From: AAAI-86 Proceedings. Copyright ©1986, AAAI (www.aaai.org). All rights reserved.
CONCEPTUAL
CLUSTERING
USING
RELATIONAL
INFORMATION
Hernd Nordhauscm
Department
of Information
IJniversity
aid
Irvine,
CA
ArpaNet:
in conceptual
~Iasscs
color
from
92717
or size.
between
can
rnatiolk
the objects
being
clustering
clustered
Using
conceptual
as
clustering
involves
as well
0 1’US
is able
algoinfornot
methods.
c~~p~,uaIly similar
classes
of Lhose classes.
In recent
search
in the area
of’ staveral
years
have focused
such
as color
cation.
Only
Stepp
of object
on feature
liowever,
mation
no
& Michalski
to classify
dresses
(acid
this
issue
uot sirnply
scriptioll),
We thus
extend
171 have
re-
For a survey
see
/Xl.
All of
of the
a coherent
description
classifi-
left this
of objects,
narrow
i.e.,
and the relalionship
thus
at-
the set of objects.
0 PIJ S implemented
by using relations
object
components
the definition
relational
but
of other
create
relationul
This
paper
in Prolog,
infor-
describes
which
ad-
over the set of objects
as in structural
of objects,
of conceptual
to form
de-
classes.
clustering
[6]
informalion.
conceptual
have
is able to generate
to be given
description
the next
In
tailing
describing
section
l
A set of relations
between
0 <:riteria
to evaluate
two proposals
to the
A tlierarchy
508
/ SCIENCE
of classes
and
a characterization
of the
from relations
and
parent. The system
each class having
tem divides
and
0 P IJ S system,
de-
recursively
we give
consists
set,
the
such
a hierarchical
conceptual
the classes
features
tree of classes,
until
a final
these
After
of the classes
of a given
0 I’ II S continues
and refining
parts,
these
classes
divide
the
classes.
clustering
are
until
formed
described
the
until
of generating
new attributes
0 I’ II S consists
in detail
cluster-
classes
value for all cur-
the cycle
algorithm
class
new attributes
attributes,
have the same
arr
the list of current
all members
new
classes,
partition-
as coio~ or size
such
tl~e previously
The sys-
exclusive
value for the given features),
llsirlg
objects,
as eclt or
description.
set into mutually
(i.e.,
of the objects
describing
to form classes.
refines
with
System
the object
generates
is exhausted
section
We conclude
this work.
OPUS
a unique
At first,
att,ributes.
generutor;
the third
In
the system.
over
divides
gener.Lted.
sections.
and the
0 1’ IJ S system
the object
ing is found.
the
to form a classification
a set of features
be used to further
c Iasses
that
New
we describe
and a set of relations
distinct
l
In contrast,
systems.
is not sufficient.
for extending
input
attributes
t”illd:
to
of the objects
to illustrate
to be classified,
rent
of a classification
inability
if it determines
2. The
all rrletribers
the objects
Lhe quality
is the
attributes
of new attributes.
two applications
ilig algorithrrl
the objects
defin-
deficiency
used to characterize
to such
the use of relations
generation
are
A set of features
Another
of their
features.
have the same
l
effectively
as chunks formed
are defined
but
of genetics,
in terms
systems
to dis-
features
not only
all attributes
sys-
is able
offspring,
and purebreds.
0 1’US
attributes
0 A set of objrcts
peas
objects
attributes
system
in the domain
of their
elitni-
clustering
have the same
clustering
used as attributes
(i ivc>Il:
which
to classify
0 P TJ S system
this
I;or exatnpte,
of hybrids
among
used
objects
new att,ributes;
the current
the
conventional
systerns,
also in terms
ing the class
The
far has
as well as features
lo include
active
to form classes.
systeti1
a systt~rn called
been
descriptions
to form
cotnponents
thc>schcorrlponer~ts
systems,
or size,
ttorlrdirl and used structural
tributcls
has
clustering.
clustering
objcc.ts,
a characterization
there
of conceptual
conceptual
thcscl systetns
and producing
into con-
color
information,
of previous
the other
relations.
classifications
objects
unlike
between
relational
grouping
tems;
different
1. Introduction
(:onceptual
a deficiency
tinguish
this
clustering
nates
which
tree of classes.
systems,
is able to find object
such
a system
to form a hierarchy
with conventional
on creating
set of features,
new attributes.
the system
possible
focused
we describe
conceptual
define
has
a fixed
paper
of the objects
Ilrllikc~ previous
rithlrl
with
In this
uses relations
ah fcal,ures
Usirlg relational
clustering
objects
Science
lrvine
berndCQic:s.uci.edu
Abstract
Work
Computer
of California,
and
the
‘in the
cannot
of two
attribute
following
‘l‘t1tl 0 I’IJ S clustering
M A G t4: cluslering
schetrle
atgorithrri
is to build a hierarchical
(clusters)
trtbcb of mutually
for a given
has associated
object
set.
attribute/value
‘t’tttb IIic~rarchy tree is built
Ilotltb iI1 the tree,
btlst partitions
is based
It CJ M-
exclusive
Each
‘I’tle simpficity
object
classes
of the
set
the algorithm
down fashion.
selects
to some
which
alone
/6j/;the
Af’ter an attribute
has been selected,
vided inLo mutually
exclusive
the same value for the chosen
tree is labeled
at that
node,
common
calIt
vided
to all members
using
once
again
the
irig algorithtn
cannot
until
further
(liven
an object
attribute
reruaiuing
attributes.
best
In order
0 1’US
clustering,
that
associated
are
procedure
is
point
di-
0 1’US
it
and tertninates.
partitions
A cotnplex
the quality
a complex
is the logical
over the remaining
we have the object
attribute/value
set {K,
pairs
to
the set over the
to measure
forms
we want
of
for each
implication
attributes
I,, M, N, O}
for attributes
A,
the higher
will t,ch. A good classification
a tligh
iirlci
between
her of terms
consists
measure
of a logical
of
B,
elcmc~nts
of UPLuttribute
of all of the
plicity
01 an uttribute
and
(1711
and
[rn]),
‘t‘he computat,ion
the complexes
for attribute
A for values
inter
systetri
are sets.)
The
‘I’tle
(I)
j(Lj > {(I)
- lyj v 1x1) A
(2) /h( > {(U
‘I’llaL is, if an object
implies
that
has a value
criteria,
alld t.he itIter
j771,7L]
jllll
J
illI)>
that
The
difference,
A, it
B, and a value
corriplexc3
are used to
0 t’ II S uses two
of the cluster
which
‘l’tir
descriptiorl
we 110~ discuss.
(Values
of
has
possible
have.
In
difference
of two
a selector
element
is, an element
of attributes
of the
in t II<>0 [‘IT s
srrrlilurity bt:twt*t~rr two selector
el-
to be 5111~(c,, cz)
i::l:::~ ..*
rfonirtt~i?rl sirrlilurrty of’ a rc~f’erenco elenlellt
e of a sc-
cl and ez, is defilletl
.S1 to selector
value
is trIax{ sirri(e, c:k)},
for all ek L .S,.
is the avtbrage of Lhe tilaxinIuIr1
t:,
all selector
S,
t:lt:rrlerits
similarities
Now, thtl
degree of srrrlifurzty of’co~~~plcx (,“k to Cl, denoted
.Sl~rlk~, is
idcrlticat
pteX
Ck
attril)utc
LO
lrftrr
the
X is the
avt’rdg:”
are corriptexc5
Referring
irig valuc5
I’,, , w tlcrcl i and j art’ all t he selectors
‘l’htl tfeyrcl: uj ciifleretwe
parl>.
COlIl~JlcX
Finally,
of selc>cLor S, to selector
of
S,.
the avcragct ov(lr at I
of 111 for attribute
of a11 attributts.
the simplicity
cluster
v
C. 0 1’II S forms thtlsta cornptexes
of all attributes.
dt~l~~rt~~inc?the quality
clusLc:rirlg
-
Im] v InJ)}
it has a value of 121 fi>r attribute
of /?I/or I ~nj t‘or aLtribute
for all values
(C
- 1x1) A (C
selector
C can
cluster
We dcfiric
involved.
of an attrib\rte.
