Figure 6: 3D initial (a) and final (b) configurations, 2D final configuration (c) in a competitive learning model
The example of colour clustering
INNE: a Neural Network
The example of image compression
In unsupervised competitive neural models, single neurons compete for being the one to fire [Her91]. We implemented 2D and 3D displays of a multivariate gaussian distribution so as to allow to generate examples for this model easily. While defining a distribution in the input space, the input points, randomly generated according to the distributions, are fed into the network, which tries to find their centers.
Figure 6: 3D initial (a) and final (b) configurations, 2D final configuration (c) in a competitive learning model
The dimension of the input space is defined by the number of input neurons. The number of output neurons defines the number of clusters in which we desire to partitionate the input points. During the computation we can interactively modify the simulation parameters and affect the network behaviour in order to analyse it and improve its performance. For instance, we can choose to refine the learning algorithm, in case some output units (dead units) appeared to be stuck and never win.
In Fig. 6-a and Fig. 6-b we can visualize the behaviour of a net in the input space. The net has 3 input neurons, according to the 3D input space, fully connected to 7 output neurons. In the initial state, the 7 visible dots are randomly localized, their position being given by the weight of arcs connecting them to the 3 input nodes. After some training, the arc weights are modified so that the dots will locate the clusters. In fact they are positioned at the center of the seven gaussian distribuitions in the final configurations. In Fig. 6-c we can see the same problem for the 2D case, run with the option called increasing pattern method which avoids the dead units and visualizes the route of the weight vectors from their initial position (0, 0) to the distribution centers. In these simulations we have used 50000 steps and a linear decay term of from 0.5 to 0.
The example of colour clustering
INNE: a Neural Network
The example of image compression