Most of the applicationsin this section are made by astronomers utilizing data mining algorithms.However, several projects and studies have also been made by data miningexperts utilizing astronomical data, because, along with other fields such ashigh energy physics and medicine, astronomy has produced many large datasetsthat are amenable to the approach. Examples of such projects include the SkyImage Cataloging and Analysis System (SKICAT) 111 for catalog productionand analysis of catalogs from digitized sky surveys, in particular the scans ofthe second Palomar Observatory Sky Survey; the Jet Propulsion LaboratoryAdaptive Recognition Tool (JARTool) 112, used for recognitionof volcanoes in the over 30,000 images of Venus returned by the Magellanmission; the subsequent and more general Diamond Eye 113; and the LawrenceLivermore National Laboratory Sapphire project 114 3.1.

Object classificationClassification is oftenan important initial step in the scientific process, as it provides a methodfor organizing information in a way that can be used to make hypotheses and tocompare with models. Two useful concepts in object classification are the completeness andthe efficiency, also known as recall and precision. They aredefined in terms of true and false positives (TP and FP) and true and falsenegatives (TN and FN). The completeness is the fraction of objects that aretruly of a given type that are classified as that type: and the efficiency is thefraction of objects classified as a given type that are truly of that type These two quantities areastrophysically interesting because, while one obviously wants both highercompleteness and efficiency, there is generally a tradeoff involved.

Theimportance of each often depends on the application, for example, aninvestigation of rare objects generally requires high completeness whileallowing some contamination (lower efficiency), but statistical clustering ofcosmological objects requires high efficiency, even at the expense ofcompleteness.3.1.1. Star-GalaxySeparationDue to their smallphysical size compared to their distance from us, almost all stars areunresolved in photometric datasets, and thus appear as point sources. Galaxies,however, despite being further away, generally subtend a larger angle, and thusappear as extended sources.

However, other astrophysical objects such asquasars and supernovae, also appear as point sources. Thus, the separation ofphotometric catalogs into stars and galaxies, or more generally, stars,galaxies, and other objects, is an important problem. The sheer number of galaxiesand stars in typical surveys (of order 108 or above) requiresthat such separation be automated.This problem is a wellstudied one and automated approaches were employed even before current datamining algorithms became popular, for example, during digitization by thescanning of photographic plates by machines such as the APM 116 and DPOSS 117. Several data miningalgorithms have been employed, including ANN 118, 119, 120, 121, 122, 123, 124, DT 125, 126, mixture modeling 127, and SOM 128, with most algorithmsachieving over 95% efficiency. Typically, this is done using a set of measuredmorphological parameters that are derived from the survey photometry, withperhaps colors or other information, such as the seeing, as a prior. Theadvantage of this data mining approach is that all such information about eachobject is easily incorporated. 3.

1.2. GalaxyMorphologyAs shown in Fig. 5, galaxies come in a range of different sizes andshapes, or more collectively, morphology. The most well-known system for themorphological classification of galaxies is the Hubble Sequence of elliptical,spiral, barred spiral, and irregular, along with various subclasses 129, 130, 131, 132, 133, 134.

This system correlatesto many physical properties known to be important in the formation andevolution of galaxies 135, 136. Because galaxy morphology is a complex phenomenon that correlatesto the underlying physics, but is not unique to any one given process, theHubble sequence has endured, despite it being rather subjective and based onvisible-light morphology originally derived from blue-biased photographicplates. The Hubble sequence has been extended in various ways, and for datamining purposes the T system 149, 150 has been extensivelyused. This system maps the categorical Hubble types E, S0, Sa, Sb, Sc, Sd, andIrr onto the numerical values -5 to 10.One can, therefore, traina supervised algorithm to assign T types to images for which measuredparameters are available.

Such parameters can be purely morphological, orinclude other information such as color. A series of papers by Lahav andcollaborators 152, 153, 154, 155, 104, 156 do exactly this, byapplying ANNs to predict the T type of galaxies at low redshift, and findingequal accuracy to human experts. ANNs have also been applied to higher redshiftdata to distinguish between normal and peculiar galaxies 157, and the fundamentallytopological and unsupervised SOM ANN has been used to classify galaxies fromHubble Space Telescope images 74, where the initialdistribution of classes is not known.

Likewise, ANNs have been used to obtainmorphological types from galaxy spectra. 1583.2.Photometric redshiftsAn area of astrophysicsthat has greatly increased in popularity in the last few years is theestimation of redshifts from photometric data (photo-zs). This isbecause, although the distances are less accurate than those obtained withspectra, the sheer number of objects with photometric measurements can oftenmake up for the reduction in individual accuracy by suppressing the statisticalnoise of an ensemble calculation.

The two common approachesto photo-zs are the template method and the empirical training setmethod. The template approach has many complicating issues 250, including calibration,zero-points, priors, multiwavelength performance (e.g.

, poor in themid-infrared), and difficulty handling missing or incomplete training data. Wefocus in this review on the empirical approach, as it is an implementation ofsupervised learning. 3.2.1. GalaxiesAt low redshifts, thecalculation of photometric redshifts for normal galaxies is quitestraightforward due to the break in the typical galaxy spectrum at 4000A.

Thus,as a galaxy is redshifted with increasing distance, the color (measured as adifference in magnitudes) changes relatively smoothly. As a result, bothtemplate and empirical photo-z approaches obtain similar results, aroot-mean-square deviation of ~ 0.02 in redshift, which is close to the bestpossible result given the intrinsic spread in the properties 251. This has been shownwith ANNs 33, 165, 156, 252, 253, 254, 124, 255, 256, 257, 179, SVM 258,259, DT 260, kNN 261, empirical polynomialrelations 262, 251, 247, 263, 264, 265, numeroustemplate-based studies, and several other methods. At higher redshifts,obtaining accurate results becomes more difficult because the 4000A break isshifted redward of the optical, galaxies are fainter and thus spectral data aresparser, and galaxies intrinsically evolve over time. While supervised learninghas been successfully used, beyond the spectral regime the obvious limitationarises that in order to reach the limiting magnitude of the photometricportions of surveys, extrapolation would be required. In this regime, or whereonly small training sets are available, template-based results can be used, butwithout spectral information, the templates themselves are being extrapolated.

However, the extrapolation of the templates is being done in a more physicallymotivated manner. It is likely that the more general hybrid approach of usingempirical data to iteratively improve the templates, 266, 267, 268, 269, 270, 271 or the semi-supervisedmethod described in Section 2.4.3 will ultimately provide a more elegantsolution. Another issue at higher redshift is that the available numbers ofobjects can become quite small (in the hundreds or fewer), thus reintroducingthe curse of dimensionality by a simple lack of objects compared to measuredwavebands.

The methods of dimension reduction (Section 2.3) can help to mitigate this effect.

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