Related papers: Robust Bichromatic Classification using Two Lines

Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…

Given a set $S$ of $n$ points in the plane, we study the two-line-center problem: finding two lines that minimize the maximum distance from each point in $S$ to its closest line. We present a $(1+\varepsilon)$-approximation algorithm for…

The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed.…

We study the Generalized Red-Blue Annulus Cover problem for two sets of points, red ($R$) and blue ($B$), where each point $p \in R\cup B$ is associated with a positive penalty ${\cal P}(p)$. The red points have non-covering penalties, and…

A set of points $X = X_B \cup X_R \subseteq \mathbb{R}^d$ is linearly separable if the convex hulls of $X_B$ and $X_R$ are disjoint, hence there exists a hyperplane separating $X_B$ from $X_R$. Such a hyperplane provides a method for…

Many estimation problems in robotics, computer vision, and learning require estimating unknown quantities in the face of outliers. Outliers are typically the result of incorrect data association or feature matching, and it is common to have…

This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which…

In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an…

In the two-dimensional orthogonal colored range counting problem, we preprocess a set, $P$, of $n$ colored points on the plane, such that given an orthogonal query rectangle, the number of distinct colors of the points contained in this…

In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G=(V,E) with n vertices it runs in O(n^2) time assuming that a partition of (V,E+e) into…

Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have…

A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. The objective of an agent with known dynamics traversing the region is to identify the true classifier while paying a…

Given a bichromatic point set $P=\textbf{R} \cup \textbf{B}$ of red and blue points, a separator is an object of a certain type that separates $\textbf{R}$ and $\textbf{B}$. We study the geometric separability problem when the separator is…

Let $S$ be a set of $n$ points in general position in the plane, $r$ of which are red and $b$ of which are blue. In this paper we prove that there exist: for every $\alpha \in \left [ 0,\frac{1}{2} \right ]$, a convex set containing exactly…

This paper presents a new approach to classification of high dimensional spectroscopy data and demonstrates that it outperforms other current state-of-the art approaches. The specific task we consider is identifying whether samples contain…

Traffic signs play a critical role in road safety and traffic management for autonomous driving systems. Accurate traffic sign classification is essential but challenging due to real-world complexities like adversarial examples and…

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

We consider the following problem: Let $\mathcal{L}$ be an arrangement of $n$ lines in $\mathbb{R}^3$ colored red, green, and blue. Does there exist a vertical plane $P$ such that a line on $P$ simultaneously bisects all three classes of…

Let $S$ be a 2-colored (red and blue) set of $n$ points in the plane. A subset $I$ of $S$ is an island if there exits a convex set $C$ such that $I=C\cap S$. The discrepancy of an island is the absolute value of the number of red minus the…

Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…