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This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
We propose a novel algorithm for unsupervised extraction of piecewise planar models from depth-data. Among other applications, such models are a good way of enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive…
Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, SLAM, object/scene recognition, and augmented reality. In this paper, we present a new registration…
Interaction group detection has been previously addressed with bottom-up approaches which relied on the position and orientation information of individuals. These approaches were primarily based on pairwise affinity matrices and were…
The standard approach for visual place recognition is to use global image descriptors to retrieve the most similar database images for a given query image. The results can then be further improved with re-ranking methods that re-order the…
We propose a new regression algorithm that learns from a set of input-output pairs. Our algorithm is designed for populations where the relation between the input variables and the output variable exhibits a heterogeneous behavior across…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
Symbolic regression (SR) is a data analysis problem where we search for the mathematical expression that best fits a numerical dataset. It is a global optimization problem. The most popular approach to SR is by genetic programming (SRGP).…
We study an $\ell_{1}$-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. Specifically, we consider the case where errors are assumed to follow an autoregressive process,…
This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special…
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
We present a novel approach which is able to explore the configuration of grouped convolutions within neural networks. Group-size Series (GroSS) decomposition is a mathematical formulation of tensor factorisation into a series of…
We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we…
Reconstructing a 3D scene from unordered images is pivotal in computer vision and robotics, with applications spanning crowd-sourced mapping and beyond. While global Structure-from-Motion (SfM) techniques are scalable and fast, they often…
We present an algorithm for resampling a function from its values on a non-Cartesian grid onto a Cartesian grid. This problem arises in many applications such as MRI, CT, radio astronomy and geophysics. Our algorithm, termed SParse Uniform…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…