Related papers: Subspace approximation with outliers
Many computer vision tasks involve processing large amounts of data contaminated by outliers, which need to be detected and rejected. While outlier detection methods based on robust statistics have existed for decades, only recently have…
We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing…
We provide improved upper and lower bounds for the Min-Sum-Radii (MSR) and Min-Sum-Diameters (MSD) clustering problems with a bounded number of clusters $k$. In particular, we propose an exact MSD algorithm with running-time $n^{O(k)}$. We…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
We propose a new $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{(d-1)}{2}})$ running time for computing the diameter of a set of $n$ points in the $d$-dimensional Euclidean space for a fixed dimension $d$,…
This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…
We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained…
We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…
Dimensionality reduction methods are very common in the field of high dimensional data analysis. Typically, algorithms for dimensionality reduction are computationally expensive. Therefore, their applications for the analysis of massive…
Interpreting objects with basic geometric primitives has long been studied in computer vision. Among geometric primitives, superquadrics are well known for their ability to represent a wide range of shapes with few parameters. However, as…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
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…
In the Priority $k$-Center problem, the input consists of a metric space $(X,d)$, an integer $k$, and for each point $v \in X$ a priority radius $r(v)$. The goal is to choose $k$-centers $S \subseteq X$ to minimize $\max_{v \in X}…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…