Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.adass.org/adass/proceedings/adass94/decarvalhor.ps Äàòà èçìåíåíèÿ: Tue Jun 13 20:53:31 1995 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 03:19:48 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: propulsion

Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
Clustering Analysis Algorithms and Their Applications to
Digital POSS­II Catalogs
R. R. de Carvalho 1 , S. G. Djorgovski, and N. Weir
California Institute of Technology, MS 105­24, Pasadena, CA 91125
U. Fayyad, K. Cherkauer 2 , J. Roden, and A. Gray
Jet Propulsion Laboratory, MS 525­3600, Pasadena, CA 91109
Abstract. We report on the preliminary results of experiments using a
Bayesian cluster method to cluster objects present in photographic images
of the POSS­II. Our goal is to explore the power of unsupervised learning
techniques to classify objects meaningfully, and perhaps to discover previ­
ously unrecognized object categories in digital sky surveys. Our primary
finding is that the program we used, AutoClass, was able to form seve­
ral sensible categories from a few simple attributes of the object images,
separating the data into four recognizable and astronomically meaningful
classes: stars, galaxies with bright central cores, galaxies without bright
cores, and stars with a visible ``fuzz'' around them. Also, in an inde­
pendent experiment we found out that the two types of galaxies have
distinct color distributions (the more concentrated class being redder, as
indeed expected if they are predominantly early Hubble types), although
no color information was given to AutoClass. This illustrates the power
of unsupervised classification techniques to discriminate between astro­
nomically distinct types of objects on the basis of data alone. We believe
that the application of such algorithms to large­scale astronomical sky
surveys can aid in cataloging the detected objects, and may even have
the potential to discover new categories of objects.
1. Introduction
The last two decades have witnessed the cataloging of the northern and southern
hemispheres through the use of high­quality photographic plates combined with
CCD frames (van Altena 1993). These digital sky surveys amount to ¸5--6
TB worth of data, resulting in catalogs of many millions---or even billions---of
objects. This richness of information requires new, efficient tools to explore the
resulting data spaces (Weir et al. 1993a).
1 On Leave of Absence from Observat'orio Nacional/Cnpq, Rio de Janeiro, CEP 20921, Brazil
2 University of Wisconsin, Madison, WI 53706
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A crucial point in constructing scientifically useful object catalogs is the
star/galaxy separation. Various supervised classification schemes can be used
to produce consistent results in this task (Valdes 1982; Beard et al. 1990; Ode­
wahn et al. 1992; Weir et al. 1995). However, a more difficult problem is
systematically and objectively to provide at least rough morphological types for
the galaxies detected, without visual inspection of the plates or scans---which is
impractical for obvious reasons. We have thus started to explore new clustering
analysis and unsupervised classification techniques for this task. Our goal is to
try to separate astronomically meaningful morphological types on the basis of
the data themselves, rather than some preconceived scheme.
Thus we investigate the possibility of finding natural (data­based) parti­
tions of the attribute spaces which show high correlations between the plate­
measured attribute space, and the CCD­based attribute space, or a high degree
of separation between expected classes such as stars versus galaxies, spirals ver­
sus ellipticals, or galaxies of different concentrations. These partitions of the
data may be used for investigations of unusual regions of the attribute space,
and may even lead to a discovery of the previously unknown objects or classes
of objects.
2. Data and Methodology
We use the data from the digitized version of the Second Palomar Observatory
Sky Survey (POSS­II). For brief descriptions of the survey, see (Djorgovski et
al. 1994; Reid and Djorgovski 1993; Weir et al. 1993b; Weir et al. 1994; Weir
1995). We have used data from 3 fields from POSS­II, numbers 380 (J­Band),
442 (J­Band), and 679 (J and F Bands).
The following attributes were used for the analysis: (1) resolution scale,
(2) resolution fraction (these two are described in Valdes 1982), (3) ellipticity,
(4) normalized core magnitude, (5) normalized area, (6) first intensity moment,
and (7) the S parameter introduced by Collins et al. (1989). We have used
only objects classified as galaxies and stars by using the Decision Tree technique
(Weir et al. 1995). It is important to emphasize that we are not intentionally
using legitimate attributes like colors, mean surface brightness and concentration
index, which are available in our catalogs, because at this point they can help
us understand the association between the classes which come out from the
experiment and the large scale distribution of galaxies. Also, the classification
is not given to the algorithm but is only used to judge its performance.
AutoClass (Cheeseman et al. 1988) is an unsupervised learning algorithm
that fits user­specified probability distribution models to a set of examples rep­
resented as feature vectors. Classes are represented probabilistically as par­
ticular parameterizations of the models. In these experiments, we used multi­
dimensional Gaussian models. AutoClass uses Bayesian techniques to estimate
the parameter values of each class. It also tries to find the most probable number
of classes by comparing the likelihoods of the fits for different numbers of classes.
Objects are then assigned probabilistic memberships in the output classes.
The Gaussians used to model the classes can range from noncovariant (i.e.,
axis­aligned) to fully covariant based on prior knowledge the user may have of
the attributes and problem. In our experiments here, we used only models that

3
Figure 1. The (g \Gamma r) color versus normalized core magnitude, for the
four types of objects found by AutoClass: galaxies without a bright core
(open circles), galaxies with a bright core (solid circles), stars (crosses),
and stars with fuzz (solid triangles).
had no covariance. We ran some simple tests using synthetic data to verify that
AutoClass's behavior was reasonable in each of these cases.
3. Discussion
In our first experiment we used data from the fields 380 and 442. AutoClass
was able to find four natural classes of objects in the data space. These four
classes were, by visual inspection, identified with stars, galaxies with a bright
core, galaxies without a bright core, and stars with fuzz around them. Thus, the
object classes found by AutoClass are astronomically meaningful, even though
the program itself does not know about stars, galaxies, and such! These results
were obtained using data in a given bin of magnitude (17 m ! r ! 18 m ), although
the same trends were found for a bin one magnitude fainter. The results are
robust and repeatable from field to field.
By inspecting the so­called confusion matrix, we found that each cluster
identified by AutoClass corresponds to the type of the objects, as classified by
the Decision Tree (a supervised classification approach). The Decision Tree
was trained to recognize only two classes of objects, stars and galaxies, and no
attempt was made to make any morphological distinctions among the galaxies.
Another experiment was done using another field in two colors (442 J and
F), both in order to check the previous finding, and also to explore a little
more deeply the meaning of these classes. Again, AutoClass found the same
four significant classes in the data space, which confirms the robustness of the
method.
Figure 1 displays the (g \Gamma r) color versus the normalized core magnitude
(one of the attributes used in the experiment). As can be seen, the two mor­
phologically distinct classes of galaxies, represented by solid and open circles,

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populate different regions of the data space, and have systematically different
colors, even though AutoClass was not given the color information. In this figure
we display stars as crosses and stars with fuzz around as solid triangles.
The confusion matrix for such experiments indicates that stars and galaxies,
as classified by Decision Tree, are well separated in different classes. Galaxies are
distributed in two classes, representing redder and bluer systems, respectively---
presumably the early and late Hubble types, respectively.
We are now exploring our database from POSS­II in a systematic way using
such techniques to map the large scale structure (clustering in the physical space)
in an unbiased fashion. One project is to objectively define and discover clusters
and groups of galaxies, which can then be used for a variety of follow­up studies.
A full paper will be presented in near future describing in detail the appli­
cation of AutoClass to POSS­II and similar data.
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Weir, N., Djorgovski, S., & Fayyad, U. 1995. AJ, in press