Big Data seaborn Solution#

Big Data definition#

Big Data - files that are complicated to process using conventional computer or software.

Example#

Table with more than 1,048,576 rows would be impossible to process in MS Excel. Python, R and MatLab are limited by RAM and memory.

Solution#

Use specialized environment as Metacentrum computers, specialized servers (Mazlík) or Google Collab!

Practical example#

Goal#

  1. Load both data sets

  2. Clear NaN values

  3. Visualize Area distribution

  4. Decide statistical distribution (parametric/nonparametric)

  5. Define statistic hypothesis

  6. Compare Area distributions

Expected results from 3D measurements#

Results

!pip install -q -r requirements.txt

^C

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib

data1Path = "Dataset/Results_MM.csv" #@param {type:"string"}

data1=pd.read_csv(data1Path)  

data1.head()
Label Area Mean StdDev Mode Min Max X Y ... %Area RawIntDen Slice FeretX FeretY FeretAngle MinFeret AR Round Solidity
0 1 Data1 2541 56.0 0.0 56 56 56 598.54486 170.83176 ... 100 142296.0 1 593 142 98.53077 55.75403 1.06228 0.94137 0.97319
1 2 Data1 2419 96.0 0.0 96 96 96 2718.95432 624.50827 ... 100 232224.0 1 2711 653 72.47443 52.97387 1.10986 0.90102 0.97032
2 3 Data1 1855 4.0 0.0 4 4 4 237.42237 661.82938 ... 100 7420.0 1 224 683 56.30993 48.00000 1.03663 0.96466 0.96867
3 4 Data1 2596 65.0 0.0 65 65 65 293.91371 820.11710 ... 100 168740.0 1 266 807 163.66396 56.02472 1.05496 0.94790 0.97320
4 5 Data1 1409 31.0 0.0 31 31 31 2998.58375 1046.93364 ... 100 43679.0 1 2989 1068 68.42869 39.00000 1.15185 0.86817 0.96739

5 rows × 36 columns

data1.describe()

C:\Users\schatzm\Anaconda3\envs\julab\lib\site-packages\numpy\lib\function_base.py:4527: RuntimeWarning: invalid value encountered in subtract
  diff_b_a = subtract(b, a)
Area Mean StdDev Mode Min Max X Y XM ... %Area RawIntDen Slice FeretX FeretY FeretAngle MinFeret AR Round Solidity
count 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 ... 1615323.0 1.615323e+06 1615323.0 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06 1.615323e+06
mean 8.076620e+05 1.331084e+02 6.671007e+03 2.810688e+02 6.488793e+03 6.444779e+03 7.109614e+03 1.440901e+03 1.394038e+03 1.440899e+03 ... 100.0 4.633171e+05 1.0 1.436129e+03 1.392875e+03 1.049987e+02 1.030235e+01 1.249056e+00 8.442305e-01 8.899525e-01
std 4.663037e+05 2.516350e+02 6.086050e+03 1.091096e+03 6.101919e+03 6.101029e+03 6.399855e+03 8.383394e+02 8.243418e+02 8.383402e+02 ... 0.0 7.302585e+05 0.0 8.382947e+02 8.243501e+02 4.822601e+01 6.097962e+00 3.688458e-01 1.536807e-01 5.326279e-02
min 1.000000e+00 1.200000e+01 1.000000e+00 0.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 3.409090e+00 3.166670e+00 3.409090e+00 ... 100.0 7.000000e+01 1.0 1.000000e+00 1.000000e+00 1.507440e+00 3.000000e+00 1.000000e+00 1.111700e-01 3.585100e-01
25% 4.038315e+05 3.700000e+01 1.956000e+03 0.000000e+00 1.768000e+03 1.723000e+03 2.069000e+03 7.161416e+02 6.896124e+02 7.161596e+02 ... 100.0 1.616980e+05 1.0 7.120000e+02 6.880000e+02 5.446232e+01 7.000000e+00 1.061510e+00 8.218400e-01 8.709700e-01
50% 8.076620e+05 5.800000e+01 4.868000e+03 0.000000e+00 4.595000e+03 4.534000e+03 5.249000e+03 1.434662e+03 1.368470e+03 1.434676e+03 ... 100.0 3.169700e+05 1.0 1.430000e+03 1.367000e+03 1.255377e+02 8.000000e+00 1.109590e+00 9.012400e-01 9.014100e-01
75% 1.211492e+06 1.160000e+02 9.709000e+03 0.000000e+00 9.492000e+03 9.442000e+03 1.045600e+04 2.148138e+03 2.046322e+03 2.148138e+03 ... 100.0 5.530990e+05 1.0 2.143000e+03 2.045000e+03 1.444623e+02 1.100000e+01 1.216780e+00 9.420500e-01 9.230800e-01
max 1.615323e+06 2.469600e+04 3.233200e+04 1.428012e+04 3.233200e+04 3.233200e+04 3.233200e+04 3.189167e+03 3.226500e+03 3.189167e+03 ... 100.0 1.135496e+08 1.0 3.187000e+03 3.228000e+03 1.791449e+02 1.612912e+02 8.994840e+00 1.000000e+00 1.000000e+00

