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
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
The ``goodness_of_fit`` module
==============================
.. sectionauthor:: Andreas Wilm
This is a short example of how to use the goodness_of_fit module.
``goodness_of_fit`` will measure the degree of correspondence (or goodness of fit) between a multidimensional scaling (i.e. a lower dimensional representation of distances between objects) and the input distance matrix.
Let's setup some example data:
.. doctest::
>>> import numpy
>>> import cogent.cluster.goodness_of_fit as goodness_of_fit
>>> distmat = numpy.array([
... [ 0. , 0.039806, 0.056853, 0.21595 , 0.056853, 0.0138 ,
... 0.203862, 0.219002, 0.056853, 0.064283],
... [ 0.039806, 0. , 0.025505, 0.203862, 0.0208 , 0.039806,
... 0.194917, 0.21291 , 0.0208 , 0.027869],
... [ 0.056853, 0.025505, 0. , 0.197887, 0.018459, 0.056853,
... 0.191958, 0.203862, 0.018459, 0.025505],
... [ 0.21595 , 0.203862, 0.197887, 0. , 0.206866, 0.206866,
... 0.07956 , 0.066935, 0.203862, 0.206866],
... [ 0.056853, 0.0208 , 0.018459, 0.206866, 0. , 0.056853,
... 0.203862, 0.21595 , 0.0138 , 0.0208 ],
... [ 0.0138 , 0.039806, 0.056853, 0.206866, 0.056853, 0. ,
... 0.197887, 0.209882, 0.056853, 0.064283],
... [ 0.203862, 0.194917, 0.191958, 0.07956 , 0.203862, 0.197887,
... 0. , 0.030311, 0.200869, 0.206866],
... [ 0.219002, 0.21291 , 0.203862, 0.066935, 0.21595 , 0.209882,
... 0.030311, 0. , 0.21291 , 0.219002],
... [ 0.056853, 0.0208 , 0.018459, 0.203862, 0.0138 , 0.056853,
... 0.200869, 0.21291 , 0. , 0.011481],
... [ 0.064283, 0.027869, 0.025505, 0.206866, 0.0208 , 0.064283,
... 0.206866, 0.219002, 0.011481, 0. ]])
>>> mds_coords = numpy.array([
... [ 0.065233, 0.035019, 0.015413],
... [ 0.059604, 0.00168 , -0.003254],
... [ 0.052371, -0.010959, -0.014047],
... [-0.13804 , -0.036031, 0.031628],
... [ 0.063703, -0.015483, -0.00751 ],
... [ 0.056803, 0.031762, 0.021767],
... [-0.135082, 0.023552, -0.021006],
... [-0.150323, 0.011935, -0.010013],
... [ 0.06072 , -0.01622 , -0.007721],
... [ 0.065009, -0.025254, -0.005257]])
You are now good to compute stress values as shown in the following.
``Stress.calcKruskalStress()``
------------------------------
This computes Kruskal's Stress AKA Stress Formula 1 (Kruskal, 1964).
Kruskal gives the following numbers as guideline:
========== ===============
Stress [%] Goodness of fit
========== ===============
20 Poor
10 Fair
5 Good
2.5 Excellent
0 Perfect
========== ===============
Our example data gives a very good stress value:
.. doctest::
>>> stress = goodness_of_fit.Stress(distmat, mds_coords)
>>> print stress.calcKruskalStress()
0.02255...
``Stress.calcSstress()``
------------------------
This computes S-Stress (Takane, 1977). S-Stress emphasises larger dissimilarities more than smaller ones. S-Stress values behave nicer then Stress-1 values:
- The value of S-Stress is always between 0 and 1
- Values less then 0.1 mean good representation.
Using the example data again:
.. doctest::
>>> stress = goodness_of_fit.Stress(distmat, mds_coords)
>>> print stress.calcSstress()
0.00883...
|
