Neural Network Toolbox™

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

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

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))
  

See Also

sim, dist, linkdist

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