Tensor completion using geodesics on Segre manifolds
We propose a Riemannian conjugate gradient (CG) optimization method for finding low rank approximations of incomplete tensors. Our main contribution consists of an explicit expression of the geodesics on the Segre manifold. These are exploited in our algorithm to perform the retractions. We apply our method to movie rating predictions in a recommender system for the MovieLens dataset, and identification of pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we recover the tensor decomposition from less than $10\%$ of the data.
Code (0)
등록된 구현이 없습니다.
Tasks
Recommendation SystemsTensor DecompositionSimilar Papers 제목 키워드 기반
Energy Guided Geometric Flow Matching
A useful inductive bias for temporal data is that trajectories should stay close to the data manifold. Traditional flow matching relies on straight conditional paths, and flow matching methods which learn geodesics rely …
Short and Straight: Geodesics on Differentiable Manifolds
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are ke…
validNonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion
Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a no…
Image InpaintingA dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill thi…
Riemannian optimizationGeomstats: A Python Package for Riemannian Geometry in Machine Learning
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and …
BIG-bench Machine LearningClusteringDimensionality ReductionGPU+1