Some new algorithms for the spectral dichotomy methods

New Estimates of the Spectral Dichotomy

We derive new estimates of the spectral dichotomy for matrices and matrix pencils which are based upon estimates of the restrictions of Green functions associated with the spectrum dichotomy problem onto the stable and unstable invariant subspaces and estimates of angles between these subspaces. De nouvelles estimations pour la dichotomie spectrale R esum e : Nous etablissons de nouvelles estim...

Some New Methods for Prediction of Time Series by Wavelets

Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...

New Methods for Spectral Clustering

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...

Effective Algorithms for Spectral Methods with Applications

Some uses of spectral methods

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.