8 rows × 35 columns

data2Path = "Dataset/Results_aptamil.csv" #@param {type:"string"}

data2=pd.read_csv(data2Path)  

data2.head()
Label Area Mean StdDev Mode Min Max X Y ... %Area RawIntDen Slice FeretX FeretY FeretAngle MinFeret AR Round Solidity
0 1 Data2 2776 15.0 0.0 15 15 15 2574.66967 80.45245 ... 100 41640.0 1 2510 79 0.84876 29.09975 4.99331 0.20027 0.94857
1 2 Data2 2628 14.0 0.0 14 14 14 1015.16629 128.37938 ... 100 36792.0 1 1013 92 95.04245 53.00000 1.28544 0.77795 0.97010
2 3 Data2 337 13.0 0.0 13 13 13 2602.27448 103.22404 ... 100 4381.0 1 2598 93 105.25512 20.78831 1.07470 0.93050 0.92837
3 4 Data2 491 16.0 0.0 16 16 16 2038.76069 290.29837 ... 100 7856.0 1 2030 280 127.69424 24.00000 1.05842 0.94480 0.96464
4 5 Data2 509 5.0 0.0 5 5 5 2717.95972 401.13654 ... 100 2545.0 1 2706 408 33.11134 24.00000 1.09402 0.91406 0.95140

5 rows × 36 columns

data2.describe()

C:\Users\schatzm\Anaconda3\envs\julab\lib\site-packages\numpy\lib\function_base.py:4527: RuntimeWarning: invalid value encountered in subtract
  diff_b_a = subtract(b, a)
Area Mean StdDev Mode Min Max X Y XM ... %Area RawIntDen Slice FeretX FeretY FeretAngle MinFeret AR Round Solidity
count 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 ... 666214.0 6.662140e+05 666214.0 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000 666214.000000
mean 333107.500000 107.186941 4778.728803 107.668110 4758.339600 4671.752471 4898.814561 1462.707549 1378.698306 1462.708680 ... 100.0 2.964580e+05 1.0 1458.731747 1377.911724 97.782395 8.929439 1.235981 0.834769 0.890030
std 192319.560456 303.942842 4594.148721 620.511333 4627.082933 4580.314488 4698.678348 820.313937 786.322358 820.315810 ... 0.0 6.119494e+05 0.0 820.405865 786.316653 47.704262 5.969685 0.278721 0.120508 0.043218
min 1.000000 11.000000 1.000000 0.000000 1.000000 1.000000 1.000000 3.425930 3.029410 3.425930 ... 100.0 2.900000e+01 1.0 1.000000 1.000000 0.848760 3.000000 1.000000 0.078880 0.371820
25% 166554.250000 31.000000 873.000000 0.000000 848.000000 830.000000 882.000000 765.134703 708.711415 765.137985 ... 100.0 4.565525e+04 1.0 761.000000 708.000000 45.000000 6.000000 1.091640 0.791510 0.869570
50% 333107.500000 46.000000 3257.365065 0.000000 3173.000000 3072.000000 3337.000000 1470.000000 1378.719670 1470.022270 ... 100.0 1.744200e+05 1.0 1466.000000 1378.000000 116.565050 7.000000 1.158650 0.863080 0.894740
75% 499660.750000 75.000000 7718.000000 0.000000 7704.000000 7545.000000 7952.000000 2163.673910 2044.148023 2163.689600 ... 100.0 3.975745e+05 1.0 2160.000000 2044.000000 135.000000 9.000000 1.263408 0.916050 0.918600
max 666214.000000 58667.000000 21305.000000 10052.812470 21305.000000 21305.000000 21305.000000 3139.107140 3086.326090 3139.107140 ... 100.0 2.731261e+08 1.0 3136.000000 3089.000000 179.292680 359.467960 12.677090 1.000000 1.000000

8 rows × 35 columns

use

Select columns of interest

d1Area = data1[['Label', 'Area','Feret','AR']]
d2Area = data2[['Label', 'Area','Feret','AR']]

d1Area.dropna(how='all')
d2Area.dropna(how='all')
Label Area Feret AR
0 Data2 2776 135.01481 4.99331
1 Data2 2628 68.26419 1.28544
2 Data2 337 22.80351 1.07470
3 Data2 491 27.80288 1.05842
4 Data2 509 27.45906 1.09402
... ... ... ... ...
666209 Data2 1787 62.64982 1.59116
666210 Data2 180 18.78829 1.38055
666211 Data2 45 8.94427 1.16188
666212 Data2 75 12.36932 1.28449
666213 Data2 62 15.52417 2.93601

