1. Map Generalization and Data Classification Gary Christopherson
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Map Generalization and Data Classification Gary Christopherson

2. Review/Preview Everything we talked about before the midterm
Everything we will be talking about before the final
Data classification
Why classify data
Classification rules
How to classify data
Map types
Map layout
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3. Data Classification
The process of sorting or arranging entities into groups or categories On a map, the process of representing members of a group by the same symbol, usually defined in a legend.
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4. What’s the point?
When there are too many data values on a map it can lose its power to tell a story or make a point
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5. How Many Symbols??
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6. How Many Symbols?? -- 1
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7. How Many Symbols?? -- 3
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8. How Many Symbols??
1107 SYMBOLS
4 SYMBOLS
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9. Too Many Colors??
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10. Jenks and Coulson’s Classification Rules
Encompass the full range of the data.
Have neither overlapping values nor vacant classes.
Be great enough in number to avoid sacrificing the accuracy of the data, but not so numerous as to impute a greater degree of accuracy than is warranted by the nature of the collected data.
Divide the data into reasonably equal groups of observations.
Have a logical mathematical relationship if practical.
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11. Map Abstraction Process
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12. Nominal Scale Data Nominal scale data merely establish identity
A phone number signifies only the unique identity of the phone jack or the cell phone
In a race, the numbers used to identify individual racers are at a nominal scale
These identity numbers do not indicate order or relative value
1. Nominal
· on a nominal scale, numbers merely establish identity
· e.g. a phone number signifies only the unique identity of the phone
· in the race, the numbers issued to racers which are used to identify individuals are on a nominal scale
· these identity numbers do not indicate any order or relative value in terms of the race outcome
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13. Nominal, or Categorical Data
Qualitative
Dealing with qualitative data that is ordered but without a measurable range
There are no absolute rules for this kind of classification, just general guidelines :
Features in different classes or categories should be more dissimilar than similar and should be symbolized differently
Features in the same class or category should be more similar than dissimilar and should be symbolized similarly
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14. Nominal/Categorical Symbolization
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15. Nominal/Categorical Symbolization
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16. Nominal/Categorical Symbolization
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17. Ordinal Scale Data
Ordinal Numbers establish order only
In the race, the finishing places of each racer, i.e. 1st place, 2nd place, 3rd place, are measured on an ordinal scale. The numbers mean something relative to each other, but we do not know how much time difference there is between each racer
2. Ordinal
· on an ordinal scale, numbers establish order only
· phone number is not more of anything than , so phone numbers are not ordinal
· in the race, the finishing places of each racer, i.e. 1st place, 2nd place, 3rd place, are measured on an ordinal scale. The numbers mean something relative to each
other BUT
· we do not know how much time difference there is between each racer
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18. Ordinal Data Quantitative
Dealing with Quantitative data that is ordered but without a measurable range
Ordinal Classes show relative values, not absolute values
In this example, 1 is less than 3, but we don’t know how much less it is
Using numbers to label ordinal data is often confusing
But be careful to use text that does not imply absolute values
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19. Ordinal Data
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20. Interval Scale Data
On an interval scale, the difference (interval) between numbers is meaningful, but the numbering scale does not start at zero – i.e. no absolute zero
Subtraction makes sense but division does not
200C is 100 degrees warmer than 100C, but you can’t say that it is twice as hot
In the race:
the time of day that each racer finished is measured on an interval scale
If racers finished at 9:10, 9:20 and 18:20, then racer one finished 10 minutes before racer two
But the racer finishing at 9:10 did not finish twice as fast as the racer finishing at 18:20
3. Interval
· on interval scales, the difference (interval) between numbers is meaningful, but the numbering scale does not start at 0
· subtraction makes sense but division does not
· e.g. it makes sense to say that 200C is 100 degrees warmer than 100C, so Celsius temperature is an interval scale, but 200C is not twice as warm as 100C
· e.g. it makes no sense to say that the phone number is more than , so phone numbers are not measurements on an interval scale
· in the race, the time of the day that each racer finished is measured on an interval scale
· if the racers finished at 9:10 GMT, 9:20 GMT and 9:25 GMT, then racer one finished 10 minutes before racer 2 and the difference between racers 1 and 2 is twice
that of the difference between racers 2 and 3
· however, the racer finishing at 9:10 GMT did not finish twice as fast as the racer finishing at 18:20 GMT
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21. Interval Data
Quantitative, but deals with quantitative data that has no absolute zero – so subtraction works but division does not
Interval Classes show a range of values
In this example the classes show a range of low elevations for states
Notice the negative numbers – this is why these values are interval scale, not ratio scale
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22. Ratio Scale Data
On a ratio scale, measurement has an absolute zero and the difference between numbers is significant …
Division makes sense
A 50 kg person weighs half as much as a 100 kg person, so weight in kg is on a ratio scale
Is weight in pounds on a ratio scale?
Is temperature on a ratio scale?
In the race:
the first place finisher finished in a time of 2:30, the second in 2:40 and the 450th place finisher took 5 hours
The 450th finisher took twice as long as the first place finisher (5/2.5 = 2)
Allows direct comparison
4. Ratio
· on a ratio scale, measurement has an absolute zero and the difference between numbers is significant
· division makes sense
· e.g. it makes sense to say that a 50 kg person weighs half as much as a 100 kg person, so weight in kg is on a ratio scale. Clearly the same is true for pounds. A
150 # person weighs half as much as a 300 pd person.
