Related papers: Classification and redshift estimation by principa…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous…
QSOs and radio-galaxies, together with the CMB, ``normal'' galaxies and clusters, represent the main source of information about the origin and evolution of the Large Scale Structure. They can be used either directly, as tracers of the…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
The Pan-STARRS1 (PS1) $3\pi$ survey is a comprehensive optical imaging survey of three quarters of the sky in the $grizy$ broad-band photometric filters. We present the methodology used in assembling the source classification and…
Clusters of galaxies are important laboratories for understanding both galaxy evolution and constraining cosmological quantities. Any analysis of clusters, however, is best done when one can reliably determine which galaxies are members of…
In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…
The redshifts of galaxies are a key attribute that is needed for nearly all extragalactic studies. Since spectroscopic redshifts require additional telescope and human resources, millions of galaxies are known without spectroscopic…
We use the measured fluxes of polycyclic aromatic hydrocarbon (PAH) emission features at 6.2, 7.7, 8.6, 11.0 and 11.2 $\mu$m in the reflection nebula NGC 2023 to carry out a principal component analysis (PCA) as a means to study previously…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
We develop an efficient method to represent nuclear densities using basis functions extracted via Principal Component Analysis (PCA). Applying PCA to densities of 75 nuclei calculated with the relativistic continuum Hartree-Bogoliubov…
This is the first paper of a series where we study the clustering of LRG galaxies in the latest spectroscopic SDSS data release, DR6, which has 75000 LRG galaxies covering over 1 $Gpc^3/h^3$ at $0.15<z<0.47$. Here we focus on modeling…
We describe a new method for measuring the true redshift distribution of any set of objects studied only photometrically. The angular cross-correlation between objects in a photometric sample with objects in some spectroscopic sample as a…
Instruments using arrays of many bolometers have become increasingly common in the past decade. The maps produced by such instruments typically include the filtering effects of the instrument as well as those from subsequent steps performed…
The identification of physically associated kiloparsec-scale quasar pairs is important for understanding galaxy evolution, the growth of supermassive black holes, and their co-evolution with host galaxies. However, their rarity and the high…
Machine learning techniques, specifically the k-nearest neighbour algorithm applied to optical band colours, have had some success in predicting photometric redshifts of quasi-stellar objects (QSOs): Although the mean of differences between…
The Red-Sequence Cluster Survey (RCS) provides a large and deep photometric catalog of galaxies in the $z'$ and $R_c$ bands for ~90 square degrees of sky, and supplemental $V$ and $B$ data have been obtained for 33.6 deg$^{2}$. We compile a…
Studies of the distribution and evolution of galaxies are of fundamental importance to modern cosmology; these studies, however, are hampered by the complexity of the competing effects of spectral and density evolution. Constructing a…