Information Technology Reference
In-Depth Information
Example 6.5. Table 6.17 shows the proximity values for point Q of Fig. 6.21.
Rényi's quadratic entropy was computed as in (6.51).
One sees that the most similar point is point 10, i.e., point P in Fig. 6.21. In
other words, vector PQ is the one that less changes the information potential
of the 9-neighborhood vector field of Q .
Tabl e 6 . 17
Entropic proximities relative to point Q (11) of Fig. 6.21.
Point
L1 L2 L3 L4 L5 L6 L7 L8 L9
11
10
12
9
13
4
3
5
6
2
One may consider that the proximity matrix defines connections between
each point and the points referenced by each column: each point is connected
to all other points following the order defined by the proximity matrix.
Each column of the proximity matrix corresponds to a layer of connections.
A layer of connections can be represented as an unweighted subgraph, where
each edge represents the connection between an object (connection set) and
the corresponding object of that layer.
Example 6.6. We now present an example of a first layer unweighted subgraph
based on a dissimilarity matrix and proximity matrix built with the Euclidian
distance. Figure 6.24b represents the first layer subgraph for the dataset
shown in Fig. 6.24a. Clusters formed with this first layer subgraph are called
elementary clusters .
(a)
(b)
Fig. 6.24
Connections based on Euclidian distance for the double spiral dataset.
 
Search WWH ::




Custom Search