Approximation Schemes for Clustering with Outliers
نویسندگان
چکیده
منابع مشابه
Approximation Schemes for Clustering with Outliers
Clustering problems are well-studied in a variety of fields such as data science, operations research, and computer science. Such problems include variants of centre location problems, k-median, and k-means to name a few. In some cases, not all data points need to be clustered; some may be discarded for various reasons. For instance, some points may arise from noise in a data set or one might b...
متن کاملApproximation Algorithms for Clustering Problems with Lower Bounds and Outliers
We consider clustering problems with non-uniform lower bounds and outliers, and obtain the first approximation guarantees for these problems. We have a setF of facilities with lower bounds {Li}i∈F and a setD of clients located in a common metric space {c(i, j)}i,j∈F∪D, and bounds k, m. A feasible solution is a pair ( S ⊆ F , σ : D 7→ S ∪ {out} ) , where σ specifies the client assignments, such ...
متن کاملLinear-Time Approximation Schemes for Clustering Problems
We present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions. More specifically, our approach leads to simple randomized algorithms for the k-means, k-median and discrete k-means problems that yield (1 + ε) approximations with probability ≥ 1/2 and running times of O(2(k/ε)O(1)dn). These are the first algor...
متن کاملApproximation schemes for the generalized geometric problems with geographic clustering
This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as Group-TSP or TSP with neighborhoods. We prove that under the condition that all regions are non-intersecting and have comparable sizes and shapes, the problem admits ...
متن کاملSublinear Projective Clustering with Outliers
Given a set of n points in <d, a family of shapes S and a number of clusters k, the projective clustering problem is to find a collection of k shapes in S such that the maximum distance from a point to its nearest shape is minimized. Some special cases of the problem include the k-line center problem where the goal is to cover the points with minimum radius hypercylinders and the k-hyperplane c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2019
ISSN: 1549-6325,1549-6333
DOI: 10.1145/3301446