*Automatic Relevance Determination*
The investigation of the redundant components of the feature vector
can be addressed
by the Automatic Relevance Determination method.
This technique (proposed by
R. Neal
and D. MacKay)
is able to detect
the relevant components of the input vector: this can be
achieved by looking at the distribution
of the synaptic weights
which connect one input unit to all of the units in the next layer.
Actually the variance of this distribution can give an idea about size of the
weights controlled by each one of the input units.

Namely:

A small variance suggests that the weights are quite close to 0:
thus the input controlling those weights is not very relevant.
Conversely a large variance is typical of distribution of weights which
are connected to a relevant input.

In our experiments we controlled the variance of the distribution of weights
through a hyperparameter
,
where is inversely
proportional to the square root of the actual variance.
The lower the the
larger the variance.

*The plot shows the relevance of the input features.
The input features are reported on the x-axis;*

the y-axis reports the
inverse of the variance of the distribution of the synaptic weights

which connect one input unit to all of the units in the next layer.

The experiments we run showed that
features describing **colour**, **size**
and **position**
of the regions are the most relevant in training the neural
network, as
the variances corresponding to those features have had large values.

All of the experiments have shown that the **coordinates** *(x,y)*
of the regions have a different weight in training the networks.
As the images are taken with the *y* axis closely aligned to the
vertical, the classification of the regions is unlikely to depend upon
the *x* coordinate.

The results presented in this web page have been published
in the paper ** Using Bayesian Neural Networks to
Classify segmented Images**
which is available as
compressed postscript
.

**Contact names**

*Francesco Vivarelli*

*Dr. Christopher K. I. Williams*

*Dr. W. Andrew Wright*

*This page is maintained by
Francesco Vivarelli*
(`vivarelf@aston.ac.uk`)

Last modified: Thu Jun 26 19:56:20 BST