JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 99, NO. E5, PAGES 10,847-10,865, MAY 25, 1994
Classification of asteroid spectra using a neural network
E. S. Howell, E. Mer6nyi, and L. A. Lebofsky
Lunar and PlanetaryLaboratory,Universityof Arizona,Tucson
Abstract. The 52-colorasteroidsurvey(Bell et al., 1988) togetherwith the
8-colorasteroidsurvey(Zellneret al., 1985) providea data set of asteroidspectra
spanning0.3-2.5 pm. An artificial neuralnetworkclusterstheseasteroidspectra
basedon their similarity to each other. We have also trained the neural network
with a categorizationlearningoutput layer in a supervisedmodeto associatethe
establishedclusterswith taxonomic classes.Results of our classificationagree with
Tholen's classificationbasedon the 8-colordata alone. When extendingthe spectral
rangeusingthe 52-colorsurveydata, we find that somemodificationof the Tholen
classesis indicated to producea cleaner, self-consistentset of taxonomic classes.
After supervisedtraining usingour modifiedclasses,
the networkcorrectlyclassifies
both the training examples,and additional spectrainto the correct classwith an
averageof 90% accuracy.Our classificationsupportsthe separationof the K class
from the S class,as suggested
by Bell et al. (1987), basedon the near-infrared
spectrum. We definetwo end-membersubclasses
which seemto have compositional
significancewithin the S class: the So class,which is olivine-richand red, and
the Sp class,which is pyroxene-richand lessred. The remaining S-classasteroids
have intermediate compositionsof both olivine and pyroxene and moderately red
continua. The network clustering suggestssome additional structure within the E-,
M-, and P-class asteroids,even in the absenceof albedo information, which is the
only discriminant betweenthese in the Tholen classification.New relationshipsare
seenbetween the C classand related G, B, and F classes.However, in both cases,
the number of spectrais too small to interpret or determinethe significanceof these
separations.
Introduction
indicate that theseare real divisionsamongthe objects
manifestedin differentways,not artifactsof the paramThe first step to understanding the relationships eterization. However,it is important to rememberthat
may
within a group of diverse objects is to classify them in differentwavelengthranges,spectraldifferences
accordingto their physical characteristics. Many re- resultfrom a singlecompositional
element,andpossibly
searchers have classified asteroids based on various cri-
teria. Tholen and Barucci [1989]have recentlypresented a comprehensive review of the various taxonomies that have been put forth. These taxonomies
are all based on similarities in the reflectancespectra
and in somecasesthe albedosof the objects. The spectrum is related to the surfacecomposition,soany taxonomy basedon these data is at least in someway related
to the surface compositionof the asteroid. However,
many asteroid spectrado not have uniquecompositional
interpretations.
What is striking about the many different systems
of classificationis not so much the differences,but the
similarities. The samegeneralgroupingsappearregardless of the parameterization chosen. These similarities
only a minor constituentof the asteroid.
While a taxonomicsystemis a usefulfirst stepin understandingthe overallstructureof the asteroidbelt, it
necessarily
doesnot includeall the informationwe have
available. In the formal classification, we must limit
ourselves to the data that are available for all of the
objectsconsidered.Thus, interpretationof this or any
asteroidtaxonomyshouldalso considerany additional
piecesof informationthat werenot includedin deriving
the taxonomy itself.
Compositionalstructureseenin the asteroidbelt reflectsnot only compositionalgradientsin the the solar
nebula, but also subsequentprocessingover the age of
the solar system. While it is clear that most of these
objectsare closerto their pristinestate than the larger
planets, they may still be sufficientlyaltered to make
determination
Copyright 1994 by the American GeophysicalUnion.
Paper number 93JE03575.
0148-0227/ 94/ 93JE-03575505.00
of solar nebula conditions difficult.
How-
ever, learningabout the alteration mechanisms
may be
equally valuable. A great successof Tholen's asteroid taxonomy is the clear indication of differencesin
10,847
HOWELL
10,848
the distribution
of different
ET AL.:
CLASSIFICATION
asteroid classes with helio-
centtic distance. However, subsequentwork by Jones
OF ASTEROID
SPECTRA
tional V-type objectshavebeenidentified[Cruikshank
et al., 1991; Binzel and Xu, 1993]. The Q classcur-
et al. [1990]showsthat significanteffectsof later heat- rently includes only near-Earth asteroids. The 52-color
ing eventsare alsopresentand alsohavea strongdepen- survey includes members of all of these classesexcept
denceon heliocentric
distance.Bell et al. [1989]discuss the Q class.
Tholen did not include the asteroid albedo in definadditional asteroidalteration processes
which may also
have a spatial dependence.In somecasesit may not ing his clusters, since scalingthe albedo appropriately
be possibleto distinguishbetweenformation processes to balance the range of color data proved difficult. Afand those attributable
to later events.
In this paper we describe the application of an ar-
ter the clusters were determined, the available albedos
were used to check for internal consistency within a
class. The E, M, and P asteroids are spectrally indis-
tificial neural network (ANN) for the classification
of
asteroid spectra, and present an augmented asteroid tinguishable, but have widely different albedos. Simtaxonomy using that technique. First, previous taxonomic systemsare briefly reviewed and the Tholen taxonomyis described,sinceour systemextendshis system
by using additional spectral information. We briefly
describe the data that were used for our classification
of the asteroids. To compare the neural network technique to the minimum tree classification method that
Tholen used, we use the same 8-color data that Tholen
used for his analysis. Then we apply the neural network technique to the combined 8-color and 52-color
ilarly, the B- and C-type asteroids are not spectrally
well separated, but do have different albedos. However,
the albedos of many asteroids are either unknown or
highly uncertain, and so limit the size of the database
defining the taxonomy. For this reason, we have followed Tholen's method of using only the spectral data,
eventhough the albedoclearly containscompositionally
valuable
information.
Although he did not do a formal classificationusing
the additional spectral information provided by the 52data acquiredby Bell et al. [1988],to take advantage color survey,Bell noticed that the Eos family asteroids
of the larg•.r spectralrange. The resultsand interpre- (a-3.0 AU) seemedto be anomalous
amongthe S class.
tation of the asteroid groupingsare presented,followed These objects show much less reddeningin the continby some notes on unusual objects and caseswhere our uum from 1 to 2.5 /•m, and he suggesteda separate
ANN
classification
Previous
differs from that of Tholen.
Taxonomies
K classfor theseobjects[Bell et al., 1987;Bell, 1988].
However, while all K-type asteroidsare in the Eos family, not all Eos family asteroidsare K types. Tedesco
et al. [1989]alsocreateda K classthat includestwoEos
family members,but extendsto other S-classobjectsas
Tholen identifiedfourteenclasses
of asteroids[Tholen, well. His taxonomy is basedon U, V, and x filter phoIn his asteroid classificationusingthe 8-colorspectra,
1984; Tholen,1989]. The meanspectrafor the Tholen
classes
are shownin Figure 1, after Tholen[1984].He
found two significantprincipal components,one related
to slope and the other to the presenceor absenceof an
absorptionband near 1/•m. Five broad asteroidgroups
were defined, the A, X, D, C, and S classesof asteroids. The A-type asteroidsare a small group of objects
whose spectra are very red, and resemblepure olivine.
The X-type asteroids include the E, M, and P types,
distinguishedfrom each other by albedo. D-type asteroid spectra are very red and do not showany absorption
features. The G-, B-, and F-type asteroidsare closely
related to the C-type asteroids. These classesare distinguished primarily by the steepnessof the spectrum
at 0.3-0.4/•m due to the Fe-O charge-transferabsorption band centeredin the ultraviolet (UV). This band
has been linked to the hydration state of the surface
minerals on asteroids,with increasedoxidation of iron
being related to the presenceof water at some time in
Mean 8-Color Spectrafor Tholen AsteroidClasses
_1
I
I
I
I
I
I
I
I
I
I
I--
1.0
•• 1.0 EM•
•
1.0
m 1.0- •
- 1.0
• 1.0•: ::•
1.0
1.0
1.0
0.8
1.0
0.8
the asteroid'shistory[Feierberg
et al., 1985].However,
not all C-type asteroidsshow evidenceof surfacehy-
dration[Joneset al., 1990;Lebofsky
et al., 1990]. The
S-type asteroidshave variable red slopes,and showeither olivine or pyroxeneabsorptionbands,or both. The
rare R, V, and Q classesare generallysimilar to the S
class,but with much strongerabsorptionbands. The
only memberof the R classis 349 Dembowska.The only
example of the V classwas 4 Vesta, but recently addi-
0.2
0.6
1.0
0.2
0.6
1.0
Wavelength(!zm)
Figure 1. Mean 8-colorspectrafor the T,5olen[1984]
asteroid classesare shown. The spectra are all at the
same scale, but offsetfor clarity. The Q classasteroids
are not representedin our data.
HOWELL
ET AL.:
CLASSIFICATION
tometry (with central wavelengthsof 0.365, 0.550, and
0.701 /•m, respectively)and the IRAS albedo,and did
not include any near-infrared data. In fact, the K class
as defined by Bell is a subset of the Tedescoet al. K
class,in spite of the differencesin the definingspectral
parameters.
OF ASTEROID
SPECTRA
10,849
The taxonomy developed by Tholen is based on the
8-color asteroid survey, which remains unchallengedas
the most complete samplingof the asteroidbelt to date.
