Related papers: Intertwining wavelets or Multiresolution analysis …
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…
The ability to image materials at the microscale from long-wavelength wave data is a major challenge to the geophysical, engineering and medical fields. Here, we present a framework to constrain microstructure geometry and properties from…
Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based…
Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. Here we…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
A vertex-subset graph problem $Q$ defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem $Q$ asks whether it is possible to transform one feasible solution for…
Understanding the structure of weighted signed networks is essential for analysing social systems in which relationships vary both in sign and strength. Despite significant advances in statistical network analysis, there is still a lack of…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs, it takes into account all paths between vertices. Formally, it is defined as d(i,j)=q_{ii}+q_{jj}-q_{ij}-q_{ji}, where q_{ij}…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard…
Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between neural…
Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although sampling and reconstruction of FTVGS with known spectral…