Related papers: Eigengalaxies: describing galaxy morphology using …
We present in this paper a new three-dimensional galaxy classification system designed to account for the diversity of galaxy properties in the nearby universe. To construct this system we statistically analyse a sample of >22,000 galaxies…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
We demonstrate the use of an eigenbasis that is derived from principal component analysis (PCA) applied on an ensemble of random-noise images that have a "red" power spectrum; i.e., a spectrum that decreases smoothly from large to small…
(Abridged) Motivated by forthcoming data from the Sloan Digital Sky Survey, we present a theoretical framework that can be used to interpret Principal Component Analysis (PCA) of disk galaxy properties. We use the formalism introduced by…
We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and…
Quantitative morphological classification of galaxies is important for understanding the origin of type frequency and correlations with environment. But galaxy morphological classification is still mainly done visually by dedicated…
Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images…
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,…
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…
As available data sets grow in size and complexity, advanced visualization tools enabling their exploration and analysis become more important. In modern astronomy, integral field spectroscopic galaxy surveys are a clear example of…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
(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…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
We present an unsupervised machine learning technique that automatically segments and labels galaxies in astronomical imaging surveys using only pixel data. Distinct from previous unsupervised machine learning approaches used in astronomy…
Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses…
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…
Mapping human genetic variation is fundamentally interesting in fields such as anthropology and forensic inference. At the same time patterns of genetic diversity confound efforts to determine the genetic basis of complex disease. Due to…
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…
We use automated surface photometry and pattern classification techniques to morphologically classify galaxies. The two-dimensional light distribution of a galaxy is reconstructed using Fourier series fits to azimuthal profiles computed in…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…