The 8-color spectrophotometry spanned 0.3-1.1 •umfor
most of the 589 asteroidssurveyed.A large rangeof heliocentric distanceswas sampled, including groupssuch
Burbine [1991] performeda principal components as the Hildas (3.9 AU) and the Trojans (5.2 AU). The
transformationusingthe 52-colorsurveydata combined
with the 8-color data. He found five significantprincipal components. The first is correlated with the overall
slopeof the spectrum. The secondis correlated with the
depth of the 1-/•m absorptionband, consistentwith the
first two principal components in the 8-color analysis
data are given as magnitudesrelative to the Sun, representedby a mean of four solar analog stars. The spectra
are normalized to 0.0 magnitude at 0.55 •um. Typical
errors are 1-3%, larger in a few cases. Tholen used
405 of the 589 objects, representingthe highest quality spectra for his cluster analysis. We omitted 50 of
[Tholen,1984]. The third is correlatedwith the depths the 589 asteroidswhich had only five of the eight colof both the 1- and 2-/•m absorption bands for most objects, separating olivine-rich objects from pyroxene-rich
objects. The fourth and fifth do not have a clear interpretation, but each contain only 2.2% of the total
variance. He found that the Tholen groups remained
distinct, and did not change or augment that taxonomy. However, it is important to note that Burbine did
not do an independent classification,but only tried the
Tholen groupings and found them adequate. He used
only 66 of the highest quality spectra for his principal
component analysis, and did not have all taxonomic
classesrepresented.
The majority of the 52-color survey asteroidsare S
class. There is considerablediversity in the spectral appearance of these objects, especially between 0.8 and
2.5/•m. However, in the visual range there is also great
diversity, and many workers have suggestedthat subdivisionsamong the S-type asteroidsmay be appropri-
ors measured, but did not exclude any on the basis of
large errors. Since the formation of the cluster structure determined by the neural network is less sensitive
to noise in the data than many classicalmethods, these
two classificationsare comparable.
sevensubgroups.Gaffeyet al. [1993]parameterizedthe
M - -2.5 log10(F)
Bell et al. [1988] carried out a smaller-scaleaster-
oid survey covering 0.8-2.5 /•m for 117 asteroids chosen to represent all of the established Tholen classes.A
circularly variable filter with 3.5%-5.2% spectral resolution was used to obtain 52-color spectrophotometry.
They found that the S-type asteroidsshowedconsiderable variability in the pyroxene and olivine absorption
bands in the near infrared, and changedtheir observing
strategy to include more of these objects; thus 59 of the
117 objects are members of Tholen's S class.
We extended the 52-color data to 0.34/•m by adding
Tholen's 8-color photomerry, matching the spectra in
the region of overlap. Bell et al. reported relative reate. Chapman[1987]suggested
a divisioninto several flectance values, so for consistency,we converted the
groupsbased on the U-B and B-V colors. These were Tholen magnitude valuesto relative reflectance,scaled
not selectedas natural divisionsamong the objects, but
to 1.0 at 0.55 •um. These quantities are related by
as convenient,unambiguousdivisionsof the group into
spectra using the pyroxene band positions and depths where M is magnitude and F is flux, or in this case
to measurepyroxenecompositionand olivine/pyroxene whereit has been divided by the solaranalogflux value,
ratio.
These
measures
were correlated
with
meteorite
compositions in an attempt to determine which asteroids might be likely parent bodies of ordinary chon-
drites. Barucciet al. [1987]combinedthe 8-colorpho-
relative
reflectance.
The 52-color spectra were taken in two sectionswith
different spectral sampling. For convenience,we resampied these data at a uniform spacing throughout the
spectralrange. Seventeenasteroidsdid not have 8-color
photomerry available, but 12 of those had UBV pho-
tometry and IRAS albedos and classified438 asteroids
using G-mode analysis. They obtain four subclasses
of
Tholen's S-type asteroids,though the majority of the tometry reported[Tedesco,
1989],and Tholenclassifiobjects are of the first or SOclass. We compareour di- cations[Tholen,1989].UsingsolarcolorsfromHardorp
visionof the S-type asteroidswith theseother groupings [1980],we convertedthesedata to reflectance,
and used
in a later section.
a cubic spline to produce 0.34- to 0.8-/•m data consistent with the other objectsfor which 8-colorphotometry
The Data
was available. The interpolations were checkedcarefully to guard against artifacts produced by the cubic
The data upon which most asteroidclassificationsys- spline. We used 65 points from 0.34 to 2.57 •um,spaced
tems have been based are reflectancespectra. The two at 0.035 •um, as the input data to the neural network.
surveyswhich we have used, the 8-color survey and the Hence we will refer to these modified spectra as the 6552-color survey, have been describedin detail by Zell- color spectra. Gaps due to telluric water absorption at
her et al. [1985]and Bell et al. [1988],respectively.
We 1.4 and 1.9 •um are also closedin this manner. Since
will briefly summarizethesedata here, and describethe the spline sampling is comparableto the original specmodificationsthat weremadebeforeenteringthesedata tral resolution of the data in most of the range, the
into the neural network.
noise variability is reproduced by the spline with only
lO,85o
HOWELL ET AL.: CLASSIFICATION
minimal smoothing. The errors are not explicitly used
by the neural network. A classificationusing only the
52-color data in its original form showedlittle differencefrom the versionbasedon resampleddata, giving
confidence that this treatment
OF ASTEROID
SPECTRA
Xo
I = Y'iWjiXi summation
x.
1 •
yj=f(I)
o
did not affect the results.
During the 52-color survey, severalasteroidswere observed on two or more different nights. These spectra
were examined individually, and in those caseswhere
the spectra were nearly identical, they were averaged
to improve the signal-to-noiseratio. When the spectra were sufficientlydifferent, they were not averaged,
and two versionswere retained. We definesignificantly
different as point to point differencesof more than two
sigma for three or more adjacent points. Two spectra
of 367 Amicitia showedsignificantvariation, but since
no visibledata were availablefor this object, it was not
included in either classification. There were four separate spectra of 43 Ariadne with two distinct shapes.
Each pair was averaged,but the two differently shaped
spectra were retained. Altogether, 20 objectswere observedon two or more nights, and six of thoseshowed
spectralvariation. These differencesmay be due to surface inhomogeneity,but could also be due to lightcurve
variations during the time necessaryto obtain the spec-
transfer
Weiglts
Xr/
Y'
element
Figure 2. The structure of a processingelement, the
buildingblockof neural networks,is shown.Each processingelement computes the weighted sum of its inputs. The weights, Wi, are adjusted during the learning process. The output of the processingelement is
a function, called the transfer function, of this sum.
In general, the transfer function is a nonlinear function. Reproduced with permission from NeuralWare,
Inc. [1991].
errors are also possible, though we feel they are less
likely. Additional observationsof these asteroidswould
be especiallyvaluable to resolve this issue.
layer receivessignalsfrom its input connections. For
example, at the ;_spurlayer, each PE will receive the
weighted sum of all the spectral channelsof a given
spectrum.This weightedsumis transformedby the socalled transfer function, which is generally a nonlinear
Artificial
function(e.g., sigmoid,hyperbolictangent,or similar
function). The result is sent to the PE's output con-
trum.
Other
sources of observational
Neural
or instrumental
Networks
The human eye and brain are extremely efficient at
pattern recognitioncomparedto traditional image processingalgorithms. Ideally, to classifygroupsof spectra into generalizedgroups, we would like to look at
and evaluate each example. However, as databasesget
large, this is not a practical technique,nor are we able
to be unbiased in our view of the data.
We tend to see
the features we can interpret as dominating the spectrum, and to ignorethosefeatureswhich we cannot interpret. Over the last decade, ANNs have been shown
to excel in the field of pattern recognitionand classi-
fication [Mer•nyi et al., 1993a; Mer•nyi et al., 1993b;
Huang and Lippman, 1987]. They are able to handle
nections,which in turn will be input to the PEs in the
next layer. The data are driven through the network
in this fashionand finally an output vector is presented
at the top layer. For example, this vector can represent
the labels of different classes,encoded in the form of
Output
t t
buffer
t
Hidden (
Ioyer
large data sets easily and quickly. A very good review
on ANNs is givenby Pao [1989].
ANNs are massivelyparallel, finely distributed computing architecturesthat mimic the information processingof the nervoussystemin a simplifiedway. They
consistof a large number of artificial neurons,or pro-
Inpuf
buffer
Figure 3. A sampleartificial neural networkintercon-
cessingelements(PEs) as shownin Figure 2. These nection pattern is shown. The circles representprosimple PEs are (usually) identical, and are densely cessingelements(PEs). Data flow from bottomto top.
wired into a net-like structure with weighted connections. This net structure is typically organized into
one input, one output, and one or more hidden layers. An example for an ANN architecture is illustrated
in Figure 3. PEs in one layer can be connectedto any
PE in other layers. For the networks in this study, all
PEs in a given layer are connectedto all PEs in the
subsequentlayer. At any time step, each PE in each
In this example, each element of the hidden layer receivesinput from eachdata channelin the input buffer.
Similarly,eachelementof the output bufferreceivesinput from all elements of the hidden layer. The dense
interconnectivity gives the network its computational
flexibility. The interconnectionpattern betweenPEs is
one of the main characteristics of a particular neural
network paradigm. Reproducedwith permissionfrom
NeuralWare,Inc. [1991].
HOWELL
ET AL.:
CLASSIFICATION
OF ASTEROID
SPECTRA
10,851
binary vectors(classA = 1, 0, ..., 0; classB = 0, 1,
..., 0, etc.).
In supervisedtraining, ANNs learn to derivethe characteristics
of a groupof spectra(a class)from a subset of that groupfor whichthe classmemberships
(the
classlabels)are known. The collectionof suchsubsets
(2-D) hiddenlayer (the Kohonenlayer), basedon their
siredoutput (the correctclasslabel) for this pattern.
The adjustmentprocedureis prescribed
by the so-called
learningrule. If the trainingsamplesare consistent,
the
training will convergeafter somenumberof iterations,
i.e., the weightswill no longerchangesignificantly.
