相关论文: Matrix Construction Using Cyclic Shifts of a Colum…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…

In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph,…

Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…

A cross matrix $X$ can have nonzero elements located only on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of matrices that are at most…

As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

Polymatroids can be considered as "fractional matroid" where the rank function is not required to be integer valued. Many, but not every notion in matroid terminology translates naturally to polymatroids. Defining cyclic flats of a…

Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…

The increasing need for data privacy and the demand for robust machine learning models have fueled the development of synthetic data generation techniques. However, current methods often succeed in replicating simple summary statistics but…

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…

We present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices. Their study is useful in the design of quasi-cyclic low-density generator matrix codes, that are…

In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…

The use of correlation matrices to evaluate the number of uncorrelated stirrer positions of reverberation chamber has widespread applications in electromagnetic compatibility. We present a comparative study of recent techniques based on…

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix…

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

Unrolled networks have been widely used for Magnetic Resonance Imaging (MRI) reconstruction due to their efficiency. However, they typically exhibit unstable output quality across cascades, resulting in sub-optimal final reconstruction…

We construct new resolvable decompositions of complete multigraphs and complete equipartite multigraphs into cycles of variable lengths (and a perfect matching if the vertex degrees are odd). We develop two techniques: {\em layering}, which…