Question

如何将矢量标准化到范围[-1;1]

我想使用函数norm，因为它会更快。

另请告诉我在规范化之后如何非规范化该向量？

Answer 1

norm对矢量进行归一化，使其平方和为1.

如果要对向量进行标准化以使其所有元素都在0和1之间，则需要使用最小值和最大值，然后可以使用该值进行非规范化。

%# 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

基于乔纳斯答案的扩展答案如下。它允许基于载体中是否存在负数和正数或者手动选择所需归一化类型的自动归一化。函数下面是一个测试脚本。

规范化功能

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

测试功能的脚本

% 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

最新的答案是使用Matlab R2017b中引入的rescale函数。要将向量A标准化为范围-1:1，您需要运行：

A = rescale(A, -1, 1);

您可以通过预先保存最小值和最大值然后再次运行rescale来撤消此操作：

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

Answer 4

一个简单的解决方案是使用现成的MATLAB函数：

mapminmax

通过将行最小值和最大值映射到[-1 1]来处理矩阵

示例：

x1 = [1 2 4; 1 1 1; 3 2 2; 0 0 0]
[y1,PS] = mapminmax(x1)

归一化后对该向量进行归一化

x1_again = mapminmax('reverse',y1,PS)

如何将向量归一化/非规范化到范围[-1; 1]

4 个答案: