Matrix Krasulina achieves fast convergence for online k-PCA.
problem Online k-PCA with low-rank data.
method Generalized Krasulina's method for matrix case, without variance reduction.
result Exponential convergence to principal subspace.
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48 results for “Matrix Krasulina”
This paper proves the convergence rate of Krasulina's estimator for least eigenvalue and eigenvector.
problem Finding the least eigenvalue and eigenvector of an unknown covariance matrix.
method Developed a convergence proof for Krasulina's estimator.
result Established the convergence rate of Krasulina's estimator for the least eigenvalue and eigenvector.
Paper proposes a distributed method to estimate principal eigenvector from high-rate streaming data.
problem Estimating principal eigenvector from high streaming data rate.
method Distributed Krasulina (D-Krasulina) and mini-batch extension (DM-Krasulina) methods.
result Achieves optimal estimation error rates under high streaming conditions.
New implicit Krasulina's k-PCA update avoids QR-decomposition and improves convergence.
problem Online k-PCA problem with orthonormality constraint.
method Derived an implicit form of Krasulina's update that bypasses orthonormality constraint.
result The new update avoids costly QR-decomposition and yields superior convergence.
We consider a situation in which we see samples in drawn i.i.d. from some distribution with mean zero and unknown covariance A. We wish to compute the top eigenvector of A in an incremental fashion - with an algorithm that maintains an estimate of the top eigenvector in O(d) space, and incrementally adju…
DeepTMR reorders matrices without prior knowledge of structural patterns.
problem Matrix reordering without prior structural knowledge.
method DeepTMR uses a neural network to automatically extract features and reorder matrices.
result Trained network produces denoised mean matrix for visualization.
Paper speeds up matrix multiplication on Intel PIII using SIMD.
problem Efficiently multiplying large matrices for faster algorithm performance.
method Implemented matrix-matrix multiply using Intel Pentium SIMD architecture.
result Average performance 2.09 times faster than public domain routines.
The paper constructs Goeritz matrices from Dehn colorings.
problem Constructing Goeritz matrices from Dehn colorings.
method Purely algebraic construction of Goeritz matrices from Dehn coloring matrices for prime knot diagrams.
result A new method to construct Goeritz matrices from Dehn colorings.
New matrix reveals cluster info in sparse directed graphs.
problem Analyzing cluster information in directed graphs.
method Proposed complex non-backtracking matrix integrating Hermitian adjacency matrix and non-backtracking matrix properties.
result The complex non-backtracking matrix holds cluster information, especially for sparse directed graphs.
The CN matrix of a pure braid projection is characterized and applied.
problem Understanding the structure of CN matrices for braid projections.
method Discussion and characterization of patterns and specific matrices.
result Characterization of CN matrix of a pure 6-braid projection and related matrices.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
problem Classifying SL(n) covariant matrix-valued valuations on Lp-spaces.
method Established a complete classification for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx), eliminating matrix symmetry assumption.
result Unique characterization of such valuations by the moment matrix in n>2, rotation matrix in 2D.
New method for matrix completion under complex missing data patterns.
problem Matrix completion with complex missing data patterns.
method Estimate the probability matrix of observation via low-rank matrix estimation and use inverse probabilities weighting to complete the target matrix.
result Optimal asymptotic convergence rates for observation probabilities and target matrix estimation.
Unified approach for robust low rank matrix estimation with adversaries.
problem Robust low rank matrix estimation in the presence of adversaries.
method Unified approach combining Huber loss and nuclear norm penalization.
result Sharp estimation error bounds for matrix compressed sensing and completion.
New methods improve recommendation accuracy for users and items with few ratings.
problem Skewed distribution and low ratings affect recommendation accuracy.
method Four matrix completion-based approaches: FARP, TMF, TMF + Dropout, IFWMF.
result Improved prediction accuracy for users and items with few ratings.
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the…
New NMF algorithm uses Toeplitz matrix for facial recognition.
problem Facial recognition performance improvement.
method Proposes TNMF algorithm with Toeplitz penalty for NMF.
result TNMF outperforms ZNMF and other constrained NMF algorithms.
A new algorithm speeds up matrix operations in Neural Networks.
problem Time-consuming matrix operations in Neural Networks.
method An algorithm that increases the degree of parallelism of matrix multiplication.
result The algorithm speeds up several matrix operations in Neural Networks.
Selective sampling improves matrix completion with known structure.
problem Reconstructing a low-rank matrix with incomplete data.
method Designing observation sets based on matrix structure and selective sampling.
result Improved reconstruction accuracy with selective sampling.
The paper defines the OU matrix for braid diagrams and finds determinant relationships.
problem Understanding the layeredness of braid diagrams.
method Defining the OU matrix and analyzing its determinant for layered braid diagrams.
result The determinant of the OU matrix for layered braid diagrams is the product of the determinants of the layers.
Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Methodcs.LG
New method improves robust low-rank matrix completion for computer vision.
problem Robust low-rank matrix completion for partially observed data.
method Formulated as a nonsmooth Riemannian optimization problem over Grassmann manifold, solved with an alternating manifold proximal gradient continuation method.
result Demonstrated advantages over existing approaches in background extraction from surveillance videos.
NIMFA is a Python library for nonnegative matrix factorization.
problem Efficiently factorizing nonnegative matrices for various applications.
method Unified interface, state-of-the-art methods, initialization approaches, quality scoring, supports dense and sparse matrices.
result Unified and efficient implementation of nonnegative matrix factorization methods.
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…
The paper tackles matrix estimation from noisy data, focusing on low-rank matrices.
problem Estimating a low-rank matrix from noisy observations.
method The paper analyzes several estimators, including constrained nuclear-norm minimization, nuclear-norm regularized least squares, and a nonconvex constrained low-rank optimization problem.
result The estimators provide upper error bounds that depend on matrix rank, observed fraction, and matrix sums, and are minimax optimal.
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 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…
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…
Proposes a robust factor analysis for matrix data.
problem Robust factor analysis for matrix data with heavy-tailed or contaminated data.
method Bilinear factor analysis based on the matrix-variate distribution.
result Significantly higher breakdown point than traditional methods.
3-manifold triangulation can be reconstructed from its intersection matrix.
problem Reconstructing the triangulation of 3-manifolds from their intersection matrix.
method Using the intersection matrix of a simplicial complex to determine the triangulation of a 3-manifold up to isomorphism.
result The intersection matrix is sufficient to determine the triangulation of a 3-manifold up to isomorphism.
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix. To the best of our knowledge, all previous algorithms either incurred a quadrat…
V-matrix method fails to consistently estimate conditional probabilities.
problem Inconsistent solutions in V-matrix method for conditional probability estimation.
method Construct constrained quadratic programming problems with inconsistent inequality constraints.
result V-matrix method may not always have a consistent solution for conditional probability estimation.
Entropic covariance modelsmath.ST
Paper presents a new framework for covariance matrix estimation with geometric insights.
problem Challenges in covariance matrix estimation, especially in finding suitable models and efficient estimation methods.
method General framework for linear restrictions on different transformations of the covariance matrix, including matrix logarithm and its inverse.
result Yields an -estimator with -estimation allowing for straightforward asymptotic and finite sample analysis.
A fast optimization method for matrix completion with side information.
problem Matrix completion with and without side information.
method fastImpute based on non-convex gradient descent.
result fastImpute converges to a global minimum and recovers the matrix accurately.
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.
New method estimates missingness probabilities for MNAR matrix completion.
problem Bias in matrix completion due to missing not at random data.
method Estimate missingness probabilities using nuclear norm structure.
result Improved matrix completion accuracy without auxiliary information.
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…
Incorporates matrix exponential into generative flows for improved performance.
problem Improving generative flow models for better density estimation.
method Integrates matrix exponential into generative flows, proposing new layers and modifying network architecture.
result The proposed model achieves great performance on density estimation.
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective funct…
Collective Matrix Completionstat.ML
This work tackles collective matrix completion with multiple and heterogeneous data sources.
problem Reconstructing data from multiple heterogeneous matrices.
method Estimation based on minimizing goodness-of-fit and nuclear norm penalization of the whole collective matrix.
result Proposed estimators achieve fast rates of convergence under two settings.
Predict artist efficiency in VFX shots using matrix completion.
problem Predicting artist efficiency in rendering VFX shots.
method Structured matrix factorization models for bounded entries.
result Effective models for predicting artist efficiency.
Bayesian non-linear matrix completion tackles large, sparse data.
problem Predict missing elements in large, sparsely observed matrices.
method Bayesian Gaussian process latent variable models with data-parallel distributed computation.
result Scalable Bayesian non-linear matrix completion outperforms linear methods.
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Goeritz and Seifert matrices derived from Dehn presentations.
problem Computing Goeritz and Seifert matrices for links.
method Using Fox's free differential calculus on modified Dehn presentations.
result Goeritz and Seifert matrices can be derived from Dehn presentations.
Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.
problem Understanding quasi-cluster algebras on non-orientable surfaces.
method Developed matrix formulae and proved skein relations for quasi-cluster variables.
result Laurent expansion and skein relations for quasi-cluster variables on non-orientable surfaces.
Proposes a new matrix factorization model for interval-valued matrices.
problem Matrix factorization for matrices with entries in a given interval.
method Bounded simplex-structured matrix factorization (BSSMF) with fast algorithm for missing data.
result BSSMF provides a unique decomposition under certain conditions.
Gradient descent proves global convergence for 4-layer matrix factorization.
problem Global convergence of gradient descent on four-layer matrix factorization under random initialization.
method New techniques to show saddle-avoidance properties and extend eigenvalue theories.
result Polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization.
New method clusters matrix-variate data with outliers.
problem Clustering matrix-variate data with outliers.
method Iterative approach using subset log-likelihoods.
result Extends OCLUST algorithm to matrix-variate normal data.
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.