Iector
B and C are:
of the
selector
are three
attribute
sim-
The
that
and there
that
of the
is more
domain
ements,
this data,
attribute.
to be the negative
of the second
to be an elcmcri t of a selector
(;ivtrrl
The
of’ the complexity
is ’
:~, because
lm,7~j)
by the
the number
A is - 1:.
complexes
lu/ and lb] over attributes
i.e.,
of the selector.
of that
is defined
of u selec-
divided
have,
is
of an attribute
complex
(I), the second selector
has a complexity
value of
:I
I. The value of complexity
for attribute
A is the av:1
for
er-age of 1, I, i, and i which is ii. Thus the silllplicity
attribute
alrd, C as follows’:
could
selectors
A cotttplex
complexity
is the average
(2) in our example
jrnj,
values
The
161. ‘I‘he complexity
(In],
descriptions
to maxirriize
selectors. Il:acti selector
for the attribute
values
two elements,
the
value of the tiunl-
of’ t Ile selector
the selector
complexity
complex
class
difference
ttre possible
of domain
complexity
among
of disjointness
of an attribute.
disjurlctiou.
of terms
values
this degree
is a norrrialixed
product
from
linkclti by internal
the disjoint-
overlap
classes.
in the complexes
a list of elerrierlts
were used
measures
clusler
classifi-
criterion
has simple
dt>gree of inter
the distance
number
If the new attributes
that
diflerence
it
A second
and arbitrary
‘I’he less values
attributes,
so that
classes.
if the above
tor is t tie nurnl,rAr of trrrns
the rluster-
0 P II S decides
the trivial
occur
rnter cluster
‘l‘lre simplicity
attribute
which
of an attribute
for the value of an attribute
with
this
At
the classes,
which
value of an attribute.
have
be further
set and a list of attributes,
sehbct that
I6jj. Suppose
cannot
the classes.
selection
The
and applies
the final classes
The
a proposed
of that, class.
attributes.
divide
2.1.1
rt~embers
An arc in the hier-
value for attributes
rlew attributes
to refine
has determined
whose
thtt classes
given
defines
classes
with ttle value for the chosen
and any other
recursively
the objcict, set is di-
attribute.
might
a partitiori-
description,
and differentiate
nt’ss of two complexes.
remaining
to choostl
a sitrlple
is used to avoid
which
clustering
is used
forms
to characterize
cation
critchria.
archy
is easy
criterion
wllich
At each
an attribute
set according
illg at,tribute
criterion
pairs for a list of altributes.
in a top
the object
on the
Ii/. The goat of the algorithm
dc!IlOtXd
(,‘i,
clrlster
01
dll
fjljk[,
k ,jIiSt
ag$ri
/l~f’~~
values,
to ttie t~xartlple,
various
Sirrl~/.
ififlkrerlc’e tfeyree of arl attribute
k- / 1, wticlre k and f
01‘ill1 Vatut5 of’ Lhe attri
for the
I
ot
of coin-
bultl X.
wc calculate
computatiorls
Ltle follow-
to calculate
the
dlld set
two
of the
LEARNING
/ 509
inttlr
(‘luster
diff’erenct> degree
for attribute
A:
size and the relationship
and the feature
plex
relation
size
eat
eat.
size
the third
the relation
relation
that
Complex
Y
argument
of the object,
of the feature.
.Y>
X eats
the first and second
are members
is a value
eat(X
to form the com-
(X ,Y, Z>, describing
and Y is of sixe Z. Note that
of a complex
Thus
(Y, 2) are composed
set, while
relations
will
be used as attributes.
b’or the selectors
of attribute
C, we compute
iri a similar
The
value
a complex
‘I’IIIIS
[JteX
IIlLlX{
; ).I,} t 111clx(0,
I} t l,l,X{l,O}X 5
1a
1’12
3
s
That
is, the set
1’2,
isfied
for sorrie
we
(I)
c-orrt~Jtex
(a)
of’
A of (i
att,rit)ute
of corn-
t :)/2
5
ii deyrcr
o/ sirrdurrty
of’ complex
(2)
to
cotriplex
(I)
of
1
I I1
I.