At
training hasconverged(no moresignificantchangesoccur in the weights),we switch to the supervisedphase
similarity to each other. Each PE becomes a representative of several input patterns: very similar patterns will be mapped onto the same PE or PEs that
are close to each other in terms of their input connection weights. The similarity measurein this caseis the
for all classesis the training set, and the spectra in Euclidean distance, but could be different if so dictated
this set are called the training spectra. These patterns by the characteristicsof the data. The minimum tree
are presentedmany times to the network along with algorithm used by Tholen also usesthe Euclidean distheir known classlabels. For a given pattern, the net- tance as the similarity measure. This topologicalmap,
work comparesits own actual output with the known together with the Euclidean distancesbetweenthe PEs
classlabel (this latter is the "desiredoutput" in neu- in terms of their weights, yield information about the
ral net terminology). Basedon the differencebetween cluster structure of the data as explained below. No
the actual and desired output, the weightsthroughout a priori assumptionon the number, size, or center of
the entire network are then adjusted so that next time
the clusters is used. The output layer is not learning
the actual output more closelyapproximatesthe de- during the unsupervisedphase. After the unsupervised
this point, the networkis trained, which meansthat it
will givethe correctlabel for the trainingpatterns,and
and train the output layer to associate the previously
clustered patterns into the classesthat are thought to
be meaningful. As we mentioned above, the network
will have difficulty if we try to teach class labels that
are in contradiction
with
the cluster
structure
it has
formed. Decisionsabout meaningful classesare based
on initial assumptionsabout taxonomic classes,and in
ing samplescan preventconvergence
of the training. In some casesadditional data, such as albedo and a possomecases,the network may be able to learn inconsis- teriori interpretations of clustersthat the network may
of the S
tent labels, but then it will not be able to make good suggest(as was the casewith the subclasses
predictionsfor unknownpatterns basedon that knowl- asteroids).
edge.
The 2-D Kohonen layer maps the n-dimensionaldata
ANNs are proven to be more robust and less sensi- space nonlinearly onto a 2-D lattice, with the presertive to noise than most conventional methods.
Their
vation of the topology, i.e., the similarity relationcapability to learn relationshipsfrom samplesof under- ship among input patterns. Unlike principal comporepresentedor unevenly representedclasses,and learn nent plots, which only present 2-D or three-dimensional
it can make predictionsfor patterns that were not includedin the training set. An inconsistentset of train-
complicated(e.g., nonlinear,embedded)classbound- (3-D) projectionsof the data, the Kohonenmap fully
aries is superiorto most standardtechniques[Huang represents the n-D data space in 2-D, in terms of the
and Lippman, 1987]. The massivelyparalleland dis- ordering of the patterns based on similarity. The infortributed architectureoffersdramatically increasedcomputing speed,often with significantlyreducedmemory
requirementscompared to conventionalsequentialcomputers. The numerousANN paradigms developedfor
variousproblemsdiffer mainly in the connectionpattern
among the PEs, the transfer function and the learning
mation about possiblecluster separationslies in the PE
weights. After appropriate analysis,separationscan be
defined and overlain on this 2-D topologicalmap in the
form of fences,the height of which representsthe degree
of separationbetweenPEs. Ultschand Simeon[1990]
describea successfulapproachto the analysisof the Korule.
honen map and representationof cluster separationsby
these fences. We used their technique with some minor modification. For example, in Figure 5a, the fences
Our Classification
Method
derived from the PE weights are superimposedon the
Kohonen
map, a wider line indicating a stronger sepThe ANN paradigm employedhere is a hybrid network. Its hidden layer is a two-dimensional self- aration, or higher fence. Further developmentof this
organizingmap (SOM) developedby Kohonen[1988], method is in progress and a more detailed discussion
which is coupledwith a categorizationlearning output will be given in a subsequentpaper (E. Mer•nyi et al.,
layer. These two layers have different learning rules. manuscriptin preparation, 1994). The fencesdeterThe mathematical formulaefor self-organizationas well mined at this stage should be consideredpreliminary.
as for the Widrow-Hoff learningrule of the output layer Naturally, these classboundariesare not rigid and can
can be foundin the work by, e.g., Pao [1989].The par- change if more objects are used in the network clusticular software implementation that we used is from tering. An advantage of this ANN paradigm is that
NeuralWare,Inc. [1991]. The layout is shownin Fig- training time is modest, so the classificationcan be easure 4. This ANN performsclassificationin two phases. ily revised as more spectra are obtained. Once trained,
First, in unsupervisedmode, it forms a topologicallyor- the network identifies unknown patterns very quickly
dered map of the input patterns in the two-dimensional and easily.
1o,852
HOWELL
ET AL.:
CLASSIFICATION
OF ASTEROID
SPECTRA
SOMu/C trained on 65 p. data• s65o15• 20+10K6/7/91
Figure 4. The layoutof the Kohonenself-organizing
map, coupledwith a categorizationlearning
output layer is shown. The bottom layer is the input data. The center square is the 2-D hidden
layer, or Kohonenmap. The output layer is shownat the top. Each processing
element(PE)
in the input (bottom) layer is connectedto all PEs in the 2-D Kohonenlayer. All PEs in the
Kohonen layer are connectedto each of the output PEs. For illustration, the input connections
to oneKohonenPE and the connections
of two KohonenPEs to the output (top) layerare drawn
here. Reproducedwith permissionfrom screengraphics,(• NeuralWare, Inc.
In the application of this ANN paradigm to asteroid 8-color and 52-color surveys into a 65-color resampled
classification,
we assumed
the Tholen[1989]classes
were spectrum. We first make a direct comparison of our
a good first estimate of the classmembershipof most classification and Tholen's. The two are based on the
asteroids. The network is initially trained using all of
the spectra with their Tholen class labels. Later, subsets of the available data are used, with someexamples
set aside as "unknowns"
to check the network's
abil-
ity to generalizefrom the examplesit has seen. These
jackknifing tests are describedin more detail in a later
section.
We turned
to the examination
of the Kohonen
map whenthe networkhad difficultylearningthe membership of certain objects. It is important to emphasize
that the cluster structure is defined by the data in the
unsupervisedtraining phase and is not changedin the
supervisedphase. The network only learns to assign
class labels to previously defined areas of the cluster
structure during training. If the labels it is taught are
too sparseor contradictory, it will not learn to identify
the class,and/or it will misclassify
patternswhichwere
not includedin the training set.
Results
The
and
8-Color
Discussion
Classification
We used the neural network to classifyasteroidsfirst
using.the8-colorspectraalone,and then combiningthe
same data, although we used a larger subsetof the 8color data for our classification,including some lower
signal-to-noisespectra. Even though the two classification techniques are very different, the similarity measures are the same. Although the cluster structure is
determined differently, we obtain very similar results,
giving us confidencein the technique. We then apply
the neural network technique to the additional spectral information in the 65-color spectra. We discussthe
classificationresults, and presentsuggestionsfor modifications to the Tholen taxonomic system.
The Kohonen SOM in Figure 5a shows the cluster
structure determined from the neural network, using
only the 8-color data. For comparison,Figure 5b shows
Tholen'sprincipalcomponentanalysis(PCA) with the
clustersdetermined using the minimum tree algorithm.
The heavy lines on the SOM indicate the degreeof separation, or fence height betweenthe PEs, heavier lines
representinghigher fences.Although most of the asteroids in our 8-color classificationagreewith their Tholen
classlabels, there are some that do not, even though
the two techniques used the same data and the same
HOWELL
ET AL.'
CLASSIFICATION
OF ASTEROID
SPECTRA
10,853
15
14
13
12
11
10
8
7
6
4
2
a
b
c
d
e
f
g
h
i
j
k
1 rn n
o
Figure 5a. The topologicalKohonen map for the 8-color spectra is shown. Each grid square
representsa processingelementin the Kohonenhidden layer as shownin Figure 4. Each object
is labeled by its Tholen type. While this map is analogousto Figure 5b, it is not a graph, but
rather a topological map. However, distanceson this map are not linear, becauseit represents
the similarity relationshipsin the full 7-dimensionalspace.The heavy linesrepresentthe degree
of separationbetweenprocessingelementsin 7-dimensionalspace. These can be more easily
visualizedas fencesof varying heights,where heavierlines representhigher fences. The object
labeledS nearthe D classin the upperleft is 152Atala. SeeTable3, explanatorynote6 regarding
this object. See text for analysisof the clusters.
similarity measure. In most casesdisagreementsoccur
when the classesare separated by albedo, not spectral
shape,suchas betweenthe E, M, and P classesor between the C and B classes. Discrepanciesmight also
arise from a mathematically provenshortcomingof the
minimum tree clusteringalgorithm, called the "chain"
effect,which meansthat two objectswill be considered
Figure 5b. This plot from Tholen[1984]showsthe
-2
$ $
-4
v o
•
•
-4
t
-2
FIRST
•
R
I
0
PRINCIPAL
•
I
,,
2
COMPONENT
I
4
I
principal component projection of the 405 high-quality
spectra gathered during the 8-color asteroid survey.
The letters correspond to the Tholen asteroid taxonomic types. The units on the axes are arbitrary. This
2-D projection best illustrates the 7-dimensionalcluster structure
of the data from which Tholen
asteroid taxonomy.
derived his
10,854
HOWELL
ET AL.: CLASSIFICATION
close if a short chain exists between them. The defini-
tion of a short chain is the length of the longestlink
in the chain that leads from one object to the other,
throughany numberof objects.Therefore,two objects
that are connectedby a large •numberof short links,
may be put in the same cluster even if they are far
apart. A completeand rigorousdiscussion
of this can
OF ASTEROID
SPECTRA
classesstill seemto do a reasonablejob. Plate 1 shows
the SOM for the 65-colorspectra,again with linesindi-
catingthe fenceheights,and grid labelsfor easeof dis-
distance of an object from identified cluster centersas
well as the chain length betweenup to three objectsin
the minimum tree to reduce this problem.
