Efficient SVD algorithm robust to outliers.
problem Outliers in data matrix affect SVD accuracy and speed.
method Spherically Normalized SVD (SpherSVD) algorithm.
result Significantly faster and more robust than existing methods.
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48 results for “SVD Analysis”
Randomized SVD shows phase transitions in noisy data.
problem Noise sensitivity of randomized SVD in large rank matrices.
method Analyzed R-SVD under low-rank signal plus noise model.
result R-SVD exhibits BBP-like phase transition with outliers above detectability threshold.
New insights into choosing between two data integration methods based on SVD.
problem Choosing between two data integration methods (Stack-SVD and SVD-Stack) for shared latent structure across multiple datasets.
method Derive exact expressions for the asymptotic performance and phase transitions of Stack-SVD and SVD-Stack, and develop optimal weighting schemes.
result Optimally weighted Stack-SVD outperforms optimally weighted SVD-Stack in the asymptotic regime.
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recen…
We compared the regular Singular Value Decomposition (SVD), truncated SVD, Krylov method and Randomized PCA, in terms of time and space complexity. It is well-known that Krylov method and Randomized PCA only performs well when k << n, i.e. the number of eigenpair needed is far less than that of matrix size. We compared…
This paper examines the impact of centering in PCA and SVD.
problem The influence of centering in PCA and SVD.
method Detailed exploration of centering in PCA and SVD.
result Two PCA embeddings derived from SVD with and without centering can be aligned under certain conditions.
The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most practical algorithms would require some form of approximation, such as sketching, when r…
Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases no…
The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.
problem Understanding the behavior of PLS-SVD in high-dimensional data integration.
method Analysis using random matrix theory and singular value decomposition.
result PLS-SVD exhibits counter-intuitive or limiting behavior in certain regimes and outperforms PCA when detecting common latent subspace.
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental algorithm for identifying a subspace of Rn from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis has shown that GROUSE converges locally at an expected linea…
Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group effects upon variable selection. To this end, we first propose group-sparse SVD model…
This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast …
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.
problem Missing data in PLS-SVD for multimodal datasets.
method Replica-symmetric analysis of spiked rectangular random matrices with missing entries.
result PLS-SVD performance transitions from uninformative to informative singular vectors at a critical signal-to-noise threshold.
New method tackles non-smooth tensor data for better recovery.
problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.
This paper introduces a method to improve GNN stability and robustness.
problem Challenges in GNN stability, generalization, and robustness.
method SVD regularization to induce contractive behavior in GNNs.
result SVD regularization enhances the stability and generalization of GNNs.
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is com…
New method approximates high-dimensional probability densities efficiently.
problem Approximating high-dimensional probability densities accurately and efficiently.
method Hierarchical tensor-network approach using randomized SVD and linear equations.
result The method effectively approximates high-dimensional densities with linear complexity.
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the original algorithm, the extended algorithm provides for a more efficient way of matrix…
Improved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correctionmath.NA
Due to the iterative nature of most nonnegative matrix factorization (\textsc{NMF}) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes have been proposed for NMF, among which one of the most popular class of methods…
K-SVD algorithm has been successfully applied to image denoising tasks dozens of years but the big bottleneck in speed and accuracy still needs attention to break. For the sparse coding stage in K-SVD, which involves constraint, prevailing methods usually seek approximate solutions greedily but are less effe…
We propose a new approach for Collaborative Filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (Movielens dataset) we compare the approach with the SVD- and NMF-based algorithms in terms of Mean Average Error (MAE). One of the experimental…
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …
The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users' ratings on items based on their latent factors. However, current Matrix Factorization models p…
Study optimizes shared singular subspace estimation from noisy matrices.
problem Estimating shared singular subspaces across multiple noisy matrices.
method Low-rank matrix denoising framework with Stack-SVD and novel estimators.
result Stack-SVD achieves minimax rate-optimality for identical shared subspaces, and novel estimators for partial sharing.
SVD training reduces DNN rank and computation load without SVD per step.
problem High memory and computational load in deep neural networks.
method Explicitly achieves low-rank DNNs during training without SVD per step, using orthogonality regularization and sparsity-inducing regularizers.
result Significantly reduces DNN rank and computation load compared to existing methods.
Ranky solves SVD for large sparse matrices in distributed systems.
problem Rank problem in large sparse matrices for SVD.
method Distributed approach to solve rank problem.
result Recovers SVD with negligible error for large sparse matrices.
The paper compares clustering techniques for personalized food kits.
problem Designing food kits that match individual consumer preferences.
method Comparative analysis of clustering techniques using conjoint analysis data.
result SVD clustering outperforms k-means in personalized food kit design.
