Related papers: MEGS: Morphological Evaluation of Galactic Structu…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

We apply and compare various Artificial Neural Network (ANN) and other algorithms for automatic morphological classification of galaxies. The ANNs are presented here mathematically, as non-linear extensions of conventional statistical…

(Abridged) Environmental differences in the stellar populations of early-type galaxies are explored using principal component analysis (PCA), focusing on differences between elliptical galaxies in Hickson Compact Groups (HCGs) and in the…

Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas…

With the development of modern technologies such as IFUs, it is possible to obtain data cubes in which one produces images with spectral resolution. To extract information from them can be quite complex, and hence the development of new…

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Ongoing and upcoming galaxy surveys are providing precision measurements of galaxy clustering. However a major obstacle in its cosmological application is the stochasticity in the galaxy bias. We explore whether the principal component…

The spectrum of a galaxy is a complicated convolution of many properties of the galaxy, such as the star formation history (SFH), initial mass function, and metallicity. Inferring galaxy properties from the observed spectrum via spectral…

We use Principal Component Analysis (PCA) to analyze a volume-limited sample from the SDSS and explore how cosmic web environments affect the interrelations between various galaxy properties, such as $(u-r)$ colour, stellar mass, specific…

Cosmological galaxy formation simulations can now produce rich and diverse ensembles of galaxy histories. These simulated galaxy histories, taken all together, provide an answer to the question "how do galaxies form?" for the models used to…

From a purely photometric perspective galaxies are generally decomposed into a bulge+disc system, with bulges being dispersion-dominated and discs rotationally-supported. However, recent observations have demonstrated that such a framework…

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model…

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…