Related papers: Randomized Functional Sparse Tucker Tensor for Com…

In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…

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…

We propose a new tensor factorization method, called the Sparse Hierarchical-Tucker (Sparse H-Tucker), for sparse and high-order data tensors. Sparse H-Tucker is inspired by its namesake, the classical Hierarchical Tucker method, which aims…

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…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

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…

Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…

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 present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…

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…

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional…

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…