Related papers: Tucker Tensor Regression and Neuroimaging Analysis
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
Accurate diagnosis of neurological disorders is contingent upon advanced imaging modalities such as Magnetic Resonance Imaging (MRI), which commonly utilize sparse imaging techniques to reconstruct images from limited data, thus reducing…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…
There is an emerging interest in tensor factorization applications in big-data analytics and machine learning. To speed up the factorization of extra-large datasets, organized in multidimensional arrays (aka tensors), easy to compute…
Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Accurate cascaded channel state information is pivotal for extremely large-scale intelligent reflecting surfaces (XL-IRS) in next-generation wireless networks. However, the large XL-IRS aperture induces spherical wavefront propagation due…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…