Related papers: Principal Components along Quiver Representations
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be…
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components…
We consider the problem of how many components to retain in the application of principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle $L$ on the $n$ dimensional projective space as homogeneous bundles and we describe their associated quiver representations. We use this approach to show that if…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…
We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a…