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…
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48 results for “Incremental SVD”
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.
Unified multilinear model for causal factor disentanglement.
problem Disentangling causal factors from complex data without direct manipulation.
method Hierarchical block multilinear factorization (M-mode Block SVD) and incremental approach.
result Interpretable object representation robust to occlusion and reduced training data.
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and…
Paper improves tensor approximation for streaming data.
problem Challenges in finding accurate low-tubal-rank tensor approximations in streaming settings.
method Extends Frequent Directions for efficient low-tubal-rank tensor approximation.
result The new algorithm achieves arbitrarily small approximation error with linear sketch size growth.
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…
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.
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…
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.
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.
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…
EVA adapts LoRA for faster, more efficient fine-tuning.
problem Fast and efficient fine-tuning of large models for specific tasks.
method EVA uses directions capturing most activation variance for initialization, maximizing gradient signal and reducing parameters.
result EVA achieves faster convergence and higher average scores across tasks, reducing parameters.
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.
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.
Unified framework for structured principal subspace estimation with bounds and rates.
problem Structured principal subspace estimation problems.
method Unified framework, minimax lower and upper bounds, information-geometric complexity.
result Minimax rates of convergence for specific settings, including optimal rates for non-negative PCA/SVD.
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…
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.
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…
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…
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.
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…
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…
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…
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 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 …
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure featu…
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.
Truncated Singular Value Decomposition (SVD) calculates the closest rank- approximation of a given input matrix. Selecting the appropriate rank defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization prob…
In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks.
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.
Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
problem Improving the convergence rate of Muon optimizer.
method Using Newton-Schulz steps for momentum orthogonalization, proving convergence rate and constant factor.
result Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal…
Singular Value Decomposition (SVD) has been used successfully in recent years in the area of recommender systems. In this paper we present how this model can be extended to consider both user ratings and information from Wikipedia. By mapping items to Wikipedia pages and quantifying their similarity, we are able to use…
Paper proposes a new optimization framework for learning eigenfunctions of operators.
problem Computing eigenvalue decomposition of high-dimensional operators.
method Operator SVD with Neural Networks via Nested Low-Rank Approximation.
result Proposed method efficiently learns top-L singular values and functions in the correct order.
Conventional out-of-distribution (OOD) detection schemes based on variational autoencoder or Random Network Distillation (RND) have been observed to assign lower uncertainty to the OOD than the target distribution. In this work, we discover that such conventional novelty detection schemes are also vulnerable to the blu…
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.
In the probabilistic topic models, the quantity of interest---a low-rank matrix consisting of topic vectors---is hidden in the text corpus matrix, masked by noise, and the Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank m…
New method solves nonsmooth low-rank matrix optimization problems efficiently.
problem Nonsmooth and low-rank matrix optimization problems in statistics and machine learning.
method Low-rank Extragradient Method with warm-start initialization.
result The extragradient method converges to an optimal solution with rate and requires only two low-rank SVDs per iteration.
We propose a rank- variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation (-SVD) in Frank-Wolfe with a top- singular-vector computation (-SVD), which can be done by repeatedly applying -SVD times. …
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.
It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the …