JULIA combines multi-linear and nonlinear models for tensor completion.
problem Complex patterns in real-world tensors require a unified model.
method JULIA unifies multi-linear and nonlinear models with flexible component assignment and efficient alternating optimization.
result JULIA outperforms existing methods in large-scale tensor completion.
We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces, fixed points of completely contractive mappings, Toeplitz operators, dy…
A new method for 1-bit matrix completion that is faster and more accurate.
problem Estimating a low-rank matrix from binary observations.
method Majorization-Minimization Gauss-Newton (MMGN) method.
result MMGN outperforms existing methods in accuracy and speed.
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More s…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…
Localized min-max method proves minimal hypersurface existence.
problem Existence of minimal hypersurfaces in complete manifolds.
method Localized min-max approach to prove existence.
result Existence of complete embedded minimal hypersurface with index at most one.
New model for high rank matrix completion with online and batch methods.
problem Matrix completion for high rank matrices with latent structure.
method Kernel trick to map data into a high dimensional feature space, explicit parametrization of low dimensional subspace, online fitting procedure.
result Online method can handle streaming data and adapt to non-stationary latent structure.
New bounds improve linkage methods for clustering, distinguishing complete-link from single-link.
problem Improving bounds on linkage methods for clustering quality.
method Developed new bounds for complete-link and average-link methods in agglomeration clustering.
result Separated complete-link from single-link in terms of approximation for diameter.
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
problem Robust matrix completion with sparse noise.
method Alternates between projected gradient step for low-rank and thresholding step for sparse noise.
result Achieves linear convergence for general thresholding functions.
Two novel methods improve network embedding for completely-imbalanced labels.
problem Improving network embedding for networks with completely-imbalanced labels.
method Two novel semi-supervised network embedding methods: RSDNE and RECT.
result Experimental results show the superiority of the proposed methods.
Paper uses tensor completion to estimate HVAC fan power baselines.
problem Estimating HVAC fan power without demand response.
method Tensor completion for multi-dimensional data analysis.
result Tensor completion outperforms existing baselining methods.
New algorithm improves tensor completion performance.
problem Tensor completion for partially observed data.
method Adaptive ADMM optimization framework for low-rank tensor completion.
result New method outperforms conventional techniques in NMSE.
We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by p…
New method improves matrix completion with functional maps.
problem Matrix completion with geometric structure.
method Functional map regularization for geometric matrix completion.
result Significant performance improvement over state-of-the-art methods.
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
Scalable method completes ill-conditioned matrices from few samples.
problem Matrix completion from few samples for ill-conditioned matrices.
method Iterative algorithm combining IRLS, smoothing Newton, and proximal gradient methods.
result Local quadratic convergence rate and well-conditioned linear systems.
In the previous paper, the authors constructed a complete holomorphic immersion of the unit disk D into C^2 whose image is bounded. In this paper, we shall prove existence of complete holomorphic null immersions of Riemann surfaces with arbitrary genus and finite topology, whose image is bounded in C^2. To construct su…
New method predicts binary matrix entries using empirical Bayes and low-rank structure.
problem Predicting unobserved entries in binary matrices.
method Empirical Bayes method motivated by Efron--Morris estimator, exploiting low-rank structure.
result Superior performance in predictive accuracy, calibration, and efficiency compared to existing methods.
Proposes a transductive matrix completion method with calibration for multi-task learning.
problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.
New method for exact matrix completion with reduced observation complexity.
problem Exact recovery of matrices with high coherence.
method Adaptive sampling method and relation to sparsest vector of column and row spaces.
result Exact recovery of μ0-coherent column space matrices with much smaller observation complexity. Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of rati…
New method solves robust matrix completion using nonlinear equations.
problem Recover low rank and sparse matrices from incomplete observations.
method Transforms problem into solving a system of nonlinear equations, then uses the alternative direction method.
result Algorithm converges linearly to the true solution under proper assumptions.
Develops a two-stage approach for robust tensor completion of visual data.
problem Estimating missing values in high-order data with outliers.
method Coarse-to-fine framework and M-estimator-based robust tensor ring recovery.
result Superior performance compared to state-of-the-art robust algorithms.
Most of previous work in knowledge base (KB) completion has focused on the problem of relation extraction. In this work, we focus on the task of inferring missing entity type instances in a KB, a fundamental task for KB competition yet receives little attention. Due to the novelty of this task, we construct a large-sca…
Method uses optimal transport to complete distributional matrices.
problem Matrix completion for distributional data.
method Nearest neighbors in Wasserstein space.
result Method recovers distributions in Wasserstein metric.
