Objectives of Lecture:
<resources for this lecture>
Enumeration rules enumerate all the possibilities. This
would include the various operations treated as "Direct Analysis
of Overlay" in the first edition of the textbook. In the
lecture on Attribute-based rules, Crosstabulation
appears as a method to treat pairs
of nominal values, Change Analysis does the same thing,
except that you know the matrix will be square (same categories
used in time 1 and time 2). These remain different from interaction
rules because there is no evaluation placed on the pairs, just
that each pair is recognized.
Direct analysis includes the change detection kinds of operations done in Exercise 3. On the face of this, you use subtraction for two nominal measures. This shouldn't mean anything EXCEPT that you can figure out what each value means. As long as the complete "truth table" of the operation can be figured out, this is just the use of subtraction (addition, etc.) to support a given Boolean function (in this case time 1 not equal to time 2).
| AND function | True | False |
| True | True | False |
| False | False | False |
| OR function | True | False |
| True | True | True |
| False | True | False |
| + function | 1 | 0 |
| 1 | 2 | 1 |
| 0 | 1 | 0 |
| + function | 1 | 0 |
| 2 | 3 | 2 |
| 0 | 1 | 0 |
with (0,1) + (0,2). Thus, if you represent nominal data
as numbers, it MIGHT just work to use addition, IF you
understand how the operation works...
| Table 5-1: Map Combination Methods | |
|---|---|
| Enumeration Rules (all combinations recognized) | |
| Crosstabulation | New categories from each unique combination |
| Change analysis | Complete matrix of all changes |
| Dominance Rules (one value wins) | |
| Exclusionary screening | One strike and you're out. |
| Exclusionary ranking | Extreme value from rankings (usually worst wins) |
| Highest bid | Extreme value from continuous data maximum profit at that site (best alternative); could be worst - highest risk |
| Highest bidder | Records identity of extreme value |
| Contributory Rules (all values contribute without regard for the others) | |
| Voting tabulation | Sum of binary exclusions |
| Linear combination | Sum of `ratings' (mean, etc.) | >
| Weighted linear combination | Weighting and rating game |
| Product | Multiplication of factors |
| Interaction Rules (pairs [or more] of values are consulted to yeild the result) | |
| Contingent weighting | Linear combination where the weights depend on some OTHER attribute value |
| Gestalt (Integrated Survey) | Informal judgement; expert opinion |
| Rules of combination | Formal interaction tables |
Rules of Combination might be discussed, but rarely considered
in all the depth of handling all interactions. Rules emerge from
the science of the layers studied - no magic bullets (no procedures
that will solve all problems).
"Linear Combination" - the Weighting and Rating Game
Vj = [[SUM]]i wi rij /[[SUM]]i wi
When the variables are continuous, suitability might have some functional form; total cost, elapsed time, ... which is not simply an average; it could be a total.
This lecture has a number of overhead examples. I apologize that they are not all loaded on the web page (due to copyright issues... some are in the text)
A presentation given
at AAG 1997 (not updated to include "enumeration")