Related papers: Decomposition of Big Tensors With Low Multilinear …

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…

Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…

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…

Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more and more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary…

The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…

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…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

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 CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…

The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…