We develop a powerful new analytic method to construct complete non-compact G2-manifolds, i.e. Riemannian 7-manifolds (M,g) whose holonomy group is the compact exceptional Lie group G2. Our construction starts with a complete non-compact asymptotically conical Calabi-Yau 3-fold B and a circle bundle M over B satisfying…
The computer program SnapPea can approximate whether or not a three manifold whose boundary consists of tori has a complete hyperbolic structure, but it can not prove conclusively that this is so. This article provides a method for proving that such a manifold has a complete hyperbolic structure based on the approximat…
New method solves matrix completion problems to certifiable optimality.
problem Certifying optimality in low-rank matrix completion.
method Disjunctive branch-and-bound scheme for convex relaxation.
result Decreases optimality gap by two orders of magnitude.
A new imputation method considers feature importance for missing value completion.
problem Missing values in datasets reduce accuracy and increase processing difficulty.
method Iterative matrix completion with feature importance learning.
result The method outperforms existing imputation algorithms on various datasets.
Complete minimal surfaces with any genus found in a specific 3-manifold.
problem Constructing minimal surfaces with arbitrary genus.
method Classical desingularization method.
result Complete embedded minimal surfaces of finite topology constructed.
We consider the problem of completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix X by maximizing the likelihood ratio with a constraint on the nuclear norm of X, and the obser…
Three completeness notions for Cartan geometries are shown not to be equivalent.
problem Inequivalence of completeness notions for Cartan geometries.
method Constructing examples and providing detailed explanations of counterexamples.
result Three completeness notions for Cartan geometries are not equivalent.
Unified Python package N2 benchmarks NN-based matrix completion methods.
problem Matrix completion with robust NN methods across diverse applications.
method Unified Python package N2 consolidates NN-based methods. result NN-based techniques outperform classical methods in real-world settings.
Paper proposes a novel method to improve matrix completion with median loss for large datasets.
problem Matrix completion with absolute deviation loss for large-scale data.
method Proposes a refinement step using pseudo data to improve inefficient estimators of median matrix completion.
result Turns inefficient estimators into a rate (near-)optimal matrix completion procedure.
This paper classifies geodesics of projectively flat sprays and introduces a method to determine sprays based on geodesics.
problem Classifying geodesics of projectively flat sprays and determining sprays based on geodesics.
method Introduction of a geodesic method to determine an n-dimensional spray based on a family of curves with 2(n-1) free parameters as geodesics.
result Classification of geodesics of projectively flat sprays and determination of sprays based on geodesics.
Study shows how fast a specific matrix completion method works.
problem Completing a rank-one matrix from a subset of revealed entries.
method Alternating minimization approach for matrix completion.
result Polynomial upper bound on convergence rate.
The paper proposes methods for predicting missing values in mixed data matrices.
problem Matrix completion for mixed data types (continuous, binary, ordinal).
method Generalized latent factor models for low-rank matrix estimation with entrywise consistency.
result Tight probabilistic error bounds for the proposed estimators.
New deep learning model for matrix completion combining linear and nonlinear relationships.
problem Matrix completion considering only linear or nonlinear relations, ignoring latent relationships.
method Combines linear and nonlinear models in a latent variables framework, using a deep neural network with two branches for columns and rows, and manifold learning as an auxiliary task.
result Experimental results show the proposed method outperforms state-of-the-art matrix completion methods.
Unified framework for nonconvex matrix completion with linearly parameterized factors.
problem Matrix completion with improved accuracy using linearly parameterized factors.
method Unified nonconvex optimization framework with Correlated Parametric Factorization condition.
result Uniform upper bounds for low-rank estimation at any local minimum.
The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given multilinear rank is known to admit a Riemannian manifold structure, thus methods of Rieman…
New saliency evaluations focus on completeness and soundness, improving explanations.
problem Current saliency evaluations focus on completeness but ignore soundness.
method Introduces new intrinsic evaluation metrics based on completeness and soundness.
result Simple saliency method matches or outperforms prior methods in new evaluations.
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer…
The paper constructs Einstein metrics on holomorphic bundles.
problem Finding complete conformally Kähler Einstein metrics on holomorphic bundles.
method Explicit momentum construction via ODE methods and Calabi ansatz.
result Non-trivial complete conformally Kähler Einstein metrics on certain holomorphic bundles are found.
New method estimates and completes tensors from ordinal data, improving accuracy and efficiency.
problem Estimating and completing tensors from incomplete, ordinal observations.
method Multi-linear cumulative link model with rank-constrained M-estimator.
result The proposed estimator achieves faster convergence and is minimax optimal.
Study improves fractional posterior for 1-bit matrix completion.
problem Estimating a binary matrix from observed entries.
method Fractional posterior approach with low-rank factorization and spectral scaled Student priors.
result Concentration results for fractional posterior, demonstrating effectiveness in matrix recovery.
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…
In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, (2) does not require any of the kernels to be complete a priori, and (3) can tackle non-linear kernels. These aspects are necessary in practical app…
AWNN improves matrix completion by adaptively weighting nearest neighbors.
problem Matrix completion with optimal nearest neighbor weights and radii selection.
method Adaptively weighted nearest neighbor method for matrix completion.
result Theoretical guarantees and synthetic experiments support the effectiveness of AWNN.