Neural Network Toolbox™

Euclidean distance weight function

Syntax

• Z = dist(W,P,FP)
  info = dist(code)
  dim = dist('size',S,R,FP)
  dp = dist('dp',W,P,Z,FP)
  dw = dist('dw',W,P,Z,FP)
  D = dist(pos)
  

Description

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

dist(W,P,FP) takes these inputs,

W	S x R weight matrix
P	R x Q matrix of Q input (column) vectors
FP	Struct of function parameters (optional, ignored)

and returns the S x Q matrix of vector distances.

dist(code) returns information about this function. The following codes are defined:

'deriv'	Name of derivative function
'fullderiv'	Full derivative = 1, linear derivative = 0
'pfullderiv'	Input: reduced derivative = 2, full derivative = 1, linear derivative = 0
'name'	Full name
'fpnames'	Returns names of function parameters
'fpdefaults'	Returns default function parameters

dist('size',S,R,FP) takes the layer dimension S, input dimension R, and function parameters, and returns the weight size [S x R].

dist('dp',W,P,Z,FP) returns the derivative of Z with respect to P.

dist('dw',W,P,Z,FP) returns the derivative of Z with respect to W.

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

dist(pos) takes one argument,

pos	N x S 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 = dist(W,P)
  

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

• pos = rand(3,10);
  D = dist(pos)
  

Network Use

You can create a standard network that uses dist by calling newpnn or newgrnn.

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

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

In either case, call sim to simulate the network with dist.

See newpnn or newgrnn for simulation examples.

Algorithm

The Euclidean distance d between two vectors X and Y is

• d = sum((x-y).^2).^0.5
  

See Also

sim, dotprod, negdist, normprod, mandist, linkdist

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