The paper analyzes how random perturbations affect RSVD and its applications.
problem Analyzing the impact of random perturbations on RSVD.
method Derives bounds for distances between exact and approximated singular vectors using RSVD.
result Established nearly-optimal convergence rates and asymptotic normality for RSVD in various inference problems.
Convolutional Neural Networks with Transformed Input based on Robust Tensor Network Decompositioncs.LG
Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured dat…
New algorithms improve RPCA for large matrices with upper rank bounds.
problem Efficiently decompose large matrices into low-rank and sparse parts.
method Combine regularization and matrix multiplication approaches with upper rank bounds.
result Proposed algorithms are faster and more robust than existing methods.
New method uses SVD entropy to price artworks.
problem Lack of fine measurements in traditional art pricing models.
method SVD entropy of painting images for content measurement.
result SVD entropy positively affects sales price at 1% significance level.
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesicsmath.DG
Study of logarithms in SVD-closed subgroups of unitary group.
problem Understanding logarithms in SVD-closed subgroups of unitary groups.
method Analysis of generalized principal logarithms and minimizing geodesics.
result Set of generalized principal logarithms is a disjoint union of diffeomorphic subsets.
Deep K-SVD Denoisingcs.LG
This work considers noise removal from images, focusing on the well known K-SVD denoising algorithm. This sparsity-based method was proposed in 2006, and for a short while it was considered as state-of-the-art. However, over the years it has been surpassed by other methods, including the recent deep-learning-based newc…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to approximate the tensor rank with the norm of singular values based on its …
Globally optimized SVD compression of LLMs via Fermi-function-based rank selection and gauge fixingcs.LG
Physics-inspired methods optimize SVD compression of LLMs.
problem Efficiently compressing large language models (LLMs) using SVD.
method FermiGrad for globally optimal rank selection and PivGa for lossless compression.
result Global optimization of SVD ranks and lossless compression of low-rank factors.
Study uses neural fields to improve geophysical inversions by reducing artifacts.
problem Improving geophysical inversions by reducing artifacts and improving model recovery.
method Employing neural fields for test-time learning in geophysical inversions.
result Test-time learning with neural fields eliminates unwanted artifacts in recovered models.
Generalizes randomized SVD for better matrix approximations using Gaussian vectors.
problem Computing accurate rank-k approximations of matrices with limited data.
method Extends randomized SVD to multivariate Gaussian vectors, incorporating prior knowledge and using Gaussian processes.
result Demonstrates improved accuracy in approximating matrices and Hilbert-Schmidt operators.
Block based Singular Value Decomposition approach to matrix factorization for recommender systemscs.LG
With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value Decomposition(SVD) based recommendation algorithms have been leveraged to produce better result…
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
Cross-Layer Subspace Coupling for LLM Compression: A Unifying Framework and Its Empirical Limitscs.LG
Unified SVD compression fails in practical tasks, highlighting the importance of per layer activation reconstruction.
problem The failure of a unified SVD compression method in practical tasks like perplexity and accuracy.
method Unified optimization problem for SVD based compression methods, focusing on cross-layer coupling.
result Downstream metrics like perplexity and accuracy degrade severely compared to standard per layer SVD LLM.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and rescaling the coordinate axes (by a predefined function of the singular value). Howe…
Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA algorithm for processing large sparse data. The algorithm has similar accuracy to th…
This work reduces the dimensionality of text data using SVD, improving performance and computational efficiency.
problem High-dimensional input spaces in text classification lead to excessive parameter count and computational infeasibility.
method Singular Value Decomposition (SVD) is applied to transform the input space into a lower-dimensional latent space.
result Neural networks trained on the lower-dimensional latent space achieve comparable or better performance with reduced computational complexity.
Paper develops a bootstrap method for estimating sketched SVD errors.
problem Lack of tools for accurately estimating sketched SVD errors.
method Develops a fully data-driven bootstrap method for numerical error estimation.
result Allows users to adaptively predict extra work needed for desired error tolerance.
This research investigates reliable local explanations for machine listening models.
problem Generating reliable local explanations for machine listening models.
method Investigates the sensitivity of SoundLIME explanations to input perturbations and proposes a novel method for identifying suitable content types.
result SoundLIME explanations are sensitive to the content in occluded input regions, and the average magnitude of input mel-spectrogram bins is the most suitable content type for temporal explanations.
A new method for efficiently updating large-scale matrices in real-time.
problem Updating large-scale matrices with evolving data in real-time.
method Incremental SVD approach that handles row/column appends, rank-1 updates, and refresh strategies.
result Incremental SVD achieves accuracy close to full SVD with a fraction of the computational cost.