In general, the relationshipsof the groupsto each
cussion.For clarification,the different classesare color
coded. For any PE, there are fencesboth diagonally
and horizontallybetweenadjoiningPEs, the heightsof
which are not necessarilyrelated. For example,the So
asteroid354 Eleonora,at 113,is well separatedfromthe
PEs in all directionsexceptdiagonallyto the lowerleft
to k12 and j12. It is not stronglyseparatedfrom the
other So objects. The groupingsare similar to the 8color clusters with the additional spectral information
other in both the Tholen PCA
being clearly most diagnosticfor the S-type asteroids
be found in the work by Fu [1976]. Tholen usedthe
and the Kohonen SOM
(Figures5a and 5b) are the same. For easein referring to the SOM, the grid of PEs are labeled on the
sincethe olivine and pyroxenebandsare providingnew
compositional
information.The diversityin the C-type
asteroidsand related G, B, and F types has decreased,
while the diversity of the S types has increasedwhen
goingfrom 8-colorto 65-colorspectra. This changeis
tinct group in both systems. The C-type asteroidsare certainlydue in part to the smallnumberof samplesof
a diversegroupin both systems.The G-type asteroids these asteroid types. The E-, M-, and P-type objects
are a well-definedsubgroupin the SOM at j5, as well still showsomegroupingsamong themselves,but it is
axes. These should not be interpreted as representing
variables, but rather as analogousto cartographicgrid
labels. The olivine-rich A-type asteroidsare a very dis-
as in the PCA. The F-type asteroidsare also separated
from the C-type objects, but lesstightly clustered. In
the SOM there are some divisionsbetween the F-type
asteroids. The B-type asteroids are only partly separated from the C-type asteroidsin spectral appearance
(note objectsat g4 and gl), but are higherin albedo.
The D-type asteroidsin the upper left corner are well
separated in both systems. In the SOM, there is an
additional separation of two main belt D-type asteroids
in PEs dl4 and d15. The T-type asteroidsseemtransitional betweenthe D- and S-type objectsin the PCA. In
the SOM, they are more closelyrelated to the S types,
and are not strongly separated. Asteroid 570 Kythera
at n14, is weakly separated from the other T-type objects. The S-type asteroidsare alsoa very diversegroup
in both systems,although not divided by large distances
as are the F types. There are somefencesseparatingS
objectssuchas at PEs k5 and 12. Asteroid ll5 Thyra, at
k5, is alsounusualin the 65-colorclassification.The isolated object at 12 is the near-Earth asteroid 1627 Ivar.
The group of S objects near the A asteroidsincludes
many of the objectsdesignatedSo in the 52-colorclassification. The X-type asteroids,that is, the E, M, and
P types, seemto showmore diversityin the SOM than
in the PCA. These objects are well separatedfrom the
S-type and D-type asteroids,but are not well separated
from the C-type asteroids. The distinction betweenCtype and P-type asteroidsis somewhatarbitrary, since
it is basedon the span of colorsamong the M-type objects. The SOM showssomeindicationthat there is a
divisionamongX-type objects,one groupin the upper
right, and anotherin the lowerleft. This possibilitywill
be considered in a later section.
The
65-Color
Classification
When we add more spectral information, we expect
that the cluster structure might be different. However, as Burbine found when performinga PCA on the
combined 8-color and 52-color survey data, the Tholen
not clearly related to the patterns seen in the 8-color
classification. Especiallyin the bottom right part of
the map, the Cv objectsare not well separatedfrom
the P-type objects, the multiple labels indicating contributions from both classtypes.
The
S class.
From examination
of the 65-color
SOM (Plate 1), someinternal groupingswere apparent among the S-classasteroids. The samegroupings
were presentwhen the neural networkwas trained on
the S-typeasteroidsalone. We introducetwo subgroups
amongthe S-type asteroids. The So type, whichare
olivine-rich and reddest, and the Sp type, which are
olivine-poorand least red. The remainingS typesare
intermediate in olivine content and continuum slope.
In the SOM for the 65-color asteroids, the olivine-rich
A-type asteroidsare more similar to the So-typeasteroidsthan to any other type, althougha high fence
surrounds the A class. This association confirms that
spectralsimilarityis correlatedwith composition
in this
case.It is importantto note that thesesubdivisions
do
not necessarilyrepresentnatural divisionsamongthe
former S-classasteroids.That is, a continuumof com-
positionsexistsfrom Soto S and from S to Sp. In our
experiments,
nomisclassification
everoccurred
between
So and Sp. With the divisionwe report,no misclassification occurred between So and S or S and Sp. How-
ever, moving theseboundarieseither toward or away
from the extrema in the continuum slope-olivinespace
mightproduceequallycleansubgroups.
Therearelow
fencesseparatingsomeSp objects,especiallynearh-j,
2-6. Given the small number of spectra, any groupings
which appear well separatedcouldinsteadbe an artifact of this particular set of examples.The important
point is the So and Sp subclasses
definethe endsof a
broad continuum of the former S-class asteroids for fu-
ture studiesof compositionally
differentobjectswhich
may lead to finer divisionswith clearerevolutionaryinterpretations.
HOWELL
ET AL.-
CLASSIFICATION
OF ASTEROID
SPECTRA
T
T
TSo
15
10,855
T
T
14
'
D
13
M
i
'
M
M
P
o
12
!P
11
iCx i
!cx icx i
i
i
10
[
......
'
9
8
7
6
,
,
5
i
'
i
4
3
2
a
b
c
d
e
f
g
h
i
j
k
1
rn
n
o
Plate 1. The topologicalmap formed in the Kohonen layer, as in Figure 5a, for our 65-color
(8-colorcombinedwith 52-color)asteroidspectrais shown.Objectsare labeledwith our modified
types, and color coded for clarity. Distances on the map are nonlinear, even more so than in
Figure 5a, due to the higher dimensionalityof the data. The degreeof separationin the 65-color
spaceis denoted by lines or fences,where heavier lines representhigher fences. Analysis of the
clusters is discussedextensively in the text.
The ordering of the S-type asteroidson the 65-color VJK colorsfor the S asteroids,so our groupingsare not
the same as Chapman's groups.
SOM indicates a trend in spectral shape, but is not useful in itself if we cannot interpret it. Visual inspection
of the spectra indicatesthat the spectralslopewas obviously a major factor in the groupingamong the S-class
asteroids. Figure 6a showsthe V-J versus J-K colors for these S-type asteroids,where the effectivewave-
Barucciet al. [1987]subdividedthe S-classasteroids
based on spectral shape differencesin the 8-color spectra. They designatetheir classesS0-S3, with most of
the objectsfalling in the primary or SOclass. This group
includes the K-class objects. Three of our So objects
lengthsare 0.55, 1.25, and 2.2/•m for V, J, and K filters, are classedas S2 in the Barucci system. These objects
respectively. The rednessof the spectrum was clearly have a steeper slope in the UV region than the main
a factor in determining the cluster structure, but did SOgroup, but are otherwiseindistinguishable.Asteroid
not explain everything. Figure 6a indicates that the 115 Thyra, at 17, is the only example of the S1 group
V-K color is diagnosticfor these asteroids. Previously, in the 65-color data. We classifythis object as Sp, but
Chapman suggestedsubdividingthe S asteroidson the it has an unusual blue spectral slope between 1.5 and
basisof U-B and B-V colors. (Central wavelengths 2.5 ium. Barucci's S1 asteroidsare characterizedby the
for U and B filters are 0.365 and 0.44 ium,respectively.) lowest overall spectral slope, but the slope from 0.3 to
However, there is no correlation between the UBV and 1.1 /•m may not be a good general predictor of slope
10,856
HOWELL
ET AL.' CLASSIFICATION
OF ASTEROID
SPECTRA
1.6
S A•teroids
-
-
1.5
1.1
•
1.os
ß
SAsteroids
[ -
ea
• oO
_
:
-.:
i 1 a a
ao ac•
o ,so
as
b
.3
.4
.5
J-K
.6
osp
.5
.7
1
1.5
2
2.5
Band II/Band I Area
2.2/'"'1"'
ISAsteroids
F Higliest Quality
I
•ee
ß
•1.8•
•
o
• oo
o
0
0
0
_
1.6
0
.5
1
1.5
2
2.5
Band II/Band I Area
0
-
eSo
osp
.5
1
1.5
2
2.5
Band II/Band I Area
Figure 6. (a) A color-colorplot for the asteroidsdesignatedS-typeby Tholenis shown[after Hartmann et al.,
1982]. The broadbandcolorsV-J and J-K, expressed
in magnitudes,characterizethe overallslopeof the
spectrum from the visible to the near infrared. The 1-or error bars are shown. The combined color, V-K,
characterizes
the differences
betweenthesethreegroupswell. (b) After Gaffeyet al. [1993],this figureillustrates
a parameterizationof the pyroxeneand olivine absorptionbandsshownto be characteristicof the olivine fraction
of the matic component(pyroxeneplus olivine). Pyroxenehas absorptionbandsnear I /zm and 2 /zm, while
olivinehas a singleabsorptioncenterednear 1.2/•m. The horizontalaxis showsthe 2-/•m to 1-/•m pyroxeneband
area ratio. The vertical axis showsthe band center of the 1-/•m absorption band, due to pyroxene, olivine or
a combination. The So and Sp groupsare moderately well separatedin this space, but the S group overlaps
both. The error bar shown is the 1-orerror in the vertical direction, but showsthe median error in the horizontal
direction.Seetext for discussion
of the error determination.(c) Combiningthe colordata in Figure 6a with the
band area ratio from Figure6b, the groupsSo, S, and Sp are well separated.This parameterizationcorresponds
to the clustersdeterminedby the neural networkon the basisof spectralsimilarity. The So and S groupsare
separatedprimarilyin spectralslope,whilethe S and Sp groupsare better separatedby bandarearatio. The
reflectancespectrumis relatedto the maticcomposition
as well as the continuumslope,whichmay or may not
be dueto compositional
differences.
The errorbar shownis the medianerrorin the horizontaldirection,and the
1-orerror in the vertical direction. Three pairs of connectedpointsare observations
of the sameobject taken on
differentnights,whichshowed
significant
spectraldifferences.
