Related papers: Robust Bichromatic Classification using Two Lines
Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…
Reinforcement Learning (RL) based solutions are being adopted in a variety of domains including robotics, health care and industrial automation. Most focus is given to when these solutions work well, but they fail when presented with out of…
We propose a methodology for robust, real-time place recognition using an imaging lidar, which yields image-quality high-resolution 3D point clouds. Utilizing the intensity readings of an imaging lidar, we project the point cloud and obtain…
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers…
Multi-dimensional scaling (MDS) plays a central role in data-exploration, dimensionality reduction and visualization. State-of-the-art MDS algorithms are not robust to outliers, yielding significant errors in the embedding even when only a…
An old question in Euclidean Ramsey theory asks, if the points in the plane are red-blue coloured, does there always exist a red pair of points at unit distance or five blue points in line separated by unit distances? An elementary proof…
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…
Machine Learning classifiers used in Brain-Computer Interfaces make classifications based on the distribution of data they were trained on. When they need to make inferences on samples that fall outside of this distribution, they can only…
We consider the online multiclass linear classification under the bandit feedback setting. Beygelzimer, P\'{a}l, Sz\"{o}r\'{e}nyi, Thiruvenkatachari, Wei, and Zhang [ICML'19] considered two notions of linear separability, weak and strong…
An important theorem of Beck says that any point set in the Euclidean plane is either ``nearly general position'' or ``nearly collinear'': there is a constant C>0 such that, given n points in the plane with at most r$ of them collinear, the…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large.…
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…
In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of $n$ points in the plane. A double-strip is a closed region in the plane whose boundary consists of four…
In the Boundary Labeling problem, we are given a set of $n$ points, referred to as sites, inside an axis-parallel rectangle $R$, and a set of $n$ pairwise disjoint rectangular labels that are attached to $R$ from the outside. The task is to…
Object detection and classification using video is necessary for intelligent planning and navigation on a mobile robot. However, current methods can be too slow or not sufficient for distinguishing multiple classes. Techniques that rely on…
The question of whether to use one classifier or a combination of classifiers is a central topic in Machine Learning. We propose here a method for finding an optimal linear combination of classifiers derived from a bias-variance framework…
Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…
For fine-grained visual classification, objects usually share similar geometric structure but present variant local appearance and different pose. Therefore, localizing and extracting discriminative local features play a crucial role in…