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Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts spectra and afterglows is discussed in this paper. The analysis indicates that three principal components are enough among the eight ones to describe the variablity of the data. The correlation between spectral index alpha and the redshift suggests that the thermal emission component becomes more dominant at larger redshifts.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any b
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlyin
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fiel
We consider the problem of principal component analysis from a data matrix where the entries of each column have undergone some unknown permutation, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that for
From a Principal Component Analysis (PCA) of 78 z~3 high quality quasar spectra in the SDSS-DR7, we derive the principal components characterizing the QSO continuum over the full wavelength range available. The shape of the mean continuum, is similar