Related papers: Hybrid Quantum Singular Spectrum Decomposition for…
Singular value decomposition (SVD) is widely used in wireless systems, including multiple-input multiple-output (MIMO) processing and dimension reduction in distributed MIMO (D-MIMO). However, the iterative nature of decomposition methods…
Quantum computing presents a promising approach for machine learning with its capability for extremely parallel computation in high-dimension through superposition and entanglement. Despite its potential, existing quantum learning…
The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…
We propose a stochastic approximation (SA) based method with randomization of samples for policy evaluation using the least squares temporal difference (LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…
Spectroscopy is an indispensable tool in understanding the structures and dynamics of molecular systems. However computational modelling of spectroscopy is challenging due to the exponential scaling of computational complexity with system…
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…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by taking the advantages of both…
Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…