Abstract. The power iteration is a classical method for computing the eigenvector associated with the largest eigenvalue of a matrix. The subspace iteration is an extension of the power iteration where the subspace spanned by n largest eigenvectors of a matrix, is determined. The natural power

We show that the power iteration, typically used to approximate the dominant eigenvector of a matrix, can be applied to a normalized affinity matrix to create a one-dimensional embedding of the underlying data. This embedding is then used, as in spectral clustering, to cluster the data via k

. Recently, an approach based on optimization by graph-cut has been developed which successfully combines both types of information. In this paper we extend the graph-cut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power

stations is fixed, (2) minimum power assignment where a user is iteratively assigned to the base station at which its signal to interference ratio is highest, and (3) diversity reception, where a user's signal is combined from several or perhaps all base stations. For the above models, the uplink

Abstract — This paper introduces a fast implementation of the power iteration method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm, referred to as the fast API method, guarantees the orthonormality of the subspace

1 A randomized algorithm for low rank matrix aproximation We are interested in finding an approximation UΣV T to the m × n matrix A, where U is an m × k orthogonal matrix, Σ is a k × k diagonal matrix, V is an n × k orthognal matrix, and k is a user set positive integer less than m; usually k ≪ m. Recently there have been several papers which have approached this problem by determining the approximate range space of A by applying it to a set of random vectors. The full SVD is then computed on A’s approximate range, giving algorithms that run in O(mkn) time; see [5, 3, 6]. The purpose of this short note is to discuss a particular variant of these algorithms which is a good choice when a high quality (as measured by operator norm) low rank approximation of a matrix is desired, and memory is a limiting quantity. The algorithm takes as input nonnegative integers q and l such that m> l> k (usually l is slightly bigger than k, say k + 10), and then goes as follows:

This paper introduces a fast implementation of the power iterations method for subspace tracking, based on an approximation less restrictive than the well known projection approximation. This algorithm guarantees the orthonormality of the estimated subspace weighting matrix at each iteration

structure) given the channel conditions and power constraint must be found. However, obtaining the optimal trans-mission policy when employing dirty paper coding is a computationally complex non-convex problem. We use duality to transform this problem into a well-structured convex multiple-access channel

This paper presents an unsupervised learning algorithm for sense disambiguation that, when trained on unannotated English text, rivals the performance of supervised techniques that require time-consuming hand annotations. The algorithm is based on two powerful constraints -- that words tend to have

-differences t test based on 10-fold cross-validation, exhibits somewhat elevated probability of type I error. A fourth test, McNemar’s test, is shown to have low type I error. The fifth test is a new test, 5 × 2 cv, based on five iterations of twofold cross-validation. Experiments show that this test also has