Related papers: Exploiting Non-Linear Structure in Astronomical Da…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
The development of fast and accurate methods of photometric redshift estimation is a vital step towards being able to fully utilize the data of next-generation surveys within precision cosmology. In this paper we apply a specific approach…
Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical…
Clustering is an effective tool for astronomical spectral analysis, to mine clustering patterns among data. With the implementation of large sky surveys, many clustering methods have been applied to tackle spectroscopic and photometric data…
Classification is valuable and necessary in spectral analysis, especially for data-driven mining. Along with the rapid development of spectral surveys, a variety of classification techniques have been successfully applied to astronomical…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
One of the main goals of modern observational cosmology is to map the large scale structure of the Universe. A potentially powerful approach for doing this would be to exploit three-dimensional spectral maps, i.e. the specific intensity of…
Spectroscopy is one of the most important tools that an astronomer has for studying the universe. This chapter begins by discussing the basics, including the different types of optical spectrographs, with extension to the ultraviolet and…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with…
Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low…
Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…
Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar…
A trade-off between speed and information controls our understanding of astronomical objects. Fast-to-acquire photometric observations provide global properties, while costly and time-consuming spectroscopic measurements enable a better…
Data-driven stellar classification has a long and important history in astronomy, dating as far back as Annie Jump Cannon's "by eye" classifications of stars into spectral types still used today. In recent years, data-driven spectroscopy…
Temporal and spectral information extracted from a stream of photons received from astronomical sources is the foundation on which we build understanding of various objects and processes in the Universe. Typically astronomers fit a number…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
Some spectral data analysis methods that are useful for the two-dimensional imaging diagnostics data are introduced. It is shown that the frequency spectrum, the local dispersion relation, the flow shear, and the nonlinear energy transfer…
Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…