Related papers: Hilbert curves for efficient exploratory landscape…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Almost all existing deep learning approaches for semantic segmentation tackle this task as a pixel-wise classification problem. Yet humans understand a scene not in terms of pixels, but by decomposing it into perceptual groups and…
We study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended, less completely, to flag Hilbert schemes,…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
Latin Hypercube Sampling (LHS) is a prominent tool in simulation design, with a variety of applications in high-dimensional and computationally expensive problems. LHS allows for various optimization strategies, most notably to ensure…
Graph sampling allows mining a small representative subgraph from a big graph. Sampling algorithms deploy different strategies to replicate the properties of a given graph in the sampled graph. In this study, we provide a comprehensive…
For many tracking and surveillance applications, background subtraction provides an effective means of segmenting objects moving in front of a static background. Researchers have traditionally used combinations of morphological operations…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…
Salient object detection has increasingly become a popular topic in cognitive and computational sciences, including computer vision and artificial intelligence research. In this paper, we propose integrating \textit{semantic priors} into…
Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and…
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the…
In this paper, we consider the problems from the area of sublinear-time algorithms of edge sampling, edge counting, and triangle counting. Part of our contribution is that we consider three different settings, differing in the way in which…
Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps…
One of the fundamental properties of a salient object region is its contrast with the immediate context. The problem is that numerous object regions exist which potentially can all be salient. One way to prevent an exhaustive search over…