Related papers: Singular Value Decomposition and Neural Networks
Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…
Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear…
We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and…
A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both…
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…
This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…
Investigating relationships between variables in multi-dimensional data sets is a common task for data analysts and engineers. More specifically, it is often valuable to understand which ranges of which input variables lead to particular…
In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…
We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…
Accurate and early diagnosis of pneumonia through X-ray imaging is essential for effective treatment and improved patient outcomes. Recent advancements in machine learning have enabled automated diagnostic tools that assist radiologists in…
We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we…
With the tremendous success of Graph Convolutional Networks (GCNs), they have been widely applied to recommender systems and have shown promising performance. However, most GCN-based methods rigorously stick to a common GCN learning…
Pore networks play a key role in understanding and quantifying flow and transport processes in complex porous media. Realistic pore-spaces may be characterized by singular regions, i.e., isolated subnetworks that do not connect inlet and…
Semantic information has been proved effective in scene text recognition. Most existing methods tend to couple both visual and semantic information in an attention-based decoder. As a result, the learning of semantic features is prone to…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a…
We present Variational Self-Supervised Learning (VSSL), a novel framework that combines variational inference with self-supervised learning to enable efficient, decoder-free representation learning. Unlike traditional VAEs that rely on…
Singular Value Decomposition (SVD) has recently seen a surge of interest as a simple yet powerful tool for large language models (LLMs) compression, with a growing number of works demonstrating 20-80% parameter reductions at minimal…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…