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;;; File:  AutoClass:doc;interpretation.text
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;;;  AUTOCLASS 3.0  Released 5/11/90    contact:  Taylor@pluto.arc.nasa.gov ;;;
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Interpretation of AutoClass Results:

  Now you have run AutoClass on your data set -- what have you got?  Typically,
the AutoClass search procedure finds many classifications, but only saves the
few best.  These are now available for inspection and interpretation.  The most
important indicator of the relative merits of these alternative classifications
is Log total posterior probability value.  Note that since the probability
lies between 0 and 1, the Log probability is negative and ranges from negative
infinity and 0. The difference between these Log probability values raised to
the power e gives the relative probability of the alternatives 
classifications.  So a difference of say 100 implies one classification is 
e^100 more likely than the other.  However, these numbers can be very 
misleading, since they give the relative probability of alternative 
classifications under the AutoClass ***assumptions***.

  Specifically, the most important AutoClass assumptions are the use of normal
models for real variables, and the assumption of independence of attributes
within a class.  Since these assumptions are often violated in practice, the
difference in posterior probability of alternative classifications can be
partly due to one classification being closer to satisfying the assumptions
than another, rather than to a real difference in classification quality.
Another source of uncertainty about the utility of Log probability values is 
that they do not take into account any specific prior knowledge the user may 
have about the domain.  This means that it is often worth looking at 
alternative classifications to see if you can interpret them, but it is worth 
starting from the most probable first.  Note that if the Log probability value
is much less than that for the one class case, it is saying that there is 
overwhelming evidence for ***some*** structure in the data, and part of this 
structure has been captured by the AutoClass classification.

  So you have now picked a classification you want to examine, based on its Log
probability value; how do you examine it?  The first thing to do is to 
generate an "influence" report on the classification using the report 
generation facilities documented in /doc/reports.text.   An influence report 
is designed to summarize the important information buried in the AutoClass 
data structures.  The first part of this report is a listing of the overall 
"influence" of each of the attributes used in the classification.  These 
influence values are a weighted average of the "influence" of each attribute 
in each class, as described below.  The next part of the report is a summary 
description of each of the classes.  The classes are arbitrarily numbered from
0 up to n, in order of descending class weights.  A class weight of say 34.1 
means that the weighted sum of membership probabilities for class is 34.1.  
Note that a class weight of 34 does not mean that 34 cases belong to that 
class, since many cases may have only partial membership in that class.

  In the report on each class, the attribute parameters for that class are
given in order of highest influence value.  The "influence" value of an
attribute in a class is an information measure that roughly indicates how
informative that attribute is in describing a class -- i.e., an indication of 
the distinguishing attributes for that class.  Only the first few attributes
usually have significant influence value.  If an influence value drops below
about 20% of the highest value, then it is probably not significant, but all
attributes are listed for completeness.  In addition to the influence value for
each attribute, the values of the attribute parameters in that class are given
along with the corresponding "global" values.  The global values are computed
directly from the data independent of the classification.  For example, if the
class mean of attribute "temperature" is 90 with standard deviation of 2.5, but
the global mean is 68 with a standard deviation of 16.3, then this class has
selected out cases with much higher than average temperature, and a rather
small spread in this high range.  Similarly, for discrete variables, the
probability of each outcome in that class is given, along with the
corresponding global probability.  This information gives a overview of how
each class differs from the average for all the data, in order of the most
significant differences.

  Having gained a description of the classes from the "influence" report, you
may want to follow-up to see which classes your favorite cases ended up in.
Conversely, you may want to see which cases belong to a particular class.  For
this kind of cross-reference information two complementary reports can be
generated.  These are more fully documented in /doc/reports.text. The "class"
report, lists all the cases which have significant membership in each class and
the degree to which each such case belongs to that class.  Cases whose class
membership is less than 90% in the current class have their other class
membership listed as well.  The cases within a class are ordered in increasing
case number.  The alternative "cases" report states which class (or classes) a
case belongs to, and the membership probability in the most probable class.
These two reports allow you to find which cases belong to which classes or the
other way around.  If nearly every case has close to 99% membership in a single
class, then it means that the classes are well separated, while a high degree
of cross-membership indicates that the classes are heavily overlapped.  Highly
overlapped classes are an indication that the idea of classification is
breaking down and that groups of mutually highly overlapped classes, a kind of
meta class, is probably a better way of understanding the data.

  In summary, the various reports that can be generated give you a way of
viewing the current classification.  It is usually a good idea to look at
alternative classifications even though they do not have the minimum Log 
probability values.  These other classifications usually have classes that 
correspond closely to strong classes in other classifications, but can differ 
in the weak classes.  The "strength" of a class within a classification can 
usually be judged by how dramatically the highest influence value attributes 
in the class differ from the corresponding global attributes.  If none of the
classifications seem quite satisfactory, it is always possible to run AutoClass
again to generate new classifications.

  Finally, the question of what to do after you have found an insightful
classification arises.  Usually, classification is a preliminary data analysis
step for examining a set of cases (things, examples, etc.) to see if they can 
be grouped so that members of the group are "similar" to each other.  AutoClass
gives such a grouping without the user having to define a similarity measure.
The built-in "similarity" measure is the mutual predictiveness of the cases.
The next step is to try to "explain" why some objects are more like others than
those in a different group.  Usually, domain knowledge suggests an answer.  For
example, a classification of people based on income, buying habits, location,
age, etc., may reveal particular social classes that were not obvious before
the classification analysis.  To obtain further information about such classes,
further information, such as number of cars, what TV shows are watched, etc.,
would reveal even more information.  Longitudinal studies would give
information about how social classes arise and what influences their
attitudes -- all of which is going way beyond the initial classification.

