3
  Unsupervised Learning Using Rough Kohonen Neural Network
                         Classifiers

                        Pawan Lingras
                              
  Department of Computer Science, Algoma University College
         Sault Ste. Marie, Ontario, Canada, P6A 2G4.
               e-mail: lingras@tbird.auc.on.ca
                              
                          Abstract

Many  of  the  existing classification methods represent  an
object  with a single precise pattern. However, some of  the
objects in the real life are more complex and hence  do  not
lend   themselves   well   to   such   a   simple   abstract
representation.  These complex objects  may  in  general  be
represented  by multiple types of patterns. Moreover,  there
may  be  several  instances of a given type of  pattern.  An
example,  of  such  an object is a highway  section.  It  is
necessary to classify highway sections into different  types
of   categories  to  establish  guidelines  regarding  their
upgrading and maintenance.
     In  a commonly used classification scheme, highways are
classified  on  the basis of trip purpose  and  trip  length
characteristics; examples of resulting classes are commuter,
business,  long  distance, and recreational.   Trip  purpose
provides  information  about  the  road  users.   It  is  an
important  criterion  in  a variety of  traffic  engineering
analyses.  Trip purpose information can be obtained directly
from the road users, but since all users cannot be surveyed,
traffic  engineers  study various traffic patterns  obtained
from  seasonal  and  permanent traffic counters  and  sample
surveys  of a few road users.  Some of the important traffic
patterns are as follows:
a)    Hourly  traffic pattern: Variation of  hourly  traffic
   volume in a given day.
b)   Daily traffic pattern: Variation of daily traffic
volume in a given week.
c)    Monthly traffic pattern: Variation of monthly  average
   daily traffic volume in a given year.

     For the purpose of classification, each highway section
needs  to  be  represented using three  different  types  of
patterns mentioned above. Moreover, for each highway section
there are several patterns of each type. For example, if one
year  data  is used for classification, there  will  be  one
monthly  pattern, 52 daily patterns, and 365 hourly patterns
for a given highway section.
     This  paper describes the rough Kohonen neural  network
classifiers for classification of complex objects. The rough
Kohonen  neural network classifiers use one  or  more  rough
Kohonen neural networks to classify different types of rough
patterns. Each value in a rough pattern is a pair  of  upper
and  lower  bounds. The conventional neural  network  models
generally  use a precise input pattern in their estimations.
The  rough  Kohonen neural networks proposed in  this  paper
consist  of  a combination of rough neurons and conventional
neurons.  Rough neurons use pairs of upper and lower  bounds
as  values  for  input and output. Similar  to  the  Kohonen
neural  networks,  the  rough Kohonen  neural  networks  use
unsupervised learning during the classification process.  In
the  unsupervised  learning, the  desired  output  from  the
neurons  is  not  known. The network  attempts  to  classify
patterns  from the training set into different  groups.  The
rough Kohonen neural networks use rough neurons in the input
layers. Variation between upper and lower bounds of a  rough
pattern  can be a useful parameter in the classification  of
the  pattern. For example, seasonal variations in the  daily
traffic volume may have some implications regarding the trip
purpose.  Hence, the distance measures in the rough  Kohonen
neural networks are based on the upper and lower bounds,  as
well as the difference between the upper and lower bounds of
the output of rough neurons.
     Recent developments in the rough set theory have  shown
that  the general concept of upper and lower bounds provides
a  wider framework that may be useful for different types of
applications.  This  study uses a non-transitive  rough  set
model   for   summarizing  the  results  of  classifications
obtained  from the rough Kohonen neural networks. The  paper
demonstrates  usefulness  of the  non-transitive  rough  set
model in making meaningful judgments regarding the nature of
traffic on highway sections.