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We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys using a principal component analysis of the Fisher matrix. We simulate realistic survey topologies with non-uniform sky coverage, and quantify the effect of survey geometry, depth and noise from intrinsic galaxy ellipticities on the parameter errors. This analysis allows us to optimise the survey geometry. Using the shear two-point correlation functions and the aperture mass dispersion, we study various degeneracy directions in a multi-dimensional parameter space spanned by Omega_m, Omega_Lambda, sigma_8, the shape parameter Gamma, the spectral index n_s, along with parameters that specify the distribution of source galaxies. If only three parameters are to be obtained from weak lensing data, a single principal component is dominant and contains all information about the main parameter degeneracies and their errors. The variance of the dominant principal component of the Fisher matrix shows a minimum for survey strategies which have small cosmic variance and measure the shear correlation up to several degrees [abridged].
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
We study the estimators of various second-order weak lensing statistics such as the shear correlation functions xi_pm and the aperture mass dispersion <M_ap^2> which can directly be constructed from weak lensing shear maps. We compare the efficiency
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