(d) Sameas Figure6c, but onlythosepointswith
errors lessthan 1.5 times the median error are included. The connectedpairs of points have been omitted, since
they indicateasteroidswhichhavelargespectralvariability.The horizontalerrorbar indicatedis the newmedian
error of the points included.
between 1 and 2.5/•m. We did not have any examples
of objects classifiedby Barucci as S3.
To test the hypothesisthat the ordering of the Stype asteroidswas related to compositionaldifferences,
way that is sensitiveto the olivine/pyroxene
ratio and
pyroxenecompositionin laboratorysamplesand meteorites. Using the asteroidspectra, we calculatedthe
1-/zmband centerwavelength,and 2-/zmbandto
we followedthe methodof Gaffeyet al. [1993]. They
band area ratio for these asteroids. The continuum was
parameterize the 1- and 2-/•m absorption bands in a
estimatedby generatinga convexhull overthe 0.7- to
HOWELL
ET AL.- CLASSIFICATION
2.5-/•m region of the 65-color spectrum. The band area
was then calculatednumerically usingthe 65-colordata
values,without additional smoothing.Comparedto the
methods employed by Gaffey et al., these calculations
are somewhat crude, but fall within the calculated er-
rors of his valuesfor the same asteroids. Figure 6b
showsthis compositionalspacefor the So, S, and Sp
OF ASTEROID
SPECTRA
10,857
report observedlightcurve variability for 115 Thyra of
up to 20%, which might have affectedthe continuum
slope. However, the raw data show no indication of
lightcurve variations over the time of these observations
(J. F. Bell, personalcommunication,
1992).
Applying the parameterizationdescribedabove,Galley et al. [1993]outlinesevenregionsbasedon compo-
asteroids excluding those for which the calculated er- sitionally distinct meteorite samples. Figure 7a shows
rors were larger than the sizesof the different regions the separation of these groups; however,we have comthat Gaffeyet al. outlined. The error bar on Figure 6b bined groupsI and II, as well as VI and VII due to the
in the band area ratio is a median error. This error is
small number of objects. We tried training the network
determinedfrom the observationalerror for eachpoint, to learn the Gaffey et al. groups, but did not achieve
and the estimated
error from the continuum
determi-
nation, but does not include a contributionfrom any
wavelength uncertainty. The error in the continuum fit
is based on formal propagation of the error in the line
fit from two points,eachof whichis a meanof five adjacent data points. However, determiningthe continuum
is difficultand basedon subjectivejudgment,especially
where the spectral coverageis limited. Becausethe continuum is often not easily determined for observational
data, band areasmay havevery large uncertaintiesdue
to both noiseand limited spectralcoverage.The Soand
Sp groupsare slightlyseparatedin this space,but there
is a complete overlap of the S group with both So and
Sp groups. Figure 6c indicates that a combination of
the band area ratio and the spectralslopematchesthe
groupings formed by the neural network. The olivine-
a high learningrate. Figure 7b showsthat, upon com-
1.1
.9
rich asteroidsalso tend to be the oneswith very red
continuum slope, and the olivine-poor objects tend to
have less reddish slopes,but there is enoughoverlap
that both parametersare necessaryto explain the cluster structure. The V-K color is a good predictor of
the group membershipexcept for the transition region
from S to Sp. In this region, the primary distinction
is the band area ratio, which is a better indicator of
pyroxenecontent. Since the olivine spectrumis very
0
.5
1
1.5
2
2.5
Band II/Band I Area
8.8
_eo
ß S Asteroids
i
-
8
steepfrom0.55to 2 /•m, the coloraloneis a sensitive
m
measureof the olivine contribution to the spectrumfor
m
these asteroids. The color can also be determined ob-
....m
servationallywith much greater accuracyand for much
fainter asteroids than the band area ratio.
Bearing in mind that the errors are large in calculating band area ratio, we eliminated the points for
which the errors are especiallylarge, that is, greater
than 1.5 times the median error. For clarity, we alsoremovedthose points correspondingto spectrafor which
there seem to be large spectral variations between observationsmade on differentnights (connectedpairs of
points in Figure 6c). These asteroidsmay be unusual
in that they are especiallyinhomogeneous
or perhaps
lightcurveor other systematicerrorsaffectthe spectra.
The remainingpoints are shownin Figure 6d, and the
new medianerror bar is illustratedin the upper right.
Note that the y-axis error bar is the calculated1-rrerror.
Figure 6d showsthe relationshipsbetween these three
1.6
Figure 7. (a) As in Figure6b, the Gaffeyet al. [1993]
groupingsof S-classasteroids are based on the chemical compositionof meteorites and laboratory samples.
For clarity, we have combinedtheir groupsI and II, and
groupsVI and VII due to the small number of objects.
Asteroidsfor whichour calculatederrorsare largerthan
the regionoccupiedby its grouphavebeenomitted. (b)
The groups defined by Gaffey et al., as in Figure 7a,
but with the same axes as Figure 6c are shown. These
compositionalgroupsdo not separatewell usingthis pa-
groupsmore clearly. The Sp asteroid115 Thyra, appearing in the lower left, has a blue-slopingcontinuum rameterization, although the So asteroidsinclude most
from 1.5 to 2.5/•m, which may indicate that the band of the Gaffeyet al. groupsI and II, and the Sp asteroids
area ratio is underestimated.Harris and Young[1983] include the Gaffey et al. groupsV, VI, and VII.
10,858
HOWELL
ET AL.- CLASSIFICATION
bining the band area ratio with the spectral slope, the
Gaffey et al. groupsno longer separatewell.
OF ASTEROID
3.5
-
C. R. Chapman(personalcommunication,
1992)used
teroids
x
2.5
-
0
--•x
more likely to have strongolivine and pyroxenedesigobjects with Chapman's "p" designation,one can rule
out So as a probableclass. Likewise,for thoseobjects
designatedby Chapman as "o", Sp is an unlikely class.
However, asteroidsremaining in the S subclassoccur
with and without these designations.It is encouraging
that the neural network results agree with those obtained by careful inspection of individual spectra. In
caseswhere the data involved are simply too extensive
for manual treatment, ANNs are a good alternative.
Near-infrared spectra of these objects would determine
their subclassmembership.
To investigatefurther implicationsfor the So, S, and
Sp asteroid classes,we examine the orbital characteristics of these objects. The semimajor axis is plotted
against albedo for theseobjectsin Figure 9. The albedosare taken from J. C. Gradie and E. F. Tedesco(unpublisheddata, 1988) when available,otherwiseIRAS
S
_
an admittedly subjectiveevaluationof the pyroxeneand
olivine absorptionband strength in his asteroidclassification. Figure 8 showsthat the So and Sp asteroidsare
nations, respectively, than S or K asteroids. For those
SPECTRA
x
•
00
:
_
-
ø¸
-
-
-
-
o
O
[]
--
xK
--
•o
oSp _
.1
.2
Albedo
.3
.4
Figure 9. We plot asteroidsemimajoraxesand albedos
determinedby J. C. Gradie and E. F. Tedesco(unpublisheddata, 1988) when available,otherwisedetermined
by IRAS [Tedesco,
1989].The So asteroidsare concentrated in the innerbelt (seetext). Oneof the two outer
belt So asteroidsis an Eosfamily member(a=3.0
and may be unusual for that reason. The S and Sp
asteroidsshow no correlation with the semimajor axis.
No clear relationship with albedo is evident.
albedos[Tedesco,1989]are used. The formerare determined from groundbasedradiometry at 10 and 20
pm, combined with visible observations. There seems
to be no albedo trend within or between the So, S, and
Sp groups. Likewise, there is no clear trend with heliocentric distance, although as found by other workers
inner asteroid belt. It has been suggestedthat this
may be an artifact of the tendency to observecloser
objectsat higher phaseangles,and thus the continuum
slopewould systematicallyappear more red. Sincenone
of these data has been corrected for phase reddening,
[Chapman,1987;Bell et al., 1988],thereis a tendency we checkedthe observational circumstancesfor possible
for So objects, that is, olivine-rich objects, to be in the phase effects. Figure 10 showsthat there was no differencein the range of observedphaseangle for the So,
100
S, and Sp groups. There is no correlation betweenthe
- Correlation
of S subclasses
_rednessof the observedcontinuum slopeand high observational phase angle. We concludethat for thesedata,
with Chapman Descriptor
80 -
60
this effect is small. These groupingsshowedno clear
K
--
Sp
correlation with any other physical parameters such as
phase coef[icient, object diameter, or other orbital char-
So
_-
•
o
S
40
20
--
K --_
Chapman
The X (E, M, and P) class. Unfortunately,the
other Tholen classeshad few representativesin the 52-
S
p (pyroxene )
acteristics.
Sp
_-
M
-
o (olivine)
Descrip[or
Figure 8. Our modified S asteroid subgroupsare
compared with Chapman's classification. Within the
Tholen S class,Chapman assigneda letter "p" to those
objects with strong pyroxeneabsorptionbands, and "o"
to those objects with a strong olivine absorption band.
Our So objects are most likely to have "o" designation,
colorsurvey.The X types(the E, M, andP types),seem
to show some separation even in the absenceof albedo
information
in both the 65-color SOM and the 8-color.
However,the groupingsseenin the 8-colorSOM are different from those seen in the 65-color
SOM.
There
are
not enoughof theseobjects to be certain of the meaning
of these separations. The main differenceseemsto be in
the spectral slope, but the compositionalinterpretation
of this is unclear. M-type asteroidswere thought to be
composedof FeNi metal, which produces a red spectral slope. But for at least some M-type objects, there
and least likely to have "p" (no examples). The Sp
is waterof hydrationpresentin'the surface
minerals,
objects on the other hand are most likely to have "p"
designations,and least likely to have "o." However,
our S group has examplesof both, as doesthe K class,
although we have only three membersof the K class.
in the near infrared certainly indicates there is great
diversity among these objects in the continuum slope,
inconsistent
with this composition[Joneset al., 1990;
Rivkin et al., 1994]. The additionalspectralcoverage
HOWELL
ET AL.' CLASSIFICATION
SPECTRA
10,859
convexdownward
(reflectance
stronglyincreasing
with
wavelength).
