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