‘
I’
her&re
the
rlqret:
u/
ctr#t!rences
are
:(
and
0
re2
SJJN~ ivtlly. ‘I‘t ie inter cluster drflerence deyree for attribute
;irl(l
I O),‘:!
:,.
is defined
r-f (X, Y, Z),
r f for the object
IIl‘lX( ; ,O)1 } t IIIILX{f ,l ,I)}
1 1
2
a
degree of deyree oj similurity
have
lo
A is (::
of an attribute
relation
X is the set
that
exarripte,
domain
because
Y,
eat
bound
sizecsnakes.
t,o mice
and
medium)
is satisfied
attribute
eat
snakes,
because
insects,
has
a value
snakes
eat
r f (X, Y,Z,)}.
value
for
Y
size(snakes,
to snakes.
small
size
medium],
is satisfied
eat
of
is sat-
of eat
is [small,
small)
and
for Y bound
size
3
r f (X,Y .Z)
the
for snake?, in the food chain
Given
of the attribute
{Z, 1 -1 Y
of all Z’s, such
Y. For
as follows.
the value
Thus,
[small.
and
Y,
the
medium]
medium
for
sized
ani-
rr1als.
‘I’llis computation
at tribute
makes
tt~rri, values
value
(~,6]
value
l~,I,cl,
sm(1u,
is further
and
llowever,
.Si911:!,
has a higher
rneasirre
‘I’versky
181 supports
irr the example,
thus
wcbigli lhe
Therefore
hierarchy
tree,
This
/ II* inter
irriport4ir.e
cluster
At eaclr
a quality
value
cluster
for
involve
only
two objects,
tween t Ire two objet ts.
tributes,
.Nc~w attributes
is a relation
relation.
trit,il tc5 are not sufficierlt.
of Ltlc sarnr
class.
while
rtbl;lt ioIls arid features.
2/. ‘I‘he user can
two criteria.
0 1’US
selected
at
I)e defined
to distinguish
when
betweerr
are chunks
lt‘or I tris purpost’,
we define
Lo t)(’ ttrc composition
f (Y ,Z>.
5 10 / SCIENCE
could
at-
rrierribers
composed
t iorr r(X ,Y> and in feature
airirrrals
current
of
a co4r&-
of a rela-
lcor exarr~ple iri the /0od
I,(1 tit3,c-ri bed
by the
feature
beat-
primitive
eaten(X,Y)
eden, meaning
describes
level
is defined
frorrr a complex
posc~l of a level
n retatiori
and
at level
to be defined
level k / 1 relations
t 1 relCltions are corrlposed
corrIpt(bx relations
us4
corriplcxity.
tributes
‘l‘hus,
process,
Only attributes
objects
are first
ttrct~ based
upon
If at, any tirrlcs
which
features
in the clustering
used to define attributes.
level
These
to define
Relations
but
rather
are used to clus-
classified
attributes
relations
ilow
Each
current
are defined.
with
a
com-
feature.
the
in
Now,
one.
anti thuh level k t I attributes.
arc’ not. directly
features,
relationship
relation
and an existing
have
by Y,
are defined
attribute
tinit> new attributes
the
eaten
two
Z. Relations
starting
91
or the inverse
describes
of order,
It:&
us-
A primitive
X is being
the
Y eats
relations
as a relation
two objects.
to the system
eat (X ,Z>
levels
“link”
more involved
supplied
SOIIK~ Y and
i~rcreasirrg
between
based
with
upon
increasing
cannot
rcbfine class~hs, the system
define
terminates
at-
having
reacht~d a final ctassilicatiorl.
