• Publications
  • Influence
On clusterings-good, bad and spectral
Two results regarding the quality of the clustering found by a popular spectral algorithm are presented, one proffers worst case guarantees whilst the other shows that if there exists a "good" clustering then the spectral algorithm will find one close to it. Expand
Efficient Algorithms for Online Decision Problems
It is shown that a very simple idea, used in Hannan's seminal 1957 paper, gives efficient solutions to all of these problems, including a (1+∈)-competitive algorithm as well as a lazy one that rarely switches between decisions. Expand
Efficient algorithms for online decision problems
This work gives a simple approach for doing nearly as well as the best single decision, where the best is chosen with the benefit of hindsight, and these follow-the-leader style algorithms extend naturally to a large class of structured online problems for which the exponential algorithms are inefficient. Expand
Latent semantic indexing: a probabilistic analysis
It is proved that under certain conditions LSI does succeed in capturing the underlying semantics of the corpus and achieves improved retrieval performance. Expand
The Random Projection Method
  • S. Vempala
  • Computer Science, Mathematics
  • DIMACS Series in Discrete Mathematics and…
  • 24 February 2005
This paper presents a meta-modelling framework for embedding metrics in Euclidean space using a random projection approach and shows how this approach can be improved on the basis of prior work on similar models. Expand
Matrix approximation and projective clustering via volume sampling
This paper proves that the additive error drops exponentially by iterating the sampling in an adaptive manner, and gives a pass-efficient algorithm for computing low-rank approximation with reduced additive error. Expand
An algorithmic theory of learning: Robust concepts and random projection
This work provides a novel algorithmic analysis via a model of robust concept learning (closely related to “margin classifiers”), and shows that a relatively small number of examples are sufficient to learn rich concept classes. Expand
Fast monte-carlo algorithms for finding low-rank approximations
An algorithm is developed that is qualitatively faster, provided the authors may sample the entries of the matrix in accordance with a natural probability distribution, and implies that in constant time, it can be determined if a given matrix of arbitrary size has a good low-rank approximation. Expand
Fast Monte-Carlo algorithms for finding low-rank approximations
This paper develops an algorithm which is qualitatively faster provided the entries of the matrix are sampled according to a natural probability distribution and the algorithm takes time polynomial in k, 1//spl epsiv/, log(1//spl delta/) only, independent of m, n. Expand
Simulated annealing in convex bodies and an O*(n4) volume algorithm
A new algorithm for computing the volume of a convex body in R^n is presented, improving on the previous best algorithm by a factor of n and using a ''morphing'' technique that can be viewed as a variant of simulated annealing. Expand