Robust regression and outlier detection
Robust regression and outlier detection
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
COLT '89 Proceedings of the second annual workshop on Computational learning theory
e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
Efficient distribution-free learning of probabilistic concepts
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Characterizations of learnability for classes of {0, …, n}-valued functions
Journal of Computer and System Sciences
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Fat-shattering and the learnability of real-valued functions
Journal of Computer and System Sciences
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Scale-sensitive dimensions, uniform convergence, and learnability
Journal of the ACM (JACM)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Prediction, learning, uniform convergence, and scale-sensitive dimensions
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Journal of Algorithms
Clustering for edge-cost minimization (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On Learning Sets and Functions
Machine Learning
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Randomized Approximation Scheme for Metric MAX-CUT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Coresets forWeighted Facilities and Their Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Sampling-based dimension reduction for subspace approximation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Algorithm for 2D Euclidean 2-Center with Outliers
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
The Planar k-Means Problem is NP-Hard
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
A smoothing principle for the Huber and other location M-estimators
Computational Statistics & Data Analysis
Universal ε-approximators for integrals
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Coresets for discrete integration and clustering
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Learning Big (Image) Data via Coresets for Dictionaries
Journal of Mathematical Imaging and Vision
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Statistical data frequently includes outliers; these can distort the results of estimation procedures and optimization problems. For this reason, loss functions which deemphasize the effect of outliers are widely used by statisticians. However, there are relatively few algorithmic results about clustering with outliers. For instance, the k-median with outliers problem uses a loss function [EQUATION] (x) which is equal to the minimum of a penalty h, and the least distance between the data point x and a center ci. The loss-minimizing choice of {c1,..., ck} is an outlier-resistant clustering of the data. This problem is also a natural special case of the k-median with penalties problem considered by [Charikar, Khuller, Mount and Narasimhan SODA'01]. The essential challenge that arises in these optimization problems is data reduction for the weighted k-median problem. We solve this problem, which was previously solved only in one dimension ([Har-Peled FSTTCS'06], [Feldman, Fiat and Sharir FOCS'06]). As a corollary, we also achieve improved data reduction for the k-line-median problem.