At each level k, new level k relations
~~frx relutr‘o~i r f (X, Y, 2)
r/mirL tlorriairr
eat
of several
re-
relations
is a direct
to define
‘I‘htl rcllatiorl
relation
of X eats
k
New at tribut.cs
one
set of binary
primitive
a feuel n relution
relations
relation
level
and there
consisting
of
t.tlirlL
a small
These
In order
We deline
ing YLprimitive
their
Att,ril)utc!s
havtk to
relations
are formed.
with
cut or parent.
as
ter objet ts.
difference
valutt of the attributes
is supplied
such
t>iL(.tIrlotlt’ in the eX~>i~l~dillg tree.
2.2 (kneratirlg
systerrr
k is increased
value is the sum of
of these
The
lations
Itbvel k
off bc~tween the inter
for hoirit’ user spc~citied cot~lfic~ierrls u and
rrraxirtlizchs the qualit,y
any
(2) also satisfies
of a class description.
is c~orriputed.
u 4 sirriplicit,y
. . . as
. . . as a subject.”
of corriplex
a t,rade
Ievc>l in the expanding
slimulus
ttiari Sz’rr~,~.
tlifft!rc~rlc~c~
arid the sirrlplicity
tAac.tI al,tribut,e
a11
evidence
( I ), but riot vice versa.
value
such
may seem
and tie provides
to thrh complexes
0 I’ 11 S rriaxirrii~t3
be as disproperties.
will prorrrotc
stimulus
t,he conditions
thtb c~orlditions of corrlplex
is,
it is from
should
similarity
riieasur-e,
once again
satisfying
That
than
hurr~arrs “terid to st~1t~c.t.the Itlore salient
I<eferririg
0 1’II S sys-
with different
difference
a rc~l’ert~rrl, and t.lit~ less salient
object
for an
ordered.
descriptions
idea of an asyrrirrietric
at first.
irl the
(b,c,ct[
classes
cluster
asyrrIrrit~t.ri(~ similarity
difference
si~rl( [u, 61, 16, c, dl) is less than
Class
the inter
that,
partially
value
therefore
to ensure
c‘or~rrtcrirrt,uitive
that
are
from
61,[a, 6, cl).
Maxirrlixing
clustcar
use of Lhe fact
of attributes
tirict, as possible
The
of the irrter
1 relation
is composed
a level k ret&ion.
limit
relations
which
nurrrber
to refine
I relatiorls
011ly t,tIe relatiorrs
classc:,
of retatiorls
clxptosion
at level k
new relations.
A level
to form
are defined.
of the number
carI be dt~fined at each
of the k
relations.
define
All inverses
the combinatorial
are defined.
with a level one relation
To
of possible
level, only a limited
arc considered
to define
wtrich dtJlirred attributes
1 are used at t,he rlext
new
used
level to
Two
3.
0 1’II S has
applications
ale described
by a set
following
sections:
in any
of features
Two examples
tjons.
Examples
3.2 The
domain
and
objects
a set of binary
of such domains
the food chain
where
rela-
are presented
dornain
in the
and the genetics
tiorriain.
ics.
The
fying
tors.
two features,
example,
size(
size and
locorrrotion,
we describe
songbirds,
songbirds
insects),
jects
are characterized
ovc’r the objects
At first,
objects.
is chosen
jcc.ts
inter
tree.
tion
attributes
with
The
eaten
locomotion
peas
which
cut
tures
as the
to classify
the
Therefore
of rnediurn
sized ob-
feature
color
hawks,
owls,
parent
left, and new
of anirnals
defirles
eat
The
‘I‘hese four attributes
For exarnplt:,
is refined
two
level one
and attributes
eaten
describe
the
size
that
and small
the exist-
of rnediurn
eat
animals,
two deeat that
are used to divide
the class
and
sized flying
size.
llawks
and
while songbirds
only
the current
there
attributes
have been
are only two classes
with
used to refine
more than
the
one ob-
ject
left, the class of frogs and toads,
and the class of hawks
and
owls.
eat
eaten
The
eat
with
level
and their
the features
toads
two
relations
inverses
to define
have the same
values
[large,
medium]
for these
is, hawks
sized
while
and
~IIC~~UIJI,
eaten
relations
frogs
chat animals
allirIlals,
large,
eat
and
hierarchy
size
[large,
small
define
loads,
eat
eat animals
are equal.
was picked
of these
attributes
so the systern
is shown
in Figure
eaten
size,
small].
namely
‘1’hal
by large alld medium
which
are eaten
Thus,
the
The
which
terrrlinates.
