Related papers: High-Performance Out-of-core Block Randomized Sing…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…
Despite the groundbreaking success of diffusion models in generating high-fidelity images, their latent space remains relatively under-explored, even though it holds significant promise for enabling versatile and interpretable image editing…
Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
Most deep learning models are based on deep neural networks with multiple layers between input and output. The parameters defining these layers are initialized using random values and are "learned" from data, typically using stochastic…
The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that…
In this paper, we introduce a randomized QLP decomposition called Rand-QLP. Operating on a matrix $\bf A$, Rand-QLP gives ${\bf A}={\bf QLP}^T$, where $\bf Q$ and $\bf P$ are orthonormal, and $\bf L$ is lower-triangular. Under the…
Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…
To realize mmWave massive MIMO systems in practice, Beamspace MIMO with beam selection provides an attractive solution at a considerably reduced number of radio frequency (RF) chains. We propose low-complexity beam selection algorithms…
In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…
Due to differences in frame structure, existing multi-rate video encoding algorithms cannot be directly adapted to encoders utilizing special reference frames such as AV1 without introducing substantial rate-distortion loss. To tackle this…
Hybrid quantum-HPC algorithms advance research by delegating complex tasks to quantum processors and using HPC systems to orchestrate workflows and complementary computations. Sample-based quantum diagonalization (SQD) is a hybrid…
The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…
Two-dimensional singular decomposition (2DSVD) has been widely used for image processing tasks, such as image reconstruction, classification, and clustering. However, traditional 2DSVD algorithm is based on the mean square error (MSE) loss,…