Related papers: A Sub-linear Time Framework for Geometric Optimiza…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into…
Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association, or to incorrect detections from signal processing and machine learning methods. This paper introduces two unifying formulations…
Outlier detection in a large-scale database is a significant and complex issue in knowledge discovering field. As the data distributions are obscure and uncertain in high dimensional space, most existing solutions try to solve the issue…
From the beginning of David Hestenes rediscovery of geometric algebra in the 1960s, outermorphisms have been a cornerstone in the mathematical development of GA. Many important mathematical formulations in GA can be expressed as…
Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling…
At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for…
Subspace learning is an important problem, which has many applications in image and video processing. It can be used to find a low-dimensional representation of signals and images. But in many applications, the desired signal is heavily…
In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
Clustering analysis is one of the critical tasks in machine learning. Traditionally, clustering has been an independent task, separate from outlier detection. Due to the fact that the performance of clustering can be significantly eroded by…
In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…
Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…
The Minimum Enclosing Ball (MEB) problem is one of the most fundamental problems in clustering, with applications in operations research, statistics and computational geometry. In this works, we give the first differentially private (DP)…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
We consider the problem of learning a mixture of linear regressions (MLRs). An MLR is specified by $k$ nonnegative mixing weights $p_1, \ldots, p_k$ summing to $1$, and $k$ unknown regressors $w_1,...,w_k\in\mathbb{R}^d$. A sample from the…
We consider clustering problems with {\em non-uniform lower bounds and outliers}, and obtain the {\em first approximation guarantees} for these problems. We have a set $\F$ of facilities with lower bounds $\{L_i\}_{i\in\F}$ and a set $\D$…
Outlier rejection and equivalently inlier set optimization is a key ingredient in numerous applications in computer vision such as filtering point-matches in camera pose estimation or plane and normal estimation in point clouds. Several…