File: VisualizationHistogram.htd

package info (click to toggle)
cain 1.10+dfsg-2
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 29,856 kB
  • sloc: cpp: 49,612; python: 14,988; xml: 11,654; ansic: 3,644; makefile: 133; sh: 2
file content (61 lines) | stat: -rw-r--r-- 2,071 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
<html>
<head>
<title>Histogram Distance</title>
</head>
<body>
<h1>Histogram Distance</h1>

<p>
In the <a href="VisualizationTables.htm">previous section</a> we
studied the transient behavior of the Schlogl model by recording the
populations in a series of histograms. We saw that the populations
settled into a bi-modal distribution. The plot showing the probability
distributions for the species population is reproduced below.
</p>

<p align="center">
<!--Saved as PNG. Reduced from 8 to 6 inches and saved as JPG.-->
<img src="VisualizationPlottingHistogramsSchloglNonzero.jpg">
</p>

<p>
The total variation metric may be used to measure the distance between
two probability distributions. For two histograms (with the same lower
bound and bin width) having bin values of <i>x<sub>i</sub></i>
and <i>y<sub>i</sub></i>, this metric is half the sum of the absolute
values of the bin differences.
</p>

<p>
<i>D</i> = &Sigma;|<i>x<sub>i</sub></i> - <i>y<sub>i</sub></i>| / 2
</p>

<p>
Because the histogram represents a probability distribution, the sum
of the bins is unity, &Sigma; <i>x<sub>i</sub></i> = 1. The factor of
1/2 in the distance metric normalizes the distance to be between 0
and 1.
</p>

<p>
Hitting the histogram distance button
<img src="HistogramDistance.png">&nbsp; in the simulation output panel
will bring up a window that allows us to select a pair of histograms.
(One may also select a set of histograms, in which case the average
distance will be computed. In this way one may, for instance,
determine the average distance for a set of species.)
Below we see that as time advances the distance beween successive
frames decreases.
</p>

<p align="center">
<img src="VisualizationHistogramSchloglDistance_0_2.jpg"><br>
<img src="VisualizationHistogramSchloglDistance_2_4.jpg"><br>
<img src="VisualizationHistogramSchloglDistance_4_6.jpg"><br>
<img src="VisualizationHistogramSchloglDistance_6_8.jpg"><br>
<img src="VisualizationHistogramSchloglDistance_8_10.jpg">
</p>


</body>
</html>