lecture 9 - spatial analysis and statistics

Question 1

what is spatial data?

Answer 1

something you can prescribe an x and a y coordinate to e.g. a map, image

Question 2

vector data

Answer 2

points, lines and areas

Question 3

raster data

Answer 3

regular grids of cells e.g pixels

Question 4

what order do the axis go in the (cartesian) coordinate system?

Answer 4

x then y

x,y

Question 5

what additional axis is sometimes added in datasets such as images?

Answer 5

z axis

Question 6

how do you calculate the distance between points on a diagonal?

Answer 6

use Pythagoras’ theorem

Question 7

what do trigonometry and Pythagoras allow us to do?

Answer 7

work out the dimensions of individual pixels
Pythagoras works out distances on images
trigonometry works out widths

Question 8

speed =

Answer 8

distance / time

Question 9

what does a cluster analysis look for?

Answer 9

spatial patterns

Question 10

spatial patterns in the cluster analysis can be described as?

Answer 10

• dispersed
• clustered
• random

Question 11

define dispersed

Answer 11

closest to uniform

Question 12

define random

Answer 12

any visually apparent cluster is due to chance

Question 13

define clustered

Answer 13

pattern or grouping

Question 14

what method is used for testing uniform distribution?

Answer 14

chi squared

Question 15

in a 3D histogram, the flatter the graph looks =

Answer 15

the more uniform the distribution is

Question 16

what method is used for testing for random distribution?

Answer 16

Chi squared - compared with the poisson distribution

*if chi squared statistic is lower than critical value, data follows a poisson distribution and is therefore random

Question 17

what is the poisson distribution used for?

Answer 17

to calculate the probability of a spacing at a given distance (or time interval/area/value)

Question 18

what method is used to test for clustered distribution?

Answer 18

nearest - neighbour criterion

*to reject null hypothesis, z value has to be >1.96 OR

Question 19

what methods can be used to test for similarities between clusters?

Answer 19

• hierarchal clustering
• nearest - neighbour clustering
• k - means clustering
• gaussian mixture clustering

Question 20

hierarchal clustering

Answer 20

• dendrogram
• assumes that each individual data point is a cluster
• based on distance between data points they are grouped again, and so on
• can easily pick the level of clustering you would like

Question 21

gaussian mixture clustering

Answer 21

• detects peaks in the datapoint concentration

* drawback of this method is = have to define the number of clusters you have to begin with