source: orange/docs/widgets/rst/visualize/linearprojection.rst @ 11778:ecd4beec2099

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1.. _Linear Projection:
2
3Linear Projection
4=================
5
6.. image:: ../../../../Orange/OrangeWidgets/Visualize/icons/LinearProjection.svg
7
8Various linear projection methods with explorative data analysis and
9intelligent data visualization enhancements.
10
11Signals
12-------
13
14Inputs:
15   - Examples (ExampleTable)
16      Input data set.
17   - Example Subset (ExampleTable)
18      A subset of data instances from Examples.
19   - Attribute Selection List
20      List of attributes to be shown in the visualization.
21
22
23Outputs:
24   - Selected Examples (ExampleTable)
25      A subset of examples that user has manually selected from the scatterplot.
26   - Unselected Examples (ExampleTable)
27      All other examples (examples not included in the user's selection).
28   - Attribute Selection List
29      List of attributes used in the visualization.
30
31
32Warning: this widget combines a number of visualization methods that are
33currently in research. Eventually, it will break down to a set of simpler
34widgets, each implementing its own method.
35
36Description
37-----------
38
39This widget provides an interface to a number of linear projection methods that
40all deal with class-labeled data and aim at finding the two-dimensional
41projection where instances of different classes are best separated. Consider,
42for a start, a projection of a **zoo.tab** data set (animal species and their
43features) shown below. Notice that it is breast-feeding (milk) and hair that
44nicely characterizes mamals from the other organisms, and that laying eggs is
45something that birds do. This specific visualization was obtained using FreeViz
46([1]_), while the widget also implements an interface to supervised
47principal component analysis ([2]_), partial least squares (for a nice
48introduction, see [3]_), and RadViz visualization and
49associated intelligent data visualization technique called VizRank
50([4]_)
51
52.. image:: images/LinearProjection-Zoo.png
53   :alt: Lienar Projection on zoo data set
54
55Projection search methods are invoked from :obj:`Optimization Dialogs` in the
56:obj:`Main` tab. Other controls in this tab and controls in the :obj:`Settings`
57tab are just like those with other visualization widgets; please refer to a
58documentation of :ref:`Scatter Plot` widget for further information.
59
60.. image:: images/LinearProjection-FreeViz.png
61   :alt: FreeViz screen shot
62
63:obj:`FreeViz` button in :obj:`Main` tab opens a dialog from which four
64different methods are accessed. The first one is FreeViz, which uses a paradigm
65borrowed from particle physics: points in the same class attract each other,
66those from different class repel each other, and the resulting forces are
67exerted on the anchors of the attributes, that is, on unit vectors of each of
68the dimensional axis. The points cannot move (are projected in the projection
69space), but the attribute anchors can, so the optimization process is a
70hill-climbing optimization where at the end the anchors are placed such that
71forces are in equilibrium. The FreeViz optimization dialog is used to invoke
72the optimization process (:obj:`Optimize Separation`) or execute a single step
73of optimization (:obj:`Single Step`). The result of the optimization may depend
74on the initial placement of the anchors, which can be set in a circle,
75arbitrary or even manually (:obj:`Set anchor positions`). The later also works
76at any stage of optimization, and we recommend to play with this option in
77order to understand how a change of one anchor affects the positions of the
78data points. Controls in :obj:`Forces` box are used to set the parameters that
79define the type of the forces between the data points (see [1]_).
80In any linear projection, projections of unit vector that are very short
81compared to the others indicate that their associated attribute is not very
82informative for particular classification task. Those vectors, that is, their
83corresponding anchors, may be hidden from the visualization using controls in
84:obj:`Show anchors` box.
85
86The other two, quite prominent visualization methods, are accessible through
87FreeViz's :obj:`Dimensionality Reduction` tab (not shown here). These includes
88supervised principal component analysis and partial least squares method.
89The general objection of these two approaches is the same as for FreeViz
90(find a projection that separates data instances of different class), but the
91results - because of different optimization methods and differences in their
92bias - may be quite different.
93
94The fourth projection search technique that can be accessed from this widget
95is VizRank search algorithm with RadViz visualization ([4]_). This is
96essentially the same visualization and projection search method as implemented
97in :ref:`Radviz`.
98
99Like other point-based visualization widget, Linear Projection also includes
100explorative analysis functions (selection of data instances and zooming).
101See documentation for :ref:`Scatter Plot` widget for documentation of these as
102implemented in :obj:`Zoom / Select` toolbox in the :obj:`Main` tab of the
103widget.
104
105
106References
107----------
108
109.. [1] Demsar J, Leban G, Zupan B. FreeViz-An intelligent multivariate
110   visualization approach to explorative analysis of biomedical data. J Biomed
111   Inform 40(6):661-71, 2007.
112
113.. [2] Koren Y, Carmel L. Visualization of labeled data using linear
114   transformations, in: Proceedings of IEEE Information Visualization 2003
115   (InfoVis'03), 2003. `PDF <http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=3DDF0DB68D8AB9949820A19B0344C1F3?doi=10.1.1.13.8657&rep=rep1&type=pdf>`_
116
117.. [3] Boulesteix A-L, Strimmer K (2006) Partial least squares:
118   a versatile tool for the analysis of high-dimensional genomic data,
119   Briefings in Bioinformatics 8(1): 32-44.
120   `Abstract <http://bib.oxfordjournals.org/cgi/content/abstract/8/1/32>`_
121
122.. [4] Leban, G., B. Zupan, et al. (2006). "VizRank: Data Visualization
123   Guided by Machine Learning." Data Mining and Knowledge Discovery 13(2):
124   119-136.
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