Related papers: A tensor factorization model of multilayer network…
The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…
Multilayer networks proved to be suitable in extracting and providing dependency information of different complex systems. The construction of these networks is difficult and is mostly done with a static approach, neglecting time delayed…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…
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…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic…
It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However,…
Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER,…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…