Related papers: Unfolding in ATLAS
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…
Deep neural networks provide unprecedented performance gains in many real world problems in signal and image processing. Despite these gains, future development and practical deployment of deep networks is hindered by their blackbox nature,…
Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Just how many different connected shapes result from slicing a cube along some of its edges and unfolding it into the plane? In this article we answer this question by viewing the cube both as a surface and as a graph of vertices and edges.…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they…
In this note we show how techniques developed for untangling planar graphs by Bose et al. [Discrete & Computational Geometry 42(4): 570-585 (2009)] and Goaoc et al. [Discrete & Com- putational Geometry 42(4): 542-569 (2009)] imply new…
The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…
Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse…
Face recognition (FR) systems continue to spread in our daily lives with an increasing demand for higher explainability and interpretability of FR systems that are mainly based on deep learning. While bias across demographic groups in FR…
Recognising and locating image patches or sets of image features is an important task underlying much work in computer vision. Traditionally this has been accomplished using template matching. However, template matching is notoriously…
Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…