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Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
In the last decade we have seen an enormous increase in the size and quality of spectroscopic galaxy surveys, both at low and high redshift. New statistical techniques to analyse large portions of galaxy spectra are now finding favour over…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…
An impressive amount of different astrophysical data converges towards the picture of a spatially flat universe undergoing a today phase of accelerated expansion. The nature of the dark energy dominating the energy content of the universe…
We review the current status of cosmological parameters, dark energy and large-scale structure, from a theoretical and observational perspective. We first present the basic cosmological parameters and discuss how they are measured with…
While the accelerated expansion of the Universe is by now well established, an underlying scalar field potential possibly responsible for this acceleration remains unconstrained. We present an attempt to reconstruct this potential using…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
We put forward a new model-independent reconstruction scheme for dark energy which utilises the expected geometrical features of the luminosity-distance relation. The important advantage of this scheme is that it does not assume explicit…
This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…
The main aim of this paper is to perform a model comparison for some reconstructions of the key properties that describe the dark energy of the Universe i.e. energy density and the equation of state (EoS). We carry out this process by using…
Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
We consider state reconstruction from the measurement statistics of phase space observables generated by photon number states. The results are obtained by inverting certain infinite matrices. In particular, we obtain reconstruction…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
The quintessence dark energy potential is reconstructed in a model-independent way. Reconstruction relies on a Gaussian process and on available expansion-rate data. Specifically, 40-point values of $H(z)$ are used, consisting of a 30-point…