2 research outputs found
High Dimensional Clustering with -nets
Clustering, a fundamental task in data science and machine learning, groups a
set of objects in such a way that objects in the same cluster are closer to
each other than to those in other clusters. In this paper, we consider a
well-known structure, so-called -nets, which rigorously captures the
properties of clustering. We devise algorithms that improve the run-time of
approximating -nets in high-dimensional spaces with and
metrics from to , where .
These algorithms are also used to improve a framework that provides approximate
solutions to other high dimensional distance problems. Using this framework,
several important related problems can also be solved efficiently, e.g.,
-approximate th-nearest neighbor distance,
-approximate Min-Max clustering, -approximate
-center clustering. In addition, we build an algorithm that
-approximates greedy permutations in time where is the spread of the input. This
algorithm is used to -approximate -center with the same time
complexity.Comment: Accepted by AAAI201