666214 rows × 4 columns

Rename Labels entry

d1Area = d1Area.replace({'Data1':'MM'})
d2Area = d2Area.replace({'Data2':'Aptamil'})

d1Area.head()
Label Area Feret AR
0 MM 2541 60.67125 1.06228
1 MM 2419 59.77458 1.10986
2 MM 1855 50.47772 1.03663
3 MM 2596 60.44005 1.05496
4 MM 1409 46.23851 1.15185 
d1Area['Area'].describe() 

count    1.615323e+06
mean     1.331084e+02
std      2.516350e+02
min      1.200000e+01
25%      3.700000e+01
50%      5.800000e+01
75%      1.160000e+02
max      2.469600e+04
Name: Area, dtype: float64

df_median = d1Area['Area'].median()

# Take a look
df_median

58.0

d2Area['Area'].describe() 

count    666214.000000
mean        107.186941
std         303.942842
min          11.000000
25%          31.000000
50%          46.000000
75%          75.000000
max       58667.000000
Name: Area, dtype: float64

df_median = d2Area['Area'].median()

# Take a look
df_median

46.0

result = pd.concat([d1Area, d2Area])

#del d1Area, d2Area

result.head()
Label Area Feret AR
0 MM 2541 60.67125 1.06228
1 MM 2419 59.77458 1.10986
2 MM 1855 50.47772 1.03663
3 MM 2596 60.44005 1.05496
4 MM 1409 46.23851 1.15185 
sns.set_theme(style="ticks", palette="pastel") 
sns.displot(result[result.index.duplicated()], x="Area", hue="Label" , multiple="stack")

C:\Users\schatzm\Anaconda3\envs\julab\lib\site-packages\seaborn\distributions.py:254: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
  baselines.iloc[:, cols] = (curves

<seaborn.axisgrid.FacetGrid at 0x19a9c8c67c0>
../_images/07_seaborn_big_data_statistics_SOLUTION_23_2.png 
sns.set_theme(style="ticks", palette="pastel")
fig = matplotlib.pyplot.gcf()
fig.set_size_inches(12, 8)

# Load the example tips dataset
tips = sns.load_dataset("tips")

# Draw a nested boxplot to show bills by day and time
ax = sns.boxplot(x="Area", y="Label",
            hue="Label", palette=["m", "g"],
            data=result, 
            showfliers = False) #get rid of outliers
            # data=result[np.mod(np.arange(result.index.size),3)!=0])
ax.set(xlabel='Area', ylabel='Label', title="Milk Area")

# Improve the legend
sns.move_legend(
    ax, loc="lower right", ncol=3, frameon=True, columnspacing=1, handletextpad=0
)

sns.despine(offset=10, trim=True)

from scipy.stats import normaltest

k2, p = normaltest(d1Area['Area'])
alpha = 1e-3
print("p = {:g}".format(p))
print('null hypothesis: Data1 (MM) comes from a normal distribution')
if p < alpha:  # null hypothesis: Data1 (MM) comes from a normal distribution
    print("The null hypothesis can be rejected")
else:
    print("The null hypothesis cannot be rejected")

k2, p = normaltest(d2Area['Area'])
alpha = 1e-3
print("p = {:g}".format(p))
print('null hypothesis: Data2 (Aptamil) from a normal distribution')
if p < alpha:  # null hypothesis: Data2 (Aptamil) from a normal distribution
    print("The null hypothesis can be rejected")
else:
    print("The null hypothesis cannot be rejected")

p = 0
null hypothesis: Data1 (MM) comes from a normal distribution
The null hypothesis can be rejected
p = 0
null hypothesis: Data2 (Aptamil) from a normal distribution
The null hypothesis can be rejected

Selecting non parametric test, and testing:

# Mann-Whitney U test
from numpy.random import seed
from numpy.random import randn
from scipy.stats import mannwhitneyu
# import random  
from random import sample 
data1=d1Area['Area'].sample(n=100, random_state=1)
data2=d2Area['Area'].sample(n=100, random_state=1)
print('null hypothesis: data sets are from the same distribution')
# compare samples
stat, p = mannwhitneyu(data1, data2)
print('Statistics=%.3f, p=%.16f' % (stat, p))
# interpret
alpha = 0.05
if p > alpha:
	print('Same distribution (fail to reject H0)')
else:
	print('Different distribution (reject H0)')

null hypothesis: data sets are from the same distribution
Statistics=6272.500, p=0.0018810635846991
Different distribution (reject H0)

