Related papers: Constant rank factorizations of smooth maps
Though achieving excellent performance in some cases, current unsupervised learning methods for single image denoising usually have constraints in applications. In this paper, we propose a new approach which is more general and applicable…
The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are…
Class imbalance is a substantial challenge in classifying many real-world cases. Synthetic over-sampling methods have been effective to improve the performance of classifiers for imbalance problems. However, most synthetic over-sampling…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
Ranking functions in information retrieval are often used in search engines to recommend the relevant answers to the query. This paper makes use of this notion of information retrieval and applies onto the problem domain of cognate…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
SHAP is a popular method for measuring variable importance in machine learning models. In this paper, we study the algorithm used to estimate SHAP scores and outline its connection to the functional ANOVA decomposition. We use this…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Data and data sources have become increasingly essential in recent decades. Scientists and researchers require more data to deploy AI approaches as the field continues to improve. In recent years, the rapid technological advancements have…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…
A vital aspect of the classification based model construction process is the calibration of the scoring function. One of the weaknesses of the calibration process is that it does not take into account the information about the relative…
In visual scene understanding tasks, it is essential to capture both invariant and equivariant structure. While neural networks are frequently trained to achieve invariance to transformations such as translation, this often comes at the…
The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually…
With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…