Related papers: A dual basis approach to multidimensional scaling
Mobile crowdsensing (MCS) is a promising sensing paradigm that leverages the diverse embedded sensors in massive mobile devices. A key objective in MCS is to efficiently schedule mobile users to perform multiple sensing tasks. Prior work…
Cooperatively optimizing a vast number of agents that are connected over a large-scale network brings unprecedented scalability challenges. This paper revolves around problems optimizing coupled objective functions under coupled…
We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…
This book provides an introduction to the theory of digital (molecular) spaces (TDS). Digital spaces are combinatorial models of continuous spaces. TDS is one of alternative branches of digital topology that studies constructing and…
The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual…
We develop a cylindrical shape decomposition (CSD) algorithm to decompose an object, a union of several tubular structures, into its semantic components. We decompose the object using its curve skeleton and restricted translational sweeps.…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using…
We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…
Classical metric spaces often fail to model data-intensive systems where repetition and frequency of values are meaningful. In applications such as transactional databases, sensor logs, and record linkage, conventional distance measures…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…