1.
and
there-
0 1’IJ S continues
example,
with
refine
attribute
t,he class
The
ferent
resulting
classes,
traits.
shape
Again
fic:d as the various
0 I’ IJ S defines
ofl’spring,
and
hierarchy
system
paper,
relations
llsing
is able
an example
to find
methods
from
and
the color
and characterized
which
Mendel
green
which produce
Research
the
clustering
object
set
the relational
classifications
the domain
peas;
peas as
ofFspring.
a conceptual
of conceptual
as
identi-
For example,
of round
Further
over
and
over the object
purebreds.
green
with
nine dif-
and recessive
with
class has members
we presented
uses
dominant
classes
and
of classes.
ventional
and
peas
which orlly have round green
4. Summary
which
crossing
He observed
defined
hybrids
wrinkled
for
as parents
the relations
two different
while the other
green
round
tem
different
all nine classes
has Inembers
one class
only
offspring.
distinguishing,
the 0 t’ IJ S system
classes
only
contains
green
hybrids
and shape.
0 I’ II S correctly
intermediate
charac-
purebreds
as parents.
of each pea and asserted
lo this
of
all having
We supplied
with
point
or green
the character-
and
the classes
the
-color
At this
Mendel’s
of green
his experiments,
color
and
for these
a yellow
with
yellow
both
purebreds
traits,
yellow
parent
peas.
the class of hybrids
purebreds
continued
two different
system
of yellow
the class
to refine
between
purebreds
by
next level
which
it
the
color
value
Furthermore,
have
peas
to distinguish
corresponds
yellow
the
At first,
off spring
hybrid.
while
about
purebreds.
as either
has green offspring,
and other
pea produces,
identified
For cxarnple,
terization.
fea-
which
For the class of yellow peas,
the class
classes
off-
parent.
and the simplicity
or a (yellow)
ixation
features
each
In the running
to refine
all peas are correctly
set.
hawks and owls have
that class.
animals.
eaten,
Frogs
new attributes,
medium,
which are eaten
owls
is used to divide
cannot
tree
llowever
for the attribute
and
eat
and concatenated
level two attributes.
values
fore that class is Itot refined.
diKerent
eat,
are formed,
difference
peas
inforrnation
the attributes
are defined.
cluster
Mendel
animals.
Next,
color
purebred
size,
the latter
of the animals
using the attribute
owls eat rnediurn
eat small
relations
by an object,
object.
ing classes.
all possible
locomotion,
first
eaten
inter
with
and
green
of purebreds,
the same
their
oj’spriny
of hybrids
had
exactly
is used as an attribute
alld green peas.
peas had yellow
of hybrids,
from
yel-
peas only produced
the same
is provided
the classes
has used locomo-
with
different
pea and the
defines
attributes
coulplex
offspring
0 1’[JS
color of each
with
both
to self-fertilize
the class
and the class
with
pea was yellow
consistently
offspring
parent,
set, in the
members:
peas
with features
When
size
yellow
ob-
was crossed
he continued
hypothesized
produce
some
offspring
pea
ances-
of genetics,
some of the yellow
Green
features,
pea, it produced
while other
thus
the object
are no attributes
the size and loc.ornotion
After
one
the system
scribe
classes,
Fifty
the relationship
value.
a class
01’1JY
size,
locomotion.
objects
Mendel
of classi-
and their
offspring
that
After
that
offspring
ob-
value as locomotion,
to divide
there
following
eat
he discovered
offspring.
as attributes
difference
After
to that
forrned :
peas,
consists
observable
father
garden
pea the resulting
yellow
All fourt,een
a yellow
low and green offspring.
the field of genet-
descendants
the founding
he self -fertilized
spring.
have to be defined.
relations.
garden
141. When
and green
two features.
the following
classes,
In response
are
cluster
and snakes.