· the zero point of weight is absolute but the zero point of the Celsius scale (used above) is not
· in our race, the first place finisher finished in a time of 2:30, the second in 2:40 and the 450th place finisher took 5 hours
· the 450th finisher took twice as long as the first place finisher (5/2.5 = 2)
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23. Ratio Scale Data
Quantitative data that has an absolute zero – so both subtraction and division work
Ratio scale classes show a range of numeric values
In this example the classes show a range of population for states
Notice there are no negative numbers – this is why these values are ratio and not interval scale data
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24. Data Classification Most maps use data that have been classified
Number of classes is usually between 5 and 10, more likely 5 than 10
Classification methods vary depending on data and on the story you are telling
ArcGIS includes a number of different classification schemes
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25. Data Classification Best carried out in the context of a histogram
X-axis shows data values – here the number of farms in a county
Y-axis shows frequency – here the number of counties
Gray bars show the number of observations – here the number of counties for each data value
Blue lines divide data into classes of aggregated data
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26. Data Classification There are nine standard classification schemes:
natural breaks, optimization, nested means, mean and standard deviation, equal interval, quantile, arithmetic, geometric, and user defined
Creating classes based on these schemes requires summary statistics and calculations – some simple and some difficult
We will look at equal interval, quantile, standard deviation, and natural breaks
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27. Summary Statistics Mean (average)
The sum of all values divided by the number of values in the set
Mode
The value that appears with the greatest frequency.
Median
The middle value of a set of values when they are ordered by rank, when there are 2 middle values (due to an even number in the set), the mean of those 2 numbers is used
Standard Deviation
The spread of values from their mean, calculated as the square root of the sum of the squared deviations from the mean value, divided by the number of elements.
Also known as the square root of the variance
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28. Equal Interval
Constant interval between classes – based on values along the x-axis
Number of observations will be different from class to class
Good if you want to make direct comparisons between different choropleth maps
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29. Calculating Equal Interval
1440 – 173 = 1277
1277 / 5 = 253.4
Calculating Equal Interval
= 426; = 679; etc
Subtract minimum value from maximum value
Divide the result of this subtraction by the number of classes you want
The result of the division will be the width of each class
Start with the minimum and add this value to get the width of the first class
Continue adding this value to the sum of the previous class until all classes have been created
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30. Quantile Equal number of observations per class
Because the number of observations will be the same from class to class, the interval between classes will be different
Good classification scheme to use if certain statistical tests require equal numbers of observations
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31. Calculating Quantiles
92 / 5 = 18.4
Calculating Quantiles
Divide the count of observations/features by the number of classes you want
This will give you the number of features for each class
Arrange your features from least to greatest value
Divide them into classes so that the number of features in each class matches the result of your division equation
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32. Calculating Quantiles
92 / 5 = 18.4
Calculating Quantiles
Divide the count of features by the number of classes you want
This will give you the number of features for each class
Arrange your features from least to greatest value
Divide them into classes so that the number of features in each class matches the result of your division equation
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33. Jenks – Natural Breaks
Minimizes variance within a class by dividing classes in areas where there are large breaks in the data
Different sized classes, and different number of features
Often the best choice for conveying information accurately to map readers
Cannot be used to make direct comparisons between maps
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34. Calculating Jenks Don’t worry about this one
It is a method of statistical data classification that partitions data into classes using an algorithm that calculates groupings of data values based on the data distribution. Jenks' optimization seeks to reduce variance within groups and maximize variance between groups.
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35. Mean and Standard Deviations
Classes determined by the mean and deviations from the mean
Best if data displays a normal distribution
Usually symbolized using a diverging color scheme
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36. Classifying by Mean and Std. Dev.
Calculate the mean of your data
Calculate the standard deviation of your data
Arrange your first class so that it straddles the mean
Then add classes at intervals of std. dev. both above and below the mean class
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37. Same Data, Different Classification Schemes
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38. Jenks and Coulson’s rules
Encompass the full range of the data.
Have neither overlapping values nor vacant classes.
Be great enough in number to avoid sacrificing the accuracy of the data, but not so numerous as to impute a greater degree of accuracy than is warranted by the nature of the collected data.
Divide the data into reasonably equal groups of observations.
Have a logical mathematical relationship if practical.
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39. Practice Put the following numbers into different classes
Quantile – five classes
Equal Interval – five classes
7, 1, 18, 20, 6, 14, 19, 13, 2, 1, 25, 2, 23, 1, 15
Quantile – (1,1,1) (2,2,6) (7,13,14) (15,18,19) (20,23,25)
Equal Interval (1,1,1,2,2) (6,7) (13,14,15) (18,19,20) (23,25)
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40. Equal Interval
1440 – 170 = 1270
1270 / 5 = 254
= 424
+ 254 = 678
+ 254 = 932
+ 254 = 1186
+ 254 = 1440
424
678
932
1186
1440
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41. Mean and Standard Deviation
Straddle the mean
630 – 125 = = 755
505 – 250 = 255
= = 1255
255
505
755
1005
1255
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