Related papers: Orthogonal Nonnegative Tucker Decomposition
This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was…
Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization…
Recent work has proposed the use of tensor decomposition to model repetitions and to separate tracks in loop-based electronic music. The present work investigates further on the ability of Nonnegative Tucker Decompositon (NTD) to uncover…
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…
In this paper, the problem of image super-resolution for Optical Coherence Tomography (OCT) has been addressed. Due to the motion artifacts, OCT imaging is usually done with a low sampling rate and the resulting images are often noisy and…
Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on the augmented Lagrangian function we introduce a flexible…
This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
We pose the problem of approximating optimally a given nonnegative signal with the scalar autoconvolution of a nonnegative signal. The I-divergence is chosen as the optimality criterion being well suited to incorporate nonnegativity…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…