Related papers: Multidimensional Scaling: Approximation and Comple…
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on…
Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
In an era of frequent extreme weather and global warming, obtaining precise, fine-grained near-surface weather forecasts is increasingly essential for human activities. Downscaling (DS), a crucial task in meteorological forecasting, enables…
A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As…
Recent advances have markedly improved the cross-scene generalization of relative depth estimation, yet its practical applicability remains limited by the absence of metric scale, local inconsistencies, and low computational efficiency. To…
Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian…
In this paper, we give approximation algorithms for the \textsc{Minimum Dominating Set (MDS)} problem on \emph{string} graphs and its subclasses. A \emph{path} is a simple curve made up of alternating horizontal and vertical line segments.…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Localization in Wireless Sensor Networks (WSNs) has been a challenging problem in the last decade. The most explored approaches for this purpose are based on multidimensional scaling (MDS) technique. The first algorithm that introduced MDS…
We consider the task of fitting low-dimensional embeddings to high-dimensional data. In particular, we study the $k$-Euclidean Metric Violation problem ($\textsf{$k$-EMV}$), where the input is $D \in \mathbb{R}^{\binom{n}{2}}_{\geq 0}$ and…
With the recent development of technology, wireless sensor networks (WSN) are becoming an important part of many applications. Knowing the exact location of each sensor in the network is very important issue. Therefore, the localization…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
Current and future wireless applications strongly rely on precise real-time localization. A number of applications such as smart cities, Internet of Things (IoT), medical services, automotive industry, underwater exploration, public safety,…
We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…