Related papers: Detecting null patterns in tensor data
Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors).…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…
This work presents a novel approach to tabular data prediction leveraging graph structure learning and graph neural networks. Despite the prevalence of tabular data in real-world applications, traditional deep learning methods often…
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
This paper proposes a standard way to represent sparse tensors. A broad theoretical framework for tensor data scattering methods used in various deep learning frameworks is established. This paper presents a theorem that is very important…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
In recent work (Soltani, Kilmer, Hansen, BIT 2016), an algorithm for non-negative tensor patch dictionary learning in the context of X-ray CT imaging and based on a tensor-tensor product called the $t$-product (Kilmer and Martin, 2011) was…
In Novel Class Discovery (NCD), the goal is to find new classes in an unlabeled set given a labeled set of known but different classes. While NCD has recently gained attention from the community, no framework has yet been proposed for…
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…
Novel Class Discovery (NCD) is the problem of trying to discover novel classes in an unlabeled set, given a labeled set of different but related classes. The majority of NCD methods proposed so far only deal with image data, despite tabular…
Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval.…
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…
A new technique for the detection of outliers in contingency tables is introduced. Outliers thereby are unexpected cell counts with respect to classical loglinear Poisson models. Subsets of cell counts called minimal patterns are defined,…
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the…
The discovery of new and interesting patterns in large datasets, known as data mining, draws more and more interest as the quantities of available data are exploding. Data mining techniques may be applied to different domains and fields…
In this paper, we aim at automatically searching an efficient network architecture for dense image prediction. Particularly, we follow the encoder-decoder style and focus on designing a connectivity structure for the decoder. To achieve…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most…