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we…

It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…

An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…

The reasoning process of Graph Neural Networks is complex and considered opaque, limiting trust in their predictions. To alleviate this issue, prior work has proposed concept-based explanations, extracted from clusters in the model's node…

Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…

Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as subsampling window width and…

This paper is the last part of a comprehensive survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

We study the spectral aspects of the graph limit theory. We give a description of graphon convergence in terms of converegnce of eigenvalues and eigenspaces. Along these lines we prove a spectral version of the strong regularity lemma.…

This paper proposes a blind detection problem for low pass graph signals. Without assuming knowledge of the exact graph topology, we aim to detect if a set of graph signal observations are generated from a low pass graph filter. Our problem…

We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

Graph signal processing (GSP) deals with the representation, analysis, and processing of structured data, i.e. graph signals that are defined on the vertex set of a generic graph. A crucial prerequisite for applying various GSP and graph…

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an…

In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections.…

Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…

While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…