Related papers: Subquadratic Kronecker Regression with Application…
Recently, tensor time-series forecasting has gained increasing attention, whose core requirement is how to perform dimensionality reduction. In this paper, we establish a least square optimization model by combining tensor singular value…
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…
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…
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…
Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…
We study the problem of estimating the trace of a matrix $\mathbf{A}$ that can only be accessed through Kronecker-matrix-vector products. That is, for any Kronecker-structured vector $\mathrm{x} = \otimes_{i=1}^k \mathrm{x}_i$, we can…
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…
We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace…
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…
We propose a test for testing the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. Through defining a Kronecker product structure set, we define if a…
Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the…
Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…
We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…
This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…
The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson coefficients, which are the analogues for the general linear…
Kronecker compressed sensing refers to using Kronecker product matrices as sparsifying bases and measurement matrices in compressed sensing. This work focuses on the Kronecker compressed sensing problem, encompassing three sparsity…
In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected…
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…
Kronecker PCA involves the use of a space vs. time Kronecker product decomposition to estimate spatio-temporal covariances. In this work the addition of a sparse correction factor is considered, which corresponds to a model of the…
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-order tensor data. Tensor observations are assumed to be generated from…