rbfdesign.m

人工神经网络的源码编程

function H = rbfDesign(X, C, R, options)
% H = rbfDesign(X, C, R, options)
%
% Gets the design matrix from the input data, centre positions
% and radii factors.
%
% Input
%       X       Input training data (n-by-p)
%       C       List of centres (n-by-m)
%       R	Scale factors: scalar, n-vector, or n-by-n matrix
%	opt	Specifying basis function type ('g' for Gaussian,
%		'c' for Cauchy) and whether bias unit is rquired
%		(if yes then 'b').
%
% Output
%       H       Design matrix (p-by-m)

% default function type
% 'g' = gaussian (0)
% 'c' = cauchy (1)
% 'm' = multiquadric (2)
% 'i' = inverse multiquadric (3)
type = 0;

% default bias
bias = 0;

% process options
if nargin > 3

	for option = options

		if option == 'g'
			type = 0;
		elseif option == 'c'
			type = 1;
		elseif option == 'm'
			type = 2;
		elseif option == 'i'
			type = 3;
		elseif option == 'b'
			bias = 1;
		else
			error('rbfDesign: illegal option')
		end

	end

end

% preliminary sizing
[n, p] = size(X);
[n1, m] = size(C);
if n ~= n1
	error('rbfDesign: mismatched X, C')
end
[rr, rc] = size(R);

% determine scaling type
if rr == 1 & rc == 1
	SCALING_TYPE = 1;	% same radius for each centre
elseif rr == 1
	if rc == n
		SCALING_TYPE = 2;	% same diagonal metric for each centre
		R = R';
	elseif rc == m
		SCALING_TYPE = 4;	% different radius for each centre
		R = R';
	else
		error('rbfDesign: mismatched C and row vector R')
	end
elseif rc == 1
	if rr == n
		SCALING_TYPE = 2;	% same diagonal metric for each centre
	elseif rr == m
		SCALING_TYPE = 4;	% different radius for each centre
	else
		error('rbfDesign: mismatched C and row vector R')
	end
elseif rr == n
	if rc == n
		SCALING_TYPE = 3;	% same metric for each centre
		IR = inv(R);
	elseif rc == m
		SCALING_TYPE = 5;	% different diagonal metric for each centre
	else
		error('rbfDesign: mismatched C and matrix R')
	end
elseif rc == n
	if rr == m
		SCALING_TYPE = 5;	% different diagonal metric for each centre
		R = R';
	else
		error('rbfDesign: mismatched C and matrix R')
	end
else
	error('rbfDesign: wrong sized R')
end

% start constructing H
H = zeros(p, m);
for j = 1:m

	% get p difference vectors for this centre
	D = X - dupCol(C(:,j),p);

	% do metric calculation
	if SCALING_TYPE == 1		% same radius for each centre
		s = diagProduct(D',D) / R^2;
	elseif SCALING_TYPE == 2	% same diagonal metric for each centre
		DR = D ./ dupCol(R, p);
		s = diagProduct(DR',DR);
	elseif SCALING_TYPE == 3	% same metric for each centre
		DR = IR * D;
		s = diagProduct(DR',DR);
	elseif SCALING_TYPE == 4	% different radius for each centre
		s = diagProduct(D',D) / R(j)^2;
	else				% different diagonal metric for each centre
		DR = D ./ dupCol(R(:,j), p);
		s = diagProduct(DR',DR);
	end

	% apply basis function
	if type == 0		% Gaussian (default)

		h = exp(-s);

	elseif type == 1	% Cauchy

		h = 1 ./ (s + 1);

	elseif type == 2	% multiquadric

		h = sqrt(s + 1);

	elseif type == 3        % inverse multiquadric

		h = 1 ./ sqrt(s + 1);

	end

	% insert result in H
	H(:, j) = h;

end

% add bias unit
if bias

	H = [H ones(p, 1)];

end