Methods based on the analysis of eigenvalues or singular values of a matrix, often called spectral methods are very popular for many applications including graph partitioning, clustering, recognition, compression. This paper will survey some of these applications and present the basic underlying ideas.

Analyzing the affinity matrix spectrum is an increasingly popular data clustering method. We propose three new algorithmic components which are appropriate for improving performance of spectral clustering. First, observing the eigenvectors suggests to use a K-lines algorithm instead of the commonly applied K-means. Second, the clustering works best if the affinity matrix has a clear block struc...

Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the inference of nonparametric models are computationally and statistically efficie...

This paper extends an earlier work [Appl. Math. Comput. 140 (2003) 77] to differential-algebraic equations with constraint singularities. Numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced form by a simple formulation. Furthermor...

We review spectral methods for the solution of hyperbolic problems. To keep the discussion concise, we focus on Fourier spectral methods and address key issues of accuracy, stability, and convergence of the numerical approximations. Polynomial methods are discussed when these lead to qualitatively different schemes as, for instance, when boundary conditions are required. The discussion includes...

User profiling is a useful primitive for constructing personalised services, such as content recommendation. In the present paper we investigate the feasibility of user profiling in a distributed setting, with no central authority and only local information exchanges between users. We compute a profile vector for each user (i.e., a lowdimensional vector that characterises her taste) via spectra...

Anum ber of spectral modeling approaches in the engineering and estimation lit.erature are potentially applicable to stochas. ic synthesis in computer graphics. Two specific approaches are developed. The orthogonality principle of estimation theory is used to derive a stochastic subdivision construction with specified autocorrelation and spectrum properties; this approach also provides an alter...

In many natural settings, the analysis goal is not to characterize a single data set in isolation, but rather to understand the difference between one set of observations and another. For example, given a background corpus of news articles together with writings of a particular author, one may want a topic model that explains word patterns and themes specific to the author. Another example come...

I apply Fourier and Chebyshev spectral methods to derive accurate and efficient algorithms for velocity continuation. As expected, the accuracy of the spectral methods is noticeably superior to that of the finite-difference approach. Both methods apply a transformation of the time axis to squared time. The Chebyshev method is slightly less efficient than the Fourier method, but has less problem...