Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 61, Issue 2, Pages 1045-1062Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2375327
Keywords
Clustering; dimensionality reduction; randomized algorithms
Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1008983] Funding Source: National Science Foundation
Ask authors/readers for more resources
We study the topic of dimensionality reduction for k-means clustering. Dimensionality reduction encompasses the union of two approaches: 1) feature selection and 2) feature extraction. A feature selection-based algorithm for k-means clustering selects a small subset of the input features and then applies k-means clustering on the selected features. A feature extraction-based algorithm for k-means clustering constructs a small set of new artificial features and then applies k-means clustering on the constructed features. Despite the significance of k-means clustering as well as the wealth of heuristic methods addressing it, provably accurate feature selection methods for k-means clustering are not known. On the other hand, two provably accurate feature extraction methods for k-means clustering are known in the literature; one is based on random projections and the other is based on the singular value decomposition (SVD). This paper makes further progress toward a better understanding of dimensionality reduction for k-means clustering. Namely, we present the first provably accurate feature selection method for k-means clustering and, in addition, we present two feature extraction methods. The first feature extraction method is based on random projections and it improves upon the existing results in terms of time complexity and number of features needed to be extracted. The second feature extraction method is based on fast approximate SVD factorizations and it also improves upon the existing results in terms of time complexity. The proposed algorithms are randomized and provide constant-factor approximation guarantees with respect to the optimal k-means objective value.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available