Related papers: Tree quasi-separable matrices: a simultaneous gene…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…
Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…
Recently, in [1], the author proved that many results that are true for PPT matrices also hold for another class of matrices with a certain symmetry in their Hermitian Schmidt decompositions. These matrices were called SPC in [1]…
The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…
We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…
In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…
We introduce a neural network that represents sentences by composing their words according to induced binary parse trees. We use Tree-LSTM as our composition function, applied along a tree structure found by a fully differentiable natural…
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic…
Consider an almost-simple algebraic group G and a choice of complex root of unity q. We study the category of quasi-coherent sheaves $\mathscr{X}_q$ on the half-quantum flag variety, which itself forms a sheaf of tensor categories over the…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC)…
Given a matrix of distribution functions and a quasi-stochastic matrix, i.e. an irreducible nonnegative matrix with maximal eigenvalue one and associated unique positive left and right eigenvectors, the article studies the properties of an…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short)…
Decision trees are prized for their interpretability and strong performance on tabular data. Yet, their reliance on simple axis-aligned linear splits often forces deep, complex structures to capture non-linear feature effects, undermining…
We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
Tree tensor networks such as the tensor train format are a common tool for high dimensional problems. The associated multivariate rank and accordant tuples of singular values are based on different matricizations of the same tensor. While…