# pvalues with scipy:
stat_results = [
  mannwhitneyu(data1, data2, alternative="two-sided"),
  # mannwhitneyu(flight, sound, alternative="two-sided"),
  # mannwhitneyu(robots, sound, alternative="two-sided")
]

pvalues = [result.pvalue for result in stat_results]
print(pvalues)

[0.0018810635846990642]

import matplotlib.pyplot as plt
with sns.plotting_context("notebook", font_scale=1.4):
    # Create new plot
    fig, ax = plt.subplots(1, 1, figsize=(12, 6))

    sns.boxplot(ax=ax, data=result, x='Label', y='Area', 
                showfliers = False,
                # palette=subcat_palette,
                # order=subcat_order
                )
    plt.title("Aptamil vs MM", y=1.06)
    # ax.set_ylabel("Goal ($)")
    # ax.set_xlabel("Project State", labelpad=20)

from statannotations.Annotator import Annotator

subcat_palette = sns.dark_palette("#8BF", reverse=True, n_colors=5)
states_palette = sns.color_palette("YlGnBu", n_colors=5)

states_order = ["Successful", "Failed", "Live", "Suspended", "Canceled"]
subcat_order = ['MM', 'Aptamil']

# Putting the parameters in a dictionary avoids code duplication
# since we use the same for `sns.boxplot` and `Annotator` calls
plotting_parameters = {
    'data':result, 
    'x':'Label', 
    'y':'Area', 
    'showfliers': False,
}

pairs = [('MM', 'Aptamil'),  # 'Robots' vs 'Flight'
        #  ('Flight', 'Sound'),   # 'Flight' vs 'Sound'
        #  ('Robots', 'Sound')   # 'Robots' vs 'Sound'
         ]

formatted_pvalues = [f"p={p:.2e}" for p in pvalues]

with sns.plotting_context('notebook', font_scale=1.4):
    # Create new plot
    fig, ax = plt.subplots(1, 1, figsize=(12, 6))

    # Plot with seaborn
    sns.boxplot(**plotting_parameters)

    # Add annotations
    annotator = Annotator(ax, pairs, **plotting_parameters)
    annotator.set_custom_annotations(formatted_pvalues)
    annotator.annotate()

    # Label and show
    plt.title("Aptamil vs MM", y=1.06)
    
    plt.savefig("./plot1A.png", bbox_inches='tight')
    plt.show()

p-value annotation legend:
      ns: p <= 1.00e+00
       *: 1.00e-02 < p <= 5.00e-02
      **: 1.00e-03 < p <= 1.00e-02
     ***: 1.00e-04 < p <= 1.00e-03
    ****: p <= 1.00e-04

MM vs. Aptamil: p=1.88e-03
../_images/07_seaborn_big_data_statistics_SOLUTION_31_1.png ../_images/07_seaborn_big_data_statistics_SOLUTION_31_2.png ../_images/07_seaborn_big_data_statistics_SOLUTION_31_3.png 
with sns.plotting_context("notebook", font_scale=1.4):
    # Create new plot
    fig, ax = plt.subplots(1, 1, figsize=(12, 6))

    # Plot with seaborn
    sns.boxplot(ax=ax, **plotting_parameters)

    # Add annotations
    annotator = Annotator(ax, pairs, **plotting_parameters)
    annotator.set_pvalues(pvalues)
    annotator.annotate()

    # Label and show
    plt.title("Aptamil vs MM", y=1.06)
    plt.show()

p-value annotation legend:
      ns: p <= 1.00e+00
       *: 1.00e-02 < p <= 5.00e-02
      **: 1.00e-03 < p <= 1.00e-02
     ***: 1.00e-04 < p <= 1.00e-03
    ****: p <= 1.00e-04

MM vs. Aptamil: Custom statistical test, P_val:1.881e-03
../_images/07_seaborn_big_data_statistics_SOLUTION_32_1.png 
from watermark import watermark
watermark(iversions=True, globals_=globals())
print(watermark())
print(watermark(packages="watermark,numpy,scipy,pandas,matplotlib,bokeh,statannotations"))

Last updated: 2023-01-05T13:50:32.141879+01:00

Python implementation: CPython
Python version       : 3.9.15
IPython version      : 8.8.0

Compiler    : MSC v.1929 64 bit (AMD64)
OS          : Windows
Release     : 10
Machine     : AMD64
Processor   : Intel64 Family 6 Model 85 Stepping 7, GenuineIntel
CPU cores   : 40
Architecture: 64bit

watermark      : 2.3.1
numpy          : 1.23.5
scipy          : 1.10.0
pandas         : 1.5.2
matplotlib     : 3.6.2
bokeh          : 3.0.3
statannotations: 0.5.0