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Normalization in Python

Learn how to normalize data by fitting to intervals on the real line and dividing by a constant

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go
import plotly.tools as tools
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Import Data

To properly visualize our data and normalization, let us import a dataset of Apple Stock prices in 2014:

In [2]:
apple_data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/2014_apple_stock.csv')
df = apple_data[0:10]

table = FF.create_table(df)
py.iplot(table, filename='apple-data-sample')
Out[2]:

Normalize by a Constant

Normalize a dataset by dividing each data point by a constant, such as the standard deviation of the data.

In [4]:
data = apple_data['AAPL_y']

data_norm_by_std = [number/scipy.std(data) for number in data]

trace1 = go.Histogram(
    x=data,
    opacity=0.75,
    name='data'
)

trace2 = go.Histogram(
    x=data_norm_by_std,
    opacity=0.75,
    name='normalized by std = ' + str(scipy.std(data)),
)

fig = tools.make_subplots(rows=2, cols=1)

fig.append_trace(trace1, 1, 1)
fig.append_trace(trace2, 2, 1)

fig['layout'].update(height=600, width=800, title='Normalize by a Constant')
py.iplot(fig, filename='apple-data-normalize-constant')
This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]

Out[4]:

Normalize to [0, 1]

Normalize a dataset by dividing each data point by the norm of the dataset.

In [5]:
data_norm_to_0_1 = [number/scipy.linalg.norm(data) for number in data]

trace1 = go.Histogram(
    x=data,
    opacity=0.75,
    name='data',
)

trace2 = go.Histogram(
    x=data_norm_to_0_1,
    opacity=0.75,
    name='normalized to [0,1]',
)

fig = tools.make_subplots(rows=2, cols=1)

fig.append_trace(trace1, 1, 1)
fig.append_trace(trace2, 2, 1)

fig['layout'].update(height=600, width=800, title='Normalize to [0,1]')
py.iplot(fig, filename='apple-data-normalize-0-1')
This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]

Out[5]:

Normalizing to any Interval

Normalize a dataset to an interval [a, b] where a, b are real numbers.

In [6]:
a = 10
b = 50
data_norm_to_a_b = [(number - a)/(b - a) for number in data]

trace1 = go.Histogram(
    x=data,
    opacity=0.75,
    name='data',
)

trace2 = go.Histogram(
    x=data_norm_to_a_b,
    opacity=0.75,
    name='normalized to [10,50]',
)

fig = tools.make_subplots(rows=2, cols=1)

fig.append_trace(trace1, 1, 1)
fig.append_trace(trace2, 2, 1)

fig['layout'].update(height=600, width=800, title='Normalize to [10,50]')
py.iplot(fig, filename='apple-data-normalize-a-b')
This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]

Out[6]:
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