Name
Abstract | ||
|---|---|---|
This paper discusses the topic of dimensionality reduction for $k$-means clustering. We prove that any set of $n$ points in $d$ dimensions (rows in a matrix $A \in \RR^{n \times d}$) can be projected into $t = \Omega(k / \eps^2)$ dimensions, for any $\eps \in (0,1/3)$, in $O(n d \lceil \eps^{-2} k/ \log(d) \rceil )$ time, such that with constant probability the optimal $k$-partition of the point set is preserved within a factor of $2+\eps$. The projection is done by post-multiplying $A$ with a $d \times t$ random matrix $R$ having entries $+1/\sqrt{t}$ or $-1/\sqrt{t}$ with equal probability. A numerical implementation of our technique and experiments on a large face images dataset verify the speed and the accuracy of our theoretical results. |
Year | Venue | Keywords |
|---|---|---|
2010 | Clinical Orthopaedics and Related Research | k means clustering,data structure,random matrix,artificial intelligent |
DocType | Volume | Citations |
Conference | abs/1011.4632 | 37 |
PageRank | References | Authors |
1.39 | 13 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christos Boutsidis | 1 | 610 | 33.37 |
| Anastasios Zouzias | 2 | 193 | 14.06 |
| Petros Drineas | 3 | 2165 | 201.55 |