如何正常化/反规范化载体以范围[-1; 1]

Question

如何可以正常化载体以范围[-1;1]

我想用功能norm，因为它会更快。

也让我知道我可以非规范化后正常化病媒？

Answer 1

norm归一向量，使其平方和是1。

如果要使得它的所有元素都是0和1之间，则需要使用的最小值和最大值，以归一化载体，其然后你可以再次使用非规范化。

%# generate some vector 
vec = randn(10,1); 

%# get max and min 
maxVec = max(vec); 
minVec = min(vec); 

%# normalize to -1...1 
vecN = ((vec-minVec)./(maxVec-minVec) - 0.5) *2; 

%# to "de-normalize", apply the calculations in reverse 
vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec 

Answer 2

乔纳斯在答案上构建的扩展答案如下。它允许基于矢量中是否存在负数和正数以及是否需要手动选择所需的归一化类型来进行自动归一化。该函数下面是一个测试脚本。

正常化功能

function [vecN, vecD] = normVec(vec,varargin) 
% Returns a normalize vector (vecN) and "de-nomralized" vector (vecD). The 
% function detects if both positive and negative values are present or not 
% and automatically normalizes between the appropriate range (i.e., [0,1], 
% [-1,0], or [-1,-1]. 
% Optional argument allows control of normalization range: 
% normVec(vec,0) => sets range based on positive/negative value detection 
% normVec(vec,1) => sets range to [0,1] 
% normVec(vec,2) => sets range to [-1,0] 
% normVec(vec,3) => sets range to [-1,1] 

%% Default Input Values 
% Check for proper length of input arguments 
numvarargs = length(varargin); 
if numvarargs > 1 
    error('Requires at most 1 optional input'); 
end 

% Set defaults for optional inputs 
optargs = {0}; 

% Overwrite default values if new values provided 
optargs(1:numvarargs) = varargin; 

% Set input to variable names 
[setNorm] = optargs{:}; 

%% Normalize input vector 
% get max and min 
maxVec = max(vec); 
minVec = min(vec); 

if setNorm == 0 
    % Automated normalization 
    if minVec >= 0 
     % Normalize between 0 and 1 
     vecN = (vec - minVec)./(maxVec - minVec); 
     vecD = minVec + vecN.*(maxVec - minVec); 
    elseif maxVec <= 0 
     % Normalize between -1 and 0 
     vecN = (vec - maxVec)./(maxVec - minVec); 
     vecD = maxVec + vecN.*(maxVec - minVec); 
    else 
     % Normalize between -1 and 1 
     vecN = ((vec-minVec)./(maxVec-minVec) - 0.5) *2; 
     vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec; 
    end 
elseif setNorm == 1 
    % Normalize between 0 and 1 
    vecN = (vec - minVec)./(maxVec - minVec); 
    vecD = minVec + vecN.*(maxVec - minVec); 
elseif setNorm == 2 
    % Normalize between -1 and 0 
    vecN = (vec - maxVec)./(maxVec - minVec); 
    vecD = maxVec + vecN.*(maxVec - minVec); 
elseif setNorm == 3 
    % Normalize between -1 and 1 
    vecN = ((vec-minVec)./(maxVec-minVec) - 0.5) *2; 
    vecD = (vecN./2+0.5) * (maxVec-minVec) + minVec; 
else 
    error('Unrecognized input argument varargin. Options are {0,1,2,3}'); 
end 

脚本测试功能

% Define vector 
x=linspace(0,4*pi,25); 
y = sin(x); 
ya=sin(x); yb=y+10; yc=y-10; 

% Normalize vector 
ya0=normVec(ya); yb0=normVec(yb); yc0=normVec(yc); 
ya1=normVec(ya,1); yb1=normVec(yb,1); yc1=normVec(yc,1); 
ya2=normVec(ya,2); yb2=normVec(yb,2); yc2=normVec(yc,2); 
ya3=normVec(ya,3); yb3=normVec(yb,3); yc3=normVec(yc,3); 

% Plot results 
figure(1) 
subplot(2,2,1) 
plot(x,ya0,'k',x,yb0,'ro',x,yc0,'b^') 
title('Auto Norm-Range') 
subplot(2,2,2) 
plot(x,ya1,'k',x,yb1,'ro',x,yc1,'b^') 
title('Manual Norm-Range: [0,1]') 
subplot(2,2,3) 
plot(x,ya2,'k',x,yb2,'ro',x,yc2,'b^') 
title('Manual Norm-Range: [-1,0]') 
subplot(2,2,4) 
plot(x,ya3,'k',x,yb3,'ro',x,yc3,'b^') 
title('Manual Norm-Range: [-1,1]') 

Answer 3

的最高最新的答案是使用在Matlab R2017b推出rescale功能。为了标准化矢量A的范围-1:1，你会运行：

maxA = max(A(:)); 
minA = min(A(:)); 
A = rescale(A, -1, 1); 
% use the normalised A 
A = rescale(A, minA, maxA);