Related papers: Tensor Analysis with n-Mode Generalized Difference…

Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Machine learning tools have empowered a qualitatively new way to perform differential cross section measurements whereby the data are unbinned, possibly in many dimensions. Unbinned measurements can enable, improve, or at least simplify…

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…

Machine learning models struggle with generalization when encountering out-of-distribution (OOD) samples with unexpected distribution shifts. For vision tasks, recent studies have shown that test-time adaptation employing diffusion models…

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Linear discriminant analysis (LDA) has been a useful tool in pattern recognition and data analysis research and practice. While linearity of class boundaries cannot always be expected, nonlinear projections through pre-trained deep neural…

This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…

We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…

The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance…

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…

In this paper, we propose a novel method for projecting data from multiple modalities to a new subspace optimized for one-class classification. The proposed method iteratively transforms the data from the original feature space of each…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

We propose tensor time series imputation when the missing pattern in the tensor data can be general, as long as any two data positions along a tensor fibre are both observed for enough time points. The method is based on a tensor time…

Geospatial sensor data is essential for modern defense and security, offering indispensable 3D information for situational awareness. This data, gathered from sources like lidar sensors and optical cameras, allows for the creation of…

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…