相关论文: Weighted Singular Value Thresholding and its Appli…

We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yields a new weighted graph connecting what we call spectral…

Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…

Self-supervised contrastive learning has demonstrated great potential in learning visual representations. Despite their success in various downstream tasks such as image classification and object detection, self-supervised pre-training for…

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…

This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…

The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…

Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…

Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine (SVM) based on the Bayesian sparsity model. Compared with the regression problem, RVM classification is difficult to be conducted because…

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (2019b) for exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for…

We propose a method of using a Weighted second-order cone programming twin support vector machine (WSOCP-TWSVM) for imbalanced data classification. This method constructs a graph based under-sampling method which is utilized to remove…

The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…

We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single…

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…

Clustering explores meaningful patterns in the non-labeled data sets. Cluster Ensemble Selection (CES) is a new approach, which can combine individual clustering results for increasing the performance of the final results. Although CES can…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

Foreground-background separation is an important problem in document image analysis. Popular unsupervised binarization methods (such as the Sauvola's algorithm) employ adaptive thresholding to classify pixels as foreground or background. In…

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…

Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…

Cross-validation (CV) is one of the main tools for performance estimation and parameter tuning in machine learning. The general recipe for computing CV estimate is to run a learning algorithm separately for each CV fold, a computationally…