mandist :: Functions (Neural Network Toolbox™)

mandist

Purpose

Manhattan distance weight function

Syntax

Z = mandist(W,P)
df = mandist('deriv')
D = mandist(pos);

Description

mandist is the Manhattan distance weight function. Weight functions apply weights to an input to get weighted inputs.

mandist(W,P) takes these inputs,

W
S x R weight matrix

P
R x Q matrix of Q input (column) vectors

`W`	`S` x `R` weight matrix
`P`	`R` x `Q` matrix of `Q` input (column) vectors

and returns the S x Q matrix of vector distances.

mandist('deriv') returns '' because mandist does not have a derivative function.

mandist is also a layer distance function, which can be used to find the distances between neurons in a layer.

mandist(pos) takes one argument,

pos
S row matrix of neuron positions

`pos`	`S` row matrix of neuron positions

and returns the S x S matrix of distances.

Examples

Here you define a random weight matrix W and input vector P and calculate the corresponding weighted input Z.

W = rand(4,3);
P = rand(3,1);
Z = mandist(W,P)

Here you define a random matrix of positions for 10 neurons arranged in three-dimensional space and then find their distances.

```
pos = rand(3,10);
D = mandist(pos)
```

Network Use

You can create a standard network that uses mandist as a distance function by calling newsom.

To change a network so an input weight uses mandist, set net.inputWeight{i,j}.weightFcn to 'mandist'. For a layer weight, set net.layerWeight{i,j}.weightFcn to 'mandist'.

To change a network so a layer's topology uses mandist, set net.layers{i}.distanceFcn to 'mandist'.

In either case, call sim to simulate the network with dist. See newpnn or newgrnn for simulation examples.

Algorithm

The Manhattan distance D between two vectors X and Y is

```
D = sum(abs(x-y))
```