Related papers: Parametrizing the mixing matrix : A unified approa…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective "unsupervised" implies that the number of mixing components is unknown and has to be determined, ideally by data…
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a…
The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…
Multi-view clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity,…
We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
The map-matching is an essential preprocessing step for most of the trajectory-based applications. Although it has been an active topic for more than two decades and, driven by the emerging applications, is still under development. There is…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular,…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
Good parametrisations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…