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Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by…
Haxell's condition is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the…
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…
We propose a generalized convolutional neural network (CNN) architecture that first decomposes the input signal into subbands by an adaptive filter bank structure, and then uses convolutional layers to extract features from each subband…
Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
Graph filters leverage topological information to process networked data with existing methods mainly studying fixed graphs, ignoring that graphs often expand as nodes continually attach with an unknown pattern. The latter requires…
Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional…
A perfect matching cut is a perfect matching that is also a cutset, or equivalently a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be…
Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is…
Binary neural networks have attracted tremendous attention due to the efficiency for deploying them on mobile devices. Since the weak expression ability of binary weights and features, their accuracy is usually much lower than that of…
Backtrack search is a fundamental technique for computing with finite permutation groups, which has been formulated in terms of points, ordered partitions, and graphs. We provide a framework for discussing the most common forms of backtrack…
State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
This article provides a mathematical analysis of singular (nonsmooth) artifacts added to reconstructions by filtered backprojection (FBP) type algorithms for X-ray CT with arbitrary incomplete data. We prove that these singular artifacts…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
In this paper we focus on subsampling stationary random processes that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum.…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…