理解 sklearn.preprocessing.MinMaxScaler

公式

非常有用的工具，可以把数据集的不同特征缩放到固定范围。

先从简单的说起，[0,1]缩放，公式

\(X_{scaled} = \frac{x-x_{min}}{x_{max}-x_{min}}\)

MinMaxScaler可以缩放到任意范围[MIN,MAX]，因此更一般化的公式是

\(X_{std} = \frac{x-x_{min}}{x_{max}-x_{min}}\)
\(X_{scaled} = \frac{X_{std}}{MAX-MIN} + MIN\)

当\(MIN\)和\(MAX\)为0和1时，公式等价于[0,1]缩放。

代码

再来看源代码。

def transform(self, X):
        """Scale features of X according to feature_range.
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Input data that will be transformed.
        Returns
        -------
        Xt : array-like of shape (n_samples, n_features)
            Transformed data.
        """
        check_is_fitted(self)

        X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES,
                        force_all_finite="allow-nan")

        X *= self.scale_
        X += self.min_
        return X

"""
    min_ : ndarray of shape (n_features,)
        Per feature adjustment for minimum. Equivalent to
        ``min - X.min(axis=0) * self.scale_``
    scale_ : ndarray of shape (n_features,)
        Per feature relative scaling of the data. Equivalent to
        ``(max - min) / (X.max(axis=0) - X.min(axis=0))``
        .. versionadded:: 0.17
           *scale_* attribute.
    data_min_ : ndarray of shape (n_features,)
        Per feature minimum seen in the data
        .. versionadded:: 0.17
           *data_min_*
    data_max_ : ndarray of shape (n_features,)
        Per feature maximum seen in the data
        .. versionadded:: 0.17
           *data_max_*
"""

这里的scale_相当于\(\frac{MAX-MIN}{x_{max}-x_{min}}\)，所以min_相当于\(MIN-x_{min}*\frac{MAX-MIN}{x_{max}-x_{min}}\)，这两个参数主要是方便以下逆变换

    def inverse_transform(self, X):
        """Undo the scaling of X according to feature_range.
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Input data that will be transformed. It cannot be sparse.
        Returns
        -------
        Xt : array-like of shape (n_samples, n_features)
            Transformed data.
        """
        check_is_fitted(self)

        X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES,
                        force_all_finite="allow-nan")

        X -= self.min_
        X /= self.scale_
        return X