Related papers: Robust Bichromatic Classification using Two Lines
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Classical separability problem involving multi-color point sets is an important area of study in computational geometry. In this paper, we study different separability problems for bichromatic point set P=P_r\cup P_b on a plane, where $P_r$…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
Binary linear classification has been explored since the very early days of the machine learning literature. Perhaps the most classical algorithm is the Perceptron, where a weight vector used to classify examples is maintained, and additive…
Rare data in a large-scale database are called outliers that reveal significant information in the real world. The subspace-based outlier detection is regarded as a feasible approach in very high dimensional space. However, the outliers…
Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…
Spatial-mode projective measurements could achieve super-resolution in remote sensing and imaging, yet their performance is usually sensitive to the parameters of the target scenes. We propose and demonstrate a robust classifier of close-by…
Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…
Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In the typical setting investigated till now, each classifier is trained…
Deep neural networks are susceptible to generating overconfident yet erroneous predictions when presented with data beyond known concepts. This challenge underscores the importance of detecting out-of-distribution (OOD) samples in the open…
In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets $R,B \subset [\Delta]^2$ with $|R|+|B|=n$, the goal is to select a set of edges between $R$ and $B$ so that…
We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…
We address the problem of computing the minimum number of triangles to separate a set of blue points from a set of red points in $\mathbb{R}^2$. A set of triangles is a \emph{separator} of one color from the other if every point of that…
The topic of this paper is related to the well-known notion of unit distance graphs. Take a graph with its edges coloured red and blue such that for some $d$ it can be mapped into the plane with all vertices going to distinct points, the…
'Optimal cutpoints' for binary classification tasks are often established by testing which cutpoint yields the best discrimination, for example the Youden index, in a specific sample. This results in 'optimal' cutpoints that are highly…
In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. Our approach rests on two main elements: (1) the splitting rules for the…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
This work presents a two-stage text line detection method for historical documents. Each detected text line is represented by its baseline. In a first stage, a deep neural network called ARU-Net labels pixels to belong to one of the three…
This paper presents a novel online learning method that aims at finding a separator hyperplane between data points labelled as either positive or negative. Since weights and biases of artificial neurons can directly be related to…