108 lines
3.0 KiB
Python
108 lines
3.0 KiB
Python
|
"""
|
||
|
|
==========================================================
|
||
|
|
Using PowerTransformer to apply the Box-Cox transformation
|
||
|
|
==========================================================
|
||
|
|
|
||
|
|
This example demonstrates the use of the Box-Cox transform through
|
||
|
|
:class:`preprocessing.PowerTransformer` to map data from various distributions
|
||
|
|
to a normal distribution.
|
||
|
|
|
||
|
|
Box-Cox is useful as a transformation in modeling problems where
|
||
|
|
homoscedasticity and normality are desired. Below are examples of Box-Cox
|
||
|
|
applied to six different probability distributions: Lognormal, Chi-squared,
|
||
|
|
Weibull, Gaussian, Uniform, and Bimodal.
|
||
|
|
|
||
|
|
Note that the transformation successfully maps the data to a normal
|
||
|
|
distribution when applied to certain datasets, but is ineffective with others.
|
||
|
|
This highlights the importance of visualizing the data before and after
|
||
|
|
transformation.
|
||
|
|
"""
|
||
|
|
|
||
|
|
# Author: Eric Chang <ericchang2017@u.northwestern.edu>
|
||
|
|
# License: BSD 3 clause
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
|
||
|
|
from sklearn.preprocessing import PowerTransformer, minmax_scale
|
||
|
|
|
||
|
|
print(__doc__)
|
||
|
|
|
||
|
|
|
||
|
|
N_SAMPLES = 3000
|
||
|
|
FONT_SIZE = 6
|
||
|
|
BINS = 100
|
||
|
|
|
||
|
|
|
||
|
|
pt = PowerTransformer(method='box-cox')
|
||
|
|
rng = np.random.RandomState(304)
|
||
|
|
size = (N_SAMPLES, 1)
|
||
|
|
|
||
|
|
|
||
|
|
# lognormal distribution
|
||
|
|
X_lognormal = rng.lognormal(size=size)
|
||
|
|
|
||
|
|
# chi-squared distribution
|
||
|
|
df = 3
|
||
|
|
X_chisq = rng.chisquare(df=df, size=size)
|
||
|
|
|
||
|
|
# weibull distribution
|
||
|
|
a = 50
|
||
|
|
X_weibull = rng.weibull(a=a, size=size)
|
||
|
|
|
||
|
|
# gaussian distribution
|
||
|
|
loc = 100
|
||
|
|
X_gaussian = rng.normal(loc=loc, size=size)
|
||
|
|
|
||
|
|
# uniform distirbution
|
||
|
|
X_uniform = rng.uniform(low=0, high=1, size=size)
|
||
|
|
|
||
|
|
# bimodal distribution
|
||
|
|
loc_a, loc_b = 100, 105
|
||
|
|
X_a, X_b = rng.normal(loc=loc_a, size=size), rng.normal(loc=loc_b, size=size)
|
||
|
|
X_bimodal = np.concatenate([X_a, X_b], axis=0)
|
||
|
|
|
||
|
|
|
||
|
|
# create plots
|
||
|
|
distributions = [
|
||
|
|
('Lognormal', X_lognormal),
|
||
|
|
('Chi-squared', X_chisq),
|
||
|
|
('Weibull', X_weibull),
|
||
|
|
('Gaussian', X_gaussian),
|
||
|
|
('Uniform', X_uniform),
|
||
|
|
('Bimodal', X_bimodal)
|
||
|
|
]
|
||
|
|
|
||
|
|
colors = ['firebrick', 'darkorange', 'goldenrod',
|
||
|
|
'seagreen', 'royalblue', 'darkorchid']
|
||
|
|
|
||
|
|
fig, axes = plt.subplots(nrows=4, ncols=3)
|
||
|
|
axes = axes.flatten()
|
||
|
|
axes_idxs = [(0, 3), (1, 4), (2, 5), (6, 9), (7, 10), (8, 11)]
|
||
|
|
axes_list = [(axes[i], axes[j]) for i, j in axes_idxs]
|
||
|
|
|
||
|
|
|
||
|
|
for distribution, color, axes in zip(distributions, colors, axes_list):
|
||
|
|
name, X = distribution
|
||
|
|
# scale all distributions to the range [0, 10]
|
||
|
|
X = minmax_scale(X, feature_range=(1e-10, 10))
|
||
|
|
|
||
|
|
# perform power transform
|
||
|
|
X_trans = pt.fit_transform(X)
|
||
|
|
lmbda = round(pt.lambdas_[0], 2)
|
||
|
|
|
||
|
|
ax_original, ax_trans = axes
|
||
|
|
|
||
|
|
ax_original.hist(X, color=color, bins=BINS)
|
||
|
|
ax_original.set_title(name, fontsize=FONT_SIZE)
|
||
|
|
ax_original.tick_params(axis='both', which='major', labelsize=FONT_SIZE)
|
||
|
|
|
||
|
|
ax_trans.hist(X_trans, color=color, bins=BINS)
|
||
|
|
ax_trans.set_title('{} after Box-Cox, $\lambda$ = {}'.format(name, lmbda),
|
||
|
|
fontsize=FONT_SIZE)
|
||
|
|
ax_trans.tick_params(axis='both', which='major', labelsize=FONT_SIZE)
|
||
|
|
|
||
|
|
|
||
|
|
plt.tight_layout()
|
||
|
|
plt.show()
|