Search Results for author: Joe Kileel

Found 19 papers, 6 papers with code

Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications

no code implementations9 Nov 2023 Yifan Zhang, Joe Kileel

We prove an upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets.

Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC

no code implementations4 Oct 2023 Hongyi Fan, Joe Kileel, Benjamin Kimia

In this paper we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry.

Pose Estimation

The G-invariant graph Laplacian

no code implementations29 Mar 2023 Eitan Rosen, Paulina Hoyos, Xiuyuan Cheng, Joe Kileel, Yoel Shkolnisky

We introduce the G-invariant graph Laplacian that generalizes the graph Laplacian by accounting for the action of the group on the data set.

Denoising Dimensionality Reduction

Diffusion Maps for Group-Invariant Manifolds

no code implementations28 Mar 2023 Paulina Hoyos, Joe Kileel

In this article, we consider the manifold learning problem when the data set is invariant under the action of a compact Lie group $K$.

Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition

1 code implementation25 Oct 2022 Yifan Zhang, Joe Kileel

We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions.

Tensor Decomposition

Snapshot of Algebraic Vision

no code implementations20 Oct 2022 Joe Kileel, Kathlén Kohn

In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision.

3D Scene Reconstruction

Tensor Moments of Gaussian Mixture Models: Theory and Applications

1 code implementation14 Feb 2022 João M. Pereira, Joe Kileel, Tamara G. Kolda

In this work, we develop theory and numerical methods for \emph{implicit computations} with moment tensors of GMMs, reducing the computational and storage costs to $\mathcal{O}(n^2)$ and $\mathcal{O}(n^3)$, respectively, for general covariance matrices, and to $\mathcal{O}(n)$ and $\mathcal{O}(n)$, respectively, for diagonal ones.

Tensor Decomposition

On the Instability of Relative Pose Estimation and RANSAC's Role

no code implementations CVPR 2022 Hongyi Fan, Joe Kileel, Benjamin Kimia

In this paper we study the numerical instabilities of the 5- and 7-point problems for essential and fundamental matrix estimation in multiview geometry.

Pose Estimation

Landscape analysis of an improved power method for tensor decomposition

no code implementations NeurIPS 2021 Joe Kileel, Timo Klock, João M. Pereira

In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira.

Tensor Decomposition

Symmetry Breaking in Symmetric Tensor Decomposition

no code implementations10 Mar 2021 Yossi Arjevani, Joan Bruna, Michael Field, Joe Kileel, Matthew Trager, Francis Williams

In this note, we consider the optimization problem associated with computing the rank decomposition of a symmetric tensor.

Tensor Decomposition

Manifold learning with arbitrary norms

1 code implementation28 Dec 2020 Joe Kileel, Amit Moscovich, Nathan Zelesko, Amit Singer

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality.

Dimensionality Reduction

Subspace power method for symmetric tensor decomposition and generalized PCA

1 code implementation9 Dec 2019 Joe Kileel, João M. Pereira

We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank even-order real symmetric tensors.

Numerical Analysis Numerical Analysis Optimization and Control

Earthmover-based manifold learning for analyzing molecular conformation spaces

1 code implementation16 Oct 2019 Nathan Zelesko, Amit Moscovich, Joe Kileel, Amit Singer

In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction.

Dimensionality Reduction

On the Expressive Power of Deep Polynomial Neural Networks

1 code implementation NeurIPS 2019 Joe Kileel, Matthew Trager, Joan Bruna

We study deep neural networks with polynomial activations, particularly their expressive power.

A clever elimination strategy for efficient minimal solvers

no code implementations CVPR 2017 Zuzana Kukelova, Joe Kileel, Bernd Sturmfels, Tomas Pajdla

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers.

Minimal Problems for the Calibrated Trifocal Variety

no code implementations18 Nov 2016 Joe Kileel

We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision.

Distortion Varieties

no code implementations6 Oct 2016 Joe Kileel, Zuzana Kukelova, Tomas Pajdla, Bernd Sturmfels

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials.

The Chow Form of the Essential Variety in Computer Vision

no code implementations15 Apr 2016 Gunnar Fløystad, Joe Kileel, Giorgio Ottaviani

The Chow form of the essential variety in computer vision is calculated.

Rigid Multiview Varieties

no code implementations10 Sep 2015 Michael Joswig, Joe Kileel, Bernd Sturmfels, André Wagner

The multiview variety from computer vision is generalized to images by $n$ cameras of points linked by a distance constraint.

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