可參考sklearn_數據處理API幫助理解！
標準歸一化
歸一化到均值爲0，方差爲1
- sklearn.preprocessing.scale函數：Standardize a dataset along any axis
- 先貼出主要的源碼，乍一看，很亂，其實細看之下，就是多了一些判斷稀疏矩陣之類的條件性代碼。
#coding=utf-8
import numpy as np
from scipy import sparse
def _handle_zeros_in_scale(scale, copy=True):
''' Makes sure that whenever scale is zero, we handle it correctly.
This happens in most scalers when we have constant features.'''
# if we are fitting on 1D arrays, scale might be a scalar
if np.isscalar(scale):
if scale == .0:
scale = 1.
return scale
elif isinstance(scale, np.ndarray):
if copy:
# New array to avoid side-effects
scale = scale.copy()
scale[scale == 0.0] = 1.0
return scale
def scale(X, axis=0, with_mean=True, with_std=True, copy=True):
"""Standardize a dataset along any axis
Center to the mean and component wise scale to unit variance.
Read more in the :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
X : {array-like, sparse matrix}
The data to center and scale.
axis : int (0 by default)
axis used to compute the means and standard deviations along. If 0,
independently standardize each feature, otherwise (if 1) standardize
each sample.
with_mean : boolean, True by default
If True, center the data before scaling.
with_std : boolean, True by default
If True, scale the data to unit variance (or equivalently,
unit standard deviation).
copy : boolean, optional, default True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSC matrix and if axis is 1).
Notes
-----
This implementation will refuse to center scipy.sparse matrices
since it would make them non-sparse and would potentially crash the
program with memory exhaustion problems.
Instead the caller is expected to either set explicitly
`with_mean=False` (in that case, only variance scaling will be
performed on the features of the CSC matrix) or to call `X.toarray()`
if he/she expects the materialized dense array to fit in memory.
To avoid memory copy the caller should pass a CSC matrix.
See also
--------
StandardScaler: Performs scaling to unit variance using the``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
""" # noqa
X = check_array(X, accept_sparse='csc', copy=copy, ensure_2d=False,
warn_on_dtype=True, estimator='the scale function',
dtype=FLOAT_DTYPES)
if sparse.issparse(X):
if with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` instead"
" See docstring for motivation and alternatives.")
if axis != 0:
raise ValueError("Can only scale sparse matrix on axis=0, "
" got axis=%d" % axis)
if with_std:
_, var = mean_variance_axis(X, axis=0)
var = _handle_zeros_in_scale(var, copy=False)
inplace_column_scale(X, 1 / np.sqrt(var))
else:
X = np.asarray(X)
if with_mean:
mean_ = np.mean(X, axis)
if with_std:
scale_ = np.std(X, axis)
# Xr is a view on the original array broadcasting on the axis in which we are interested in
#下面這一行一開始着實讓人不太懂，感覺是一直對Xr操作，怎麼突然返回X，後來才知道Xr是X的一個視圖，
#np.rollaxis返回的是輸入數組的視圖，兩者只是形式上不同，本質是相等的，通過assert(X==Xr)可以證實。
Xr = np.rollaxis(X, axis)
if with_mean:
Xr -= mean_
mean_1 = Xr.mean(axis=0)
# Verify that mean_1 is 'close to zero'. If X contains very
# large values, mean_1 can also be very large, due to a lack of
# precision of mean_. In this case, a pre-scaling of the
# concerned feature is efficient, for instance by its mean or
# maximum.
if not np.allclose(mean_1, 0):
warnings.warn("Numerical issues were encountered "
"when centering the data "
"and might not be solved. Dataset may "
"contain too large values. You may need "
"to prescale your features.")
Xr -= mean_1
if with_std:
scale_ = _handle_zeros_in_scale(scale_, copy=False)
Xr /= scale_
if with_mean:
mean_2 = Xr.mean(axis=0)
# If mean_2 is not 'close to zero', it comes from the fact that
# scale_ is very small so that mean_2 = mean_1/scale_ > 0, even
# if mean_1 was close to zero. The problem is thus essentially
# due to the lack of precision of mean_. A solution is then to
# subtract the mean again:
if not np.allclose(mean_2, 0):
warnings.warn("Numerical issues were encountered "
"when scaling the data "
"and might not be solved. The standard "
"deviation of the data is probably "
"very close to 0. ")
Xr -= mean_2
return X
- 簡化版scale代碼
def scale_mean_var(input_arr，axis=0):
#from sklearn import preprocessing
#input_arr= preprocessing.scale(input_arr.astype('float'))
mean_ = np.mean(input_arr,axis=0)
scale_ = np.std(input_arr,axis=0)
#減均值
output_arr= input_arr- mean_
#判斷均值是否接近0
mean_1 = output_arr.mean(axis=0)
if not np.allclose(mean_1, 0):
output_arr -= mean_1
#將標準差爲0元素的置1
#scale_ = _handle_zeros_in_scale(scale_, copy=False)
scale_[scale_ == 0.0] = 1.0
#除以標準差
output_arr /=scale_
#再次判斷均值是否爲0
mean_2 = output_arr .mean(axis=0)
if not np.allclose(mean_2, 0):
output_arr -= mean_2
return output_arr
最大最小歸一化
- sklearn.preprocessing.minmax_scale函數：Transforms features by scaling each feature to a given range.
X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min
- 簡化版代碼很簡單
def max_min(input_arr,o_min,o_max):
"""
Transforms features by scaling each feature to a given range.
"""
i_min = np.min(input_arr)
i_max = np.max(input_arr)
out_arr = np.clip(input_arr,i_min,i_max)
out_arr = (out_arr- i_min)/(i_max - i_min)
if o_max==1 and o_min==0：
return out_arr
else:
out_arr = out_arr*(o_max-o_min)+o_min
return out_arr
最大絕對值歸一化
- maxabs_scale函數：Scale each feature by its maximum absolute value.
def maxabs_scale(input,axis=0):
"""
Scale each feature to the [-1, 1] range without breaking the sparsity
"""
if not isinstance(input,numpy.ndarray):
input = np.asarray(input).astype(np.float32)
maxabs = np.max(abs(input),axis=0)
out_array = input/maxabs
return out_array