Thoughonlya fewof theseobjectshave
beenobserved
at 3 •m, hydratedobjectsoccurin both
the Cv andCx groups.Giventhesuccess
of the G-type
asteroid
grouping
asindicating
surface
hydration,
wedo
not propose
thissystemasa replacement
of theTholen
taxonomy.Instead,it is simplya groupingbasedon a
differentparameter,perhapsa differentcompositional
5O
S Asteroids
ß 40
OF ASTEROID
3O
element. Until this elementcan be positivelyidentified,
ß So
-
interpretationof this groupingis not possible.
There are not enoughB- and F-type asteroidsin this
sampleto determinethe relationship
of theseclasses
to
the other classes.In the 8-color classification,the B and
1.6
1.8
2
2.2
F classes
separatefairly well fromthe C and G classes,
eventhoughthe divisionbetweenB and C asteroids
is basedon albedo. However,in the 65-colorclassification, the smallnumberof samplesmakesthisseparation
V-K
Figure 10. The phasefunction dependson wavelength,
and therefore can introduce a slope to the spectrum.
The 65-color spectra are not correctedfor observational
phase explicitly, so we look for a corrleation between
spectral slope and observationalphase angle. The So,
S, .and Sp groupsshowsimilar rangesof observedphase
angles,with no tendencyfor the reddestobjectsto be
those observedat highest phase angle. We conclude
that in this wavelengthrange the phase reddeningis a
less clear. We therefore combine these objects in a new
class,designated
B+F, a combination
of the TholenB
and F classes. This label should not be confused with
Tholen's notation which would indicate BF for an ob-
ject mostlikelyB, but possibly
F. Asteroid2 Pallashas
an unusualspectrum,and was labeledB classin the
training. Furtherinvestigation
of theseasteroidsis a
promisingarea of future research.
small effect.
but whether this is entirely a compositionaldifferenceis
not clear. Other possible causesof continuum reddening that have been proposedare phaseeffects,particle
size effects,or regolithweathering[Britt, 1991]. Additional
observations
are needed to further
understand
Discussion
of ANN
Consistency
Tests
Classification
A classificationsystem can be consideredself-consistent if it can correctly predict the classmembershipof
this group of asteroidsand investigatethe diversity of
the groups.
test patternsbasedon the informationcontainedwithin
it. A test pattern is a pattern whoselabel is knownbut
was not includedin the training set. The modifiedclas-
The C, G, B, and F classes. The additional
near-infrared spectral data for the C classand related
G, B, and F classesis difficult to interpret. The clear
distinctions seen in the 8-color clustering were mainly
due to the strength and placement of the UV Fe-O
charge-transferabsorptionband. Although this band
is still presentin the 65-color data, it is a small part of
the spectrum not obviouslycorrelatedwith the appear-
sification for the 65-color data is self-consistent, that
tively correlatedwith the water of hydration in surface
minerals. Based only on hydration state, some rearrangement of the C and G classesmay be indicated.
Nearly all G-type asteroids observed to date show a
water of hydration band, but about half of the C-type
asteroids sampled are also hydrated. Not enough Btype or F-type objectshave been sampledto draw firm
conclusionsabout these objects. The continuum slope
from 1 to 2.5 •m may or may not be due to an additional
compositionalcomponent, but if so, it indicates a still
differentgrouping.We presenta groupingof the C-type
objects which is primarily basedon the continuum slope
curvature from 1 to 2.5 •um. The slope of Cv objects
is concavedownward(reflectanceweaklyincreasingor
decreasingwith wavelength),while the Cx objectsare
them into a reliable training material and a representative test set. Instead, a smallerthan desirablenumber
is set aside for testing. After the networkis trained
with the complementarydata that are still believedto
be representative,its predictionsfor the test casesare
recorded.This processis repeatedwith severaldifferent
test set selectionsuntil enoughpatterns participated in
the tests to draw conclusions.In our case,the 65-color
data set had only 117 spectrain our 15 modifiedclasses
which, as seenfrom Figure 11, are rather unevenlyrep-
is, the ANN producesa 98.5% correctlearningrate
for these class memberships. By "correct" we mean
that the neural network correctly reproducesthe label
it was taught for 98.5% of the spectrain the training
set. The ANN has a 90% averagepredictionrate for
unknownpatterns,that is, patternsomittedfrom the
trainingset. The predictioncapabilities
of the network
anceof the near-infraredregion.Feierberget al. [1985] weretestedby "jackknifing."This procedureis common
have shown that the UV Fe-O band strength is posi- when the number of patterns is too small to partition
resented.The threesingleobjectclasses
(B, R, and V)
were not put to test. However, these asteroidspectra
participated in the network training so that any test
spectrumcould be predictedas one of thesetypes. We
randomly selectedtwo objectsfrom each of the So, S,
10,860
HOWELL
ET AL.' CLASSIFICATION
65-Color
Grouped
by ANN
A
Asteroid
Classes
..,v'
/
OF ASTEROID
SPECTRA
Spectra
Grouped
by Tholen Classes
/
/
/
BCv
B+F
Cv
Cx
241
somaam,
324
b•mbers,
lg
130
olek•r
.......
44
84
317
422
berohn,
D
130
•ll
cloe•,
beren•k,
o•
½1oelll
K
M
P
Figure 11. The 65-colorspectraare shownat a consistent
verticalscale.The generaldifferences
in shapebetweenthe differenttaxonomicgroupingscan be seen. On the left, the spectraare
groupedaccordingto our modifiedANN classes,while on the right they are groupedby their
Tholen classes.Objectswhichhavetwo or moreclasslabelsare placedin the first class,to which
it is most similar. Relative reflectanceis plotted, normalizedto 1.0 at 0.55/•m. For reference,the
reflectanceof A-type asteroid446 Aeternitasrangesfrom 0.4 to 2.0. Generaldifferences
between
the groupingsare discussed
in the text. Table 3 discusses
individualobjectswhoseclassifications
differ in the two systems.
HOWELL
ET AL-
65-Color
Grouped
CLASSIFICATION
OF ASTEROID
Asteroid
by ANN
SPECTRA
Spectra
Grouped
Classes
10,861
by Tholen
Classes
s
So
oeo
2?0
ae?
42
42
103
•,32
348
386
?
,.M'&
364
i4s•,
1827
s
380
mdustrl,
• is
tndustrl.
32
20
as?
33
t•m&tnr
4
T
v
3oe
Fig. 11. (continued)
10,862
HOWELL
ET AL.: CLASSIFICATION
and Sp classesand one object from each of the other
classes,thus having 16 test casesand 101 training samples in one jackknife. We repeated this six times, with
differentrandomselections.Altogether,68 spectraparticipated in at least one test set. Among the So, S, and
Sp classes,26 weretested. Misclassifications
amongE,
M, and P types were not counted, although we kept
these separateclassdesignations.The resultsare summarized in Table 1. Trained with our modified class la-
OF ASTEROID
SPECTRA
color data are more closelyrelated to other C-classasteroids than to the P class, so we list them as C class.
The network determines weighted multiple classasso-
cie•tions.For thoseobjectsthat showedat least 30%
contribution by at least one other classin at least two
of the sixjackknifetests,we list the additionalclassdesignation. In somecases,the albedo narrowsthe class
membership
possibilities
(seeTable 2 notes). We define the B+F class as a combination of Tholen's B and
bels,the networkachievesa 98% learningsuccess
rate. F classes,with the exception of 2 Pallas, which was
The networkhasa 90% averagepredictionrate for pat- trained as B. The remaining B and F asteroidsare not
terns omitted in the jackknifingtests. For comparison, distinguishablein our 65-colorclassificationdue to the
we ran the same experiment with exactly the sametest
set selections,
for the originalTholenclassdesignations.
As shownin Table 1, the learningand predictionsuccessrates were 97.3% and 71%, respectively.Because
of the small number of patterns, the resolutionof the
predictionrate is 6% (i.e., if one,two or three patterns
are misclassified,the prediction rate is 94%, 88% and
82%, respectively).The resolutionof the trainingsuccess rate is 1%. Our results indicate that we achieved a
cleanerclassstructure for the 65-colorspectrathan the
initially assumed class memberships. The network is
small number of samples. In the jackknife testing, 2
Pallas showeda similarity to the Cv class,so its ANN
classificationis BCv. The spectrum of 1 Ceres is also
unusual,and it showedsimilarity to 2 Pallas, giving it a
CvB class. However, the two objects are differentfrom
each other.
Among 20 objectsobservedon two or more separate
occasions,six showedsignificantspectral variation as
describedearlier. One of these objects, 367 Amicitia,
was not included due to lack of visual observations.
Two
spectra of 43 Ariadne, 863 Benkoela, 18 Melpomene,
utilizing the additionalspectralinformationeffectively. 258 Tyche, and 135 Hertha were analyzed separately.
