I found these two question and answers sessions that may help you out.
Regards,
-Bill
1. How does natural break work in MapInfo?
We base our Natural Break algorithm on the procedure described by Jenks and
Caspall in their article "Error on Choroplethic Maps: Definition,
Measurement, Reduction" from the Annals of American Geographers, June,
1971.
The Natural Break scheme is designed to collect entries into groups, while
introducing a minimum of error. If you have sorted entries with numerical
values of 1,2,3,100 and you want to create two groups, you would not want
[1,2] in the first group and [3,100]) in the second, because now the second
group is not representative of the best distribution; it has a lot of
error.
The criterion we use for measuring error is the total statistical error for
each group, calculated as the total difference between each entry and the
group average.
With the entries [1,2,3,100]: Make two groups
Error of the [1,2] and [3,100]:
.5 +.5+48.5+48.5=98
Error of [1,2,3] and [100]:
1 + 0 + 1 + 0=2
The numbers verify what is intrinsically obvious; the second grouping is
better. So, in order to get the best natural break, MapInfo divides the
entries roughly equally into groups (i.e., grouping 500 entries into 10
groups, the starting point (after sorting) would be the first 50 in the
first group, then the next 50 in the second group, etc.).
If we move entries from group 1 to group 2, does the total error go up or
down? Through a combination of intelligent moving decisions, and then a
set of forced moves, we attempt to find the minimum error possible.
Note: We do not always necessarily find the minimum error possible. Consider this.
This is drastically simplified; there is a lot more going on here than will be
immediately obvious. It will
convey the point, however.
|
| *
| ** **** ** ** *
| ** A ** * * * * * *
| *** * * * * *D *
| ** * * * ** *
| * B * * *
| **** * *
| * *
| **C**
| *
|
|___________________________________________________________
Let's say the initial, equal-count distribution puts us roughly at point A. The
intelligent guessing will move
us to the bottom of A. Then, the forced moving might make us realize, hey! We can do
better with B! So
if the forced moving gets us over the edge to B, then the intelligent moving will get
us down to the minimum
error for this rough configuration: Error B. Now, the forced moving probably won't be
enough to get us into
the realm of C. So, we will stop, confident that we have done the best we can, at the
configuration giving
error B, when we could have done better with the configuration giving error C, the
lowest.
This is not to suggest that the method we use is poor-- far from it. To guarantee the
least error every time,
you would have to try all possible combinations. That is too time-intensive; it would
take lifetimes for a large
table.
So, we do some intelligent guessing, and some shaking, and we generally get a good,
useful result without
taking a tremendous amount of time. Finding the "natural breaks" is an iterative
refinement process. We
adjust range breaks so that the Tabular Accuracy Index (or TAI) is maximized, and the
Tabular Error (TE)
is minimized. The TAI of a set of ranges can be computed as follows:
where i is a the range number
RangeError(i) = SumOf(ABS(RangeMean(i) - DataValue))
OverallError = SumOf(ABS(OverallMean - DataValue))
TE = SumOf(RangeError(i))/OverallError)
TAI = 1 - TE
2. Quantiling:
Differences beteween thematic shading using quantile or equal ranges range
methods
What is the difference between a ranged shade using quantile on the same
field you are shading by, and a ranged shade using equal ranges?
E.g., shade states with 5 ranges on Pop_1990 round by none using:
1) equal ranges
2) quantile using Pop_1990
With equal ranges, you might get something like:
24 - 30 million
18 - 24
12 - 18
6 - 12
0 - 6 million.
(Given that the state with the largest population is California, with around 30
million.) Ranges are defined by looking at the range of values.
With Quantiling, MapInfo attempts to define the range so that the total for a
given range -- in this case, the total population for all of the states that fall
into that range -- is roughly the same for each of the ranges.
So, in the example, MapInfo will start with the states with the least
population, and keep adding states to the bottom range until adding another
state would make the range grand total exceed, say, 50 million
(a fifth of the total population for the US).
Mail List:[EMAIL PROTECTED]
From: "Lathrop, Travis" <[EMAIL PROTECTED]> on
11/08/2000 11:53 AM CST
To: "'[EMAIL PROTECTED]'"
<[EMAIL PROTECTED]>
cc:
Subject: MI-L
Can someone please explain natural breaks, and quantile breaks when
creating
a ranged thematic map to me? The book does a poor job of explaining the
two.
Travis Lathrop
Intercarrier Service
913/762-4806
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