Search Results for author: Joe Kileel

Found 13 papers, 5 papers with code

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.

Computer Vision

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.

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.

Computer Vision

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.

Computer Vision

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