Although noisy, both versionsof 863 Benkoela classified as A. One spectrum of 43 Ariadne classifiedas Sp
The Spectra
while the other classifiedas S, but very near the boundary betweenS and Sp. One spectrumof 18 Melpomene
Our modified classes for the asteroids with 65-color
classifiedas SoT, the other as S. One 258 Tyche specspectra are listed in Table 2. Figure 11 showsthe 65- trum classifiedas Sp, the other as SSp. In the caseof
color spectra grouped according to the ANN classifi- 135 Hertha, one of the spectra classifiedas M, but the
cation on the left. For comparison, the spectra are other classifiedas T, although it is somewhatnoisy. If
grouped by Tholen's classificationon the right. The these variations are due to compositional variation on
objectsBell et al. [1988]designated
asK, areseparated the asteroid, then the implication is that asteroidinhofrom Tholen's S class, and 422 Berolina is classed as mogeneitiesoccur at a level that is easily detectable at
EM, rather than its original DX Tholen class,since it near-infrared wavelengths. However, these variations
hasa high albedo(J. C. Gradieand E. F. Tedesco,un- may also result from systematic errors. Rotationally
publisheddata, 1988). Table 3 lists thoseobjectsfor resolved spectra of these objects are needed to settle
which our class determination
differs from the Tholen
this important issue,sincethe fundamentalmeaningof
class either in the 8-color classification, the 65-color a taxonomic classis quite different if objects routinely
classification,or both. Specialcasesor unusualobjects show different classes on different faces.
are also listed with explanatory notes. For those objects that did not show a clear class a•nity, Tholen Summary and Conclusions
listed other possibilitiesin order of preference. For exWe classified combined 8- and 52-color asteroid reample, CP is most likely C, but possiblyP. Our 8-color
classificationshowedall of the CP objects in the 65- flectance spectra with a Kohonen-type artificial neural
Table
1. ANN
65-Color
Asteroid
ANN Taxonomy
Classification
Tholen Taxonomy
Jackknife Learnipg Prediction Learnipg
Number
Prediction
Rate %
Rate %
Rate %
Rate %
1
2
3
4
5
6
98
99
99
99
98
98
88
88
94
88
88
94
99
98
96
97
96
98
76
76
70
64
70
70
Average
98.5
90
97.3
71
HOWELL ET AL.: CLASSIFICATION
Table
2. ANN
Number
1
2
OF ASTEROID
SPECTRA
10,863
Asteroid Classification
Asteroid
Class
Number
Asteroid
Class
Number
Asteroid
Ceres
Pallas
CvB
BCv
67
68
Asia
Leto
Sp
S
336
346
Lacadiera
Hermentaria
Class
D
S
3
Juno
Sp
69
Hesperia
M
349
Dembowska
4
Vesta
V
76
Freia
P
352
Gisela
SSp
5
6
Astraea
Hebe
Sp
Sp
80
82
Sappho
Alkmene
So
Sp
354
356
Eleonora
Liguria
So
Cv
7
9
Iris
Metis
S
S
86
89
Semele
Julia
CvP
S
364
368
Isara
Haidea
So
D
B+F
S
92
96
Undina
Aegle
M
T
376
379
Geometria
Huenna
So
B+F
387
Aquitania
Sp
10
11
Hygiea
Parthenope
13
Egeria
16
18
12
So
101
Helena
Sp
Cv
103
Hera
SSp
Cv
389
Industria
19
20
Psyche
M
Melpomene S,SoT
Fortuna
Massalia
Cx
Sp
113
114
Amalthea
Kassandra
So
T
422
431
Berolina
Nephele
21
Lutetia•
M
130
Elektra
Cx
511
Davida
Cx
22
Kalliope
Phocaea
M
So
135
138
Hertha
Tolosa
M,T
521
Brixia
CvP
26
27
29
31
32
33
Proserpina
Euterpe
Amphitrite
Euphrosyne
Pomona
Polyhymnia
Sp
S
Sp
Cx
Sp
Sp
145
152
153
218
221
233
Adeona
Atala
Hilda
Bianca
EosI
Asterope
CvP
D(S)
P
SpS
K
T
554
584
639
653
661
674
Peraga
Semiramis
Latona
Berenike
Cloelia
Rachele
Cv
So
So
K
K
Sp
37
39
Fides
Laetitia
S
S
235
241
Carolina
Germania
S
Cx
702
704
Alauda
Interamnia
15
25
Victoria
Eunomia
S
106
115
116
Dione
Thyra
Sirona
40
Harmonia
Sp
246
Asporina
42
Isis
So
258
Tyche
43
44
Ariadne
Nysa
Sp,S
E
264
267
Libussa
Tirza
46
Hestia
P
270
Anahita
57
59
63
64
Mnemosyne
Elpis
Ausonia
Angelina
Sp
Cx
So
E
289
308
317
324
Nenetta
Polyxo
Roxane*
Bamberga
65
Cybele
P
Sp
Sp
S
385
446
476
532
Ilmatar
R
Aeternitas
Hedwig
Herculina
Sp
Sp
EM
B+F
A
P
S
Cx
B+F
A
714
Ulula
Sp,SSp
762
Pulcova
S
Sp
D
772
773
Tanete
Irmintraud
Cx
D
S
849
Ara
M
A
TSo
E
Cx
863
980
1036
1627
Benkoela
Anacostia
Ganymed
Ivar
A
T
Sp
S
B+F
Classificationdeterminedby the neural network usingthe 65-colorspectraare presented.In caseswhere two or more
classescontributed at least 30% in at least one third of the jackknife tests, multiple classlabels are shown. In most cases,
one classwas clearlydominant.Labelsare listedin decreasing
orderof contribution.In caseswheretwo differentspectra
for the sameobject classifieddifferently,the classes
are separatedby a comma. SeeTable 3 note 6 for a descriptionof
observationalproblemswith 152 Atala.
•Asteroid 21 Lutetia classifiedas MCv; however,its albedo excludesthe Cv class.
I Asteroid221 Eosclassified
as KCvP; however,its albedoexcludes
both Cv and P classes.
*Asteroid317 Roxaneclassified
as ECv; however,its albedoexcludes
the Cv class.
network. Although the methodis very differentfrom
that usedby Tholen to determinehis now widely used
taxonomicsystem, our resultsare generallyconsistent
with Tholen's taxonomywhen basedon a similar data
set. We extend the spectralrangeof the data to include
the near infrared, and introduceour classification,
augmentingthe Tholen taxonomy:someclassesare rearranged,and certainobjectsare assigned
classlabelsdif-
We find someevidenceto suggestthe C classand related G, B, and F classesshowdifferentclusteringswith
the extended spectral coverage. One such rearrangement is presented,althoughthe compositionalinterpretation is not clear. The number of samples of these
objectsis small, and more observationsare requiredto
clarify thesegroupings.Similarly,the X asteroids,that
is, the E, M, and P classes,exhibit clusterswithin the
ferent from Tholen's. Two compositionallymeaningful groupthat are not relatedto albedo,but the numberof
subclasses are defined within the S asteroids. We define
objectsis currently too small to interpret the meaning
So as olivine-rich, red asteroids,and Sp as olivine-poor, of these groups.
The neural network approachused here is powerful
lessred objects. This classificationis self-consistent
to
a high degree,i.e., the neural networktrained with our in clusteringand classifyinghigh-dimensionalspectral
modifiedclasslabelsproduces98%learningsuccess,
and data. Sinceartificial neural networksare well suited to
combine data of disparate natures, we may be able to
a 90% averagepredictionrate for unseenpatterns.
10,864
Table
HOWELL ET AL.: CLASSIFICATION
OF ASTEROID
SPECTRA
3. Asteroid Classification Differences
Asteroid
2
10
18
21
135
Tholen Class
ANN 8-Color Class
Pallas
B
B
Hygiea
Melpomene
C
S
C
S
Lutetia
Hertha
M
M
M
M
ANN 65-Color Class
BCv
B+F
SoT,S
Notes
1
2
3
M
M,T
4
5
152
Atala
D(S)
D
D
6
221
Eos
S
S
K
7
258
261
308
Tyche
Prymno
Polyxo
S
B
T
S
C
T
317
379
Roxane
Huenna
E
B
F
C
422
Berolina
DX
554
Peraga
FC
F
Cv
12
Berenike
Cloelia
Anacostia
Heiskanen
1973 DH
S
S
SU
C
C
S
S
T
B
X
K
K
T
13
13
14
653
661
980
2379
2407
Sp,SSp
8
TSo
9
E
B+F
10
EM
11
Classifications
of objectswhichdifferfrom their originalTholen class,unusualobjectsand specialcases.In caseswhere
no classis reported,the objectdid not havethe appropriateobservations
to includeit in that classification.For example,
someobjectsthat were not observedin the 8-colorsurveydid have UBV colors,and so were includedin the 65-color
classification.(1) 2 Pallashas a uniquespectrumthat is well separatedfrom the other B asteroids,and may deserve
a separateclass. It was trained as the only B asteroid,but classifiedas havingsignificantcontributionfrom the Cv
class.(2) 10 Hygieaclassifes
as B+F, althoughtthere is a contributionfrom the Cx class.The albedois 0.079:k 0.005,
measuredby both IRAS and J. C. GradieandE. F. Tedesco(unpublished
data, 1988),whichis consistent
with the B class.
(3) 18 Melpomenewasobservedto havesignificantly
differentspectraon two separatedaysof observation.This object
appearsto be inhomogeneous.
(4) 21 Lutetia showsan affinityto the Cv class,but it has an IRAS albedoof 0.21, which
clearlyexcludesthis possibility.It hasan unusuallyfiat spectrumfor an M classasteroid.(5) 135 Hertha is classedas M
by Tholen. One spectrumclassifiesas T, but it is noisy. Another spectrumfrom anotherdate is consistentwith the M
class. The IRAS albedo, 0.13, is more consistentwith the M class,but not far from the T classalbedo range of 0.05-0.10.
(6) 152 Atala has beenreclassified
as S by Tholen basedon observations
subsequent
to the 8-colorsurvey.The spectrum
shown here classifiesas D in both our 8-color and 65-color systems, as well as in Tholen's original taxonomy. Tholen
suggeststhat the spectrumwas contaminatedby a red star duringthe 8-colorsurveyobservations.This object was not
omitted from the analysis,sinceit illustratesa casewhere training the networkwith an inconsistentlabel did not affectits
ability to correctlyclassifythe spectralshape.Althoughthis object waslabeledS, the networkrepeatedlyclassifiedit as D
basedon spectralappearance.This objectneedsto be observedagainin visibleand near-infraredwavelengths.(7) 221 Eos
showsan affinity to the Cv and P types in the 65-colorclassification,but its IRAS albedo of 0.13 is not consistentwith
theseclasses.Its family membershipis consistentwith a K classification.(8) 258 Tyche was observedon two separate
occaisons.One of thesespectraclassifiedas S, the other as Sp. This object seemsto be inhomogeneous.
