Related papers: Robust Bichromatic Classification using Two Lines

Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference…

We consider a two-type oriented competition model on the first quadrant of the two-dimensional integer lattice. Each vertex of the space may contain only one particle of either Red type or Blue type. A vertex flips to the color of a…

We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio…

Given a set $P$ of $n$ red and blue points in the plane, a \emph{planar bichromatic spanning tree} of $P$ is a spanning tree of $P$, such that each edge connects between a red and a blue point, and no two edges intersect. In the bottleneck…

This paper introduces a novel method leveraging bi-encoder-based detectors along with a comprehensive study comparing different out-of-distribution (OOD) detection methods in NLP using different feature extractors. The feature extraction…

In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…

A 1-plane graph is a graph embedded in the plane such that each edge is crossed at most once. A 1-plane graph is optimal if it has maximum edge density. A red-blue edge coloring of an optimal 1-plane graph $G$ partitions the edge set of $G$…

This paper presents a region-partition based attraction field dual representation for line segment maps, and thus poses the problem of line segment detection (LSD) as the region coloring problem. The latter is then addressed by learning…

In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly…

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k…

In this paper, an outlier elimination algorithm for ellipse/ellipsoid fitting is proposed. This two-stage algorithm employs a proximity-based outlier detection algorithm (using the graph Laplacian), followed by a model-based outlier…

In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring…

In recent years, the learned local descriptors have outperformed handcrafted ones by a large margin, due to the powerful deep convolutional neural network architectures such as L2-Net [1] and triplet based metric learning [2]. However,…

Supervised classification methods often assume the train and test data distributions are the same and that all classes in the test set are present in the training set. However, deployed classifiers often require the ability to recognize…

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression…

Roof plane segmentation from airborne LiDAR point clouds is an important technology for 3D building model reconstruction. One of the key issues of plane segmentation is how to design powerful features that can exactly distinguish adjacent…

A change detection system takes as input two images of a region captured at two different times, and predicts which pixels in the region have undergone change over the time period. Since pixel-based analysis can be erroneous due to noise,…

In recent years, the interest in interpretable classification models has grown. One of the proposed ways to improve the interpretability of a rule-based classification model is to use sets (unordered collections) of rules, instead of lists…

Given a set $P$ of $n$ points in the plane, its separability is the minimum number of lines needed to separate all its pairs of points from each other. We show that the minimum number of lines needed to separate $n$ points, picked randomly…