Related papers: An efficient algorithm computing composition facto…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
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…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i=1}^r u_i^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and $u_i \in \mathbb{C}^n$.In order to obtain efficient decomposition algorithms, it is…
Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Tsigaridas for symmetric tensor canonical polyadic (CP)…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…
We present efficient algorithms to decide whether two given counting functions on non-abelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on non-abelian free groups…
Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…