dist

Euclidean distance weight function

Syntax

Z = dist(W,P)

dim = dist('size',S,R,FP)

dw = dist('dw',W,P,Z,FP)

D = dist(pos)

info = dist(code)

Description

Z = dist(W,P) takes an S-by-R weight matrix, W, and an R-by-Q matrix of Q input (column) vectors, P, and returns the S-by-Q matrix of vector distances, Z.

Weight functions apply weights to an input to get weighted inputs.

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

dw = 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.

D = dist(pos) takes N-by-S matrix of neuron positions, pos and returns the S-by-S matrix of distances, D.

info = dist(code) returns information about this function. For more information, see the code argument description.

Examples

Calculate the Weighted Input By Using the dist Function

This example shows how to calculate the corresponding weighted input Z, given a random weight matrix W and input vector P.

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)

Input Arguments

W — Weight matrix

matrix

Weight matrix, specified as an S-by-R matrix.

P — Input matrix

matrix

Inputt matrix, specified as an R-by-Q matrix of Q input (column) vectors.

S — Layer dimension

scalar

Layer dimension, specified as a scalar.

R — Input dimension

scalar

Input dimension, specified as a scalar.

pos — Neuron positions

matrix

Matrix of neutron positions, specified as an N-by-S matrix.

code — Information option

'name' | 'output' | 'active' | 'fullderiv' | 'fpnames' | 'fpdefaults'

Information you want to retrieve from the function, specified as one of the following:

• 'name' returns the name of this function.

• 'deriv' returns the name of the derivative function

• 'fullderiv' returns 1 for full derivative and 0 for linear derivative.

• 'pfullderiv' returns 2 for reduced derivative, 1 for full derivative, and 0 for linear derivative.

• 'fpnames' returns the names of the function parameters.

• 'fpdefaults' returns the default function parameters.

Output Arguments

Z — Vector distances

matrix

Vector distances, returned as an S-by-Q matrix.

dim — Weight size

Weight size, returned as

dw — Derivative of w

cell array

Derivative of Z with respect to W, returned as a cell array.

D — Distances

matrix

Distances, returned as an S-by-S matrix.

More About

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.inputWeights{i,j}.weightFcn to 'dist'. For a layer weight, set net.layerWeights{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.

Algorithms

The Euclidean distance d between two vectors X and Y is

d = sum((x-y).^2).^0.5