LO refine
facts:
of their
when
from
in genetics
orlly 011 their
not
Mendel,
that
produce
For example,
is created
songbirds,
I+‘or
set.
as the first attribute
hierarchy
eat.
the following
to describe
has the sanle siniplicity
but. a higher
using
eat(songbirds,
by the same
0 E’lJ S uses features
size
relation,
songbirds).
facts are asserted
anilnals
locomotion(songbirds,
worms),
and eat (hawk,
rc>lational
and
using
medium),
* eatcsongbirds.
fly)
we characterize
based
Cregor
an example
problem
but also or1 features
a green
domain,
Domain
clust,ering
objects
served
In the food chain
Genetics
I,et us now consider
information,
not possible
clustering.
of genetics
with
a
this
con-
presented
We
where
sys-
to define
the system
LEARNING
/ 511
1 Classification
Figure
is ahIt: to form
thtlrrnorr,
the classes
we introduced
uscti in the classification
‘I‘hi:, work can
tic LO assume
available
buil(l
that
conlirr~led,
tion:,
‘i‘tlc~ present
relat iorls.
version
enhance
of chemistry,
chrtit:s) 1,ticir reactive
can
si~~iilar predic-
handle
working
its power.
some compounds
depending
in which
be formed
Using
1,ernary
IY, yet iI1 a more efficient
manner.
;tct ivc>ly (~llgagt~d irl working
11. ary
are classified
as
other
prop-
alkalis
react.
relaliolis,
At the moment,
in these
we are
like to t hdllk
help
OII
I’at La~lgley,
t.his work,
p~~)plt~ from
the rnachirrt~ learnirlg
IIL(’valuable
corrlnleI1t.s
wah supported
in part
f’rolrl t tie Inforr~ratiotl
search .
on drafts
by
Scietlces
IIon
IIose and ILar~tly
of the Ninth International
ference
on Artificial
Intelligence,
Langley,
G. 1,. The
search
discovery.
111 Muchine
Approuch,
Vol. I!, H. S. Michalski,
Michalski,
tual clustering:
bona1
I)ivision,
NO0014
4 (1980),
84
tion:
/ SCIENCE
and T.
Los Altos,
and ‘I’. M. Mitchell,
1983, 331
goal
Michalski,
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lnterna-
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An Artijiciuf
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J.
G.
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Carborrell,
Approach,
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into conjunctive
oJ Policy
219
[B] Michalski,
Office of Naval He-
of scientific
acquisition
A theoretical
data
Journal
IJI Machine
Contract
Bradshaw,
aspects
J. G. Carbonell,
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An
Kaufman
R. S. K nowledge
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This
Learning:
Con-
1985.
H. A., and
Four
clus-
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19X6, 425 469.
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to conceptual
691-697,
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as well as the numerous
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1’. Approaches
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al IJC1 who gave
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I uould
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Ilniversity
clustering
of Information
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Iltis, t1. The f,l/t
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conceptual
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[4]
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to c; 1,11 IJ 13 l<K
A hierarchical
M Mit,chell,
binary
with
in
on (among
in a wdy similar
only
For example,
For example,
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wil tI cLc.ids to forrrl salts.
could
he
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of the system
a11d salts
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can either
in other
[Z]
predict-
be disc.onfirrned,
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alkalis
clax,t?,
predictions
or ~,hey call
An exlension
thrt domain
itcitlb,
available,
of classtlb
information,
D.
Report
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a rclvisiorl
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partial
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Tech.
It is unrealis-
describing
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An incremental
domain
new attributes
in two ways.
all the information
the hierarchy
As IIWW data
and purekreds.
to define
for food chain
process.
be ext,ended
initially.
ing rllissing
of hybrids
a method
Tree
of Similarity.
Psyrhological
Review