二维矩阵中各个列的最小-最大归一化 [英] Min-max normalization of individual columns in a 2D matrix

问题描述

我有一个包含4列/属性和150行的数据集.我想使用最小-最大规范化来规范化此数据.到目前为止，我的代码是:

I have a dataset which has 4 columns/attributes and 150 rows. I want to normalize this data using min-max normalization. So far, my code is:

minData=min(min(data1))
maxData=max(max(data1))
minmaxeddata=((data1-minData)./(maxData))

此处，minData和maxData返回全局最小值和最大值.因此，此代码实际上对2D矩阵中的所有值应用了最小-最大值归一化，因此全局最小值为0，全局最大值为1.

Here, minData and maxData returns the global minimum and maximum values. Therefore, this code actually applies a min-max normalization over all values in the 2D matrix so that the global minimum is 0 and the global maximum is 1.

但是，我想对每个列分别执行相同的操作.具体来说，应该独立于其他列对2D矩阵的每一列进行min-max归一化.

However, I would like to perform the same operation on each column individually. Specifically, each column of the 2D matrix should be min-max normalized independently from the other columns.

我尝试仅使用min(data1)和max(data1)，但收到错误消息，提示矩阵尺寸必须一致.

I tried using just using min(data1) and max(data1), but got the error saying that the Matrix dimensions must agree.

但是，通过使用全局最小值和最大值，我得到了[0-1]范围内的值，并使用此归一化数据集进行了实验.我想知道我的结果是否有问题?我的理解也存在问题吗?任何指导将不胜感激.

However, by using the global minimum and maximum, I got the values in the range of [0-1] and have done experimentations using this normalized dataset. I would like to know whether there is any problem in my results? Is there a problem in my understanding as well? Any guidance would be appreciated.

推荐答案

如果我对您的理解正确，则希望对data1的每一列进行规范化.另外，由于每一列都是独立数据集，并且很可能具有不同的动态范围，因此不建议执行全局的min-max操作.我建议您按照最初的想法，分别对每一列进行标准化.

If I understand you correctly, you wish to normalize each column of data1. Also, as each column is an independent data set and most likely having different dynamic ranges, doing a global min-max operation is probably not recommended. I would recommend that you go with your initial thoughts in normalizing each column individually.

随着错误的发生，您不能用min(data1)减去data1，因为当data1是矩阵时，min(data1)会产生行向量.您正在用向量减去一个矩阵，这就是为什么会出现该错误的原因.

Going with your error, you can't subtract data1 with min(data1) because min(data1) would produce a row vector while data1 is a matrix. You are subtracting a matrix with a vector which is why you are getting that error.

如果您想实现自己的要求，请使用 bsxfun 广播矢量，并重复data1一样多的行.因此:

If you want to achieve what you're asking, use bsxfun to broadcast the vector and repeat it for as many rows as you have data1. Therefore:

mindata = min(data1);
maxdata = max(data1);
minmaxdata = bsxfun(@rdivide, bsxfun(@minus, data1, mindata), maxdata - mindata);

---

示例

>> data1 = [5 9 9 9 3 3; 3 10 2 1 10 1; 2 4 4 6 5 5]

data1 =

 5     9     9     9     3     3
 3    10     2     1    10     1
 2     4     4     6     5     5

运行上面的规范化代码时，我得到:

When I run the above normalization code, I get:

minmaxdata =

    1.0000    0.8333    1.0000    1.0000         0    0.5000
    0.3333    1.0000         0         0    1.0000         0
         0         0    0.2857    0.6250    0.2857    1.0000

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