(9) 308 Polyxo
has an unusual spectrum for the T class,and it has a contribution from the So classbasedon the steep slope from 0.5 to
1.5 pm. Howeverit doesnot have pyroxeneor olivine absorptionbands. This asteroidwas noted as anomalousby Tholen
aswell. (10) 317 Roxanehasa fairly fiat spectrum,and showsa contributionfromthe Cv class.However,its IRAS albedo
of 0.50 clearlyidentifiesthis objectas an E-type asteroid.(11) 422 Berolinais classedasDX but doesnot showany affinity
to the D asteroids.J. C. Gradie and E. F. Tedesco(unpublisheddata, 1988) find a high albedo(0.5 :k 0.2), whichnarrows
the possibilitiesto E or M. This object doesnot have an 8-color spectrum,but does have UBV colors. This object is
includedwith the E asteroids
in Figure11, but it is still possiblyan M, giventhe uncertaintyin albedo.(12) 554Peragais
classifiedas Cv in the 65-colorsystem,but still showssomeaffinity to the B+F class.Its IRAS albedo, 0.05, is consistent
with either F or Cv classes,but not the B class.(13) Both 653 Berenikeand 661 Cloelia classifyas K usingthe 65-color
spectrum. Both belongto the Eos family, which strengthensthe K classification,eventhough the spectra are quite noisy.
(14) 980 Anacostiais classifiedas SU by Tholen,indicatingan unusualspectrum.It is mostsimilarto the T classbut has
a smallcontributionby the So class.Burbineet al. [1991]suggestthat the spectrumof this objectresembles
spinel.
extend the presentedclassificationin the future, by including other, nonspectralparameterssuch as albedo,
phase function, asteroid size, and orbital parameters.
The current limiting factor is the size of the database.
We therefore strongly encourageobserversto gather
additional
data
for more
asteroids
and to coordinate
efforts to gather many different types of data for the
same asteroids
to facilitate
correlations
between differ-
ent classesand to determine variability within a class..
Acknowledgments.
We would like to thank Jeff Bell
and Dave Tholen for providingtheir asteroidspectrain electronic form. Also, thanks are due to Mike Gaffey for providing the data in Figure 7 prior to publication. Dave Tholen
and an anonymous reviewer's comments substantially improved this paper. We also appreciate the suggestionsprovided by Jeff Bell. We acknowledgeuseful discussions
with
Tom Burbine and Clark Chapman. Helpful suggestions
were
provided by Mike Nolan on an earlier draft. This work was
conductedon the Central Computing Facility of the Lunar
HOWELL
ET AL.: CLASSIFICATION
OF ASTEROID
SPECTRA
10,865
mote comets and related bodies: VJHK colorimetry and
surface materials, Icarus, 52, 377-408, 1982.
Huang, W., and R. Lippman, Comparisonsbetween neural
network and conventional classifiers, in Institute of Electrical and Electronics Engineers, New York, First International Conference on Neural Networks, San Diego, vol.
IV, pp. 485-494, 1987.
References
Jones, T. D., L. A. Lebofsky, J. S. Lewis, and M. S. Marley,
The composition and origin of the C, P, and D asteroids:
Water as a tracer of thermal evolution in the outer belt,
Barucci, M. A., M. T. Capria, A. Coradini, and M. FulchiIcarus, 88, 172-192, 1990.
gnoni, Classificationof asteroidsusing G-mode analysis,
Kohonen, T., Self-Organization and Associative Memory,
Icarus, 7œ,304-324, 1987.
Springer-Verlag, New 'fork, 1988.
Bell, J. F., A probable asteroidalparent body for the CV or
Lebofsky, L. A., T. D. Jones, P. D. Owensby, M. A. FeierCO chondrites, Bull. Am. Astron. Soc., 19, 841, 1987.
berg, and G.J. Consolmagno,The nature of low albedo
Bell, J. F., A probable asteroidalparent body for the CV or
asteroids from 3-tzm spectrophotometry, Icarus, 83, 12CO chondrites, Meteoritics, œ$,256-257, 1988.
26, 1990.
Bell, J. F., B. R. Hawke, and P. D. Owensby, Carbonaceous
chondrites from S-type asteroids?, Bull. Am. Astron. Mer•nyi, E., K. Edgett, and R. B. Singer, DeucalionisRegio,
Mars: Evidence for a new type of immobile weathered soil
Soc., 19, 841, 1987.
unit, Icarus, submitted, 1993a.
Bell, J. F., P. D. Owensby,B. R. Hawke and M. J. Gaffey,
The 52-color asteroid survey: Final results and interpre- Merdnyi, E., R. B. Singer, and W. H. Farrand, Classifica-
and Planetary Laboratory. For artificial neural network simulation, we used the NeuralWorks ProfessionalII Package,
by (•) NeuralWare, Inc., provided by the Planetary Image
Research Laboratory. This work has been partially supported by grants NAGW-1975 and NAGW-1146.
tation, (abstract), Lunar Planet. Sci. Uonf., XIX, 57,
1988.
Bell, J. F., D. R. Davis, W. K. Hartmann, and M. J. Gaffey,
Asteroids:The big picture, in AsteroidsH, edited by R. P.
Binzel et al., pp. 921-945, University of Arizona Press,
Tucson, 1989.
Binzel, R. P., and S. Xu, Chips off of asteroid 4 Vesta: Evidence for the parent body of basaltic achondrite meteorites, Science, 260, 186-191, 1993.
Britt, D. T., "SpaceWeathering": Are regolith processesan
important factor in the S-type controversy?, Meteoritics,
26, 324, 1991.
Burbine, T. H., Principal component analysis of asteroid
and meteorite spectra from 0.3 to 2.5/•m, Master's thesis,
University of Pittsburgh, Pittsburgh, Pa, 1991.
Burbine, T. H., M. J. Gaffey, and J. F. Bell, S-asteroids
387 Aquitania and 980 Anancostia: Possiblefragments
of the breakup of a spinel-bearing parent body with
CO3/CV3 affinities, Meteoritics,27, 424-434, 1991.
Chapman, C. R., The asteroid belt: Compositional structure and size distributions, Bull. Am. Astron. Soc., 19,
839, 1987.
Chapman, C. R., D. Morrison, and B. Zellner, Surfaceproperties of asteroids:A synthesisof polarimetry, radiometry,
and spectrophotometry, Icarus, 25, 104-130, 1975.
Cruikshank, D. P., D. J. Tholen, W. K. Hartmann, J. F. Bell
and R. H. Brown, Three basaltic earth-approachingasteroids and the sourceof the basaltic meteorites, Icarus, 89,
1, 1991.
Feierberg, M. A., L. A. Lebofsky, and D. J. Tholen, The
nature of C-classasteroidsfrom 3-/•m spectrophotometry,
Icarus, 63, 183-191, 1985.
Fu, K. S. (Ed.), Digital Pattern Recognition,SpringerVerlag, New York, 1976.
Gaffey, M. J., J. F. Bell, R. H. Brown, T. Burbine, J. L.
Piatek, K. L. Reed, and D. A. Chakey, Mineralogical variations within the S-type asteroid class, Icarus, 106, 573602, 1993.
Hardorp, J., The sun among the stars, Astron. Astrophys.,
tion of the LCVF
AVIRIS
test site with
a Kohonen
HydratedE-classandM-classasteroids,(abstract),Lunar
Pla,et. Sci. Conf., XXV, 1135, 1994.
Tedesco, E. F., J. G. Williams, D. L. Matson, G.J. Veeder,
J. C. Gradie, and L. A. Lebofsky, A three-parameter asteroid taxonomy, Astron. J., 97, 580-606, 1989.
Tedesco, E. F., UBV colors, and IRAS albedos and diameters, in Asteroids II, edited by R. P. Binzel et al.,
pp. 1090-1138, University of Arizona Press, Tucson, 1989.
Tholen, D. J., Asteroid taxonomy from cluster analysis of
photometry. Ph.D. dissertation, University of Arizona,
Tucson, 1984.
Tholen, D. J., Asteroid taxonomic classification, in Asteroids H, edited by R. P. Binzel et al., pp. 1139-1150, University of Arizona Press, Tucson, 1989.
Tholen, D. J., and M. A. Barucci, Asteroid taxonomy, in
Asteroids II, edited by R. P. Binzel et al., pp. 298-315,
University of Arizona Press, Tucson, 1989.
Ultsch, A., and H. P. Simeon, Kohonen's self organizing feature map for exploratory data analysis, in International
Neural Netowrk Conference90 Paris, Kluwer Academic,
Dordrecht, pp. 305-308, 1990.
Zellner, B., D. J. Tholen, and E. F. Tedesco,The eight-color
asteroid survey: Results for 589 minor planets, Icarus, 61,
355-416, 1985.
E. S. Howell, L. A. Lebofsky and E. Merdnyi Lunar
and Planetary Laboratory, University of Arizona, Tuc-
son, AZ 85721 (e-maih ehowell@LPL.arizona.edu;
lebofsky@LPL.arizona.edu;
erzsebet@LPL.arizona.edu)
91, 221, 1980.
Harris, A. W., and J. W. Young, Asteroid rotation, Icarus,
54{, 59-109, 1983.
Hartmann, W. K., D. P. Cruikshank, and J. Degewij, Re-
artifi-
cial neural network. in Proceedingsof the Fourth Airborne
GeoscienceWorkshop,Washington, D.C., Oct. 25-29, pp.
117-120, 1993b.
NeuralWare, Inc., Neural computing, in NeuralWorks Professional H Manual, Pittsburgh, Pa., 1991.
Pao, Y.-H., Adaptive Pattern Recognition and Neural Networks, Addison-Wesley, Reading, Mass., 1989.
Rivkin, A. S., D. T. Britt, E. S. Howell, and L. A. Lebofsky,
(ReceivedJuly 22, 1992;revisedDecember10, 1993;
acceptedDecember17, 1993.)