Related papers: p-Adic scaled space filling curve indices for high…
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different space-filling…
While high-dimensional search-by-similarity techniques reached their maturity and in overall provide good performance, most of them are unable to cope with very large multimedia collections. The 'big data' challenge however has to be…
In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…
Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index, which replaces or complements traditional index structures with machine learning models, has been actively…
We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is…
In this paper, we propose a new global geometry constraint for depth completion. By assuming depth maps often lay on low dimensional subspaces, a dense depth map can be approximated by a weighted sum of full-resolution principal depth…
Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
The analysis of the spatial arrangement of colors and roughness/smoothness of figures is relevant due to its wide range of applications. This paper proposes a texture classification method that extracts data from images using the Hilbert…
We construct geohashing procedure based on using of space-filling H-curve. This curve provides a way to construct geohash with less computations than the construction based on usage of Hilbert curve. At the same time, H-curve has better…
Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of…
Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic…
Deep learning models have been widely applied across various domains and industries. However, many fields still face challenges due to limited and insufficient data. This paper proposes a Feature Augmentation on Adaptive Geodesic Curve…
Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…
Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to…
Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of…
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…