Category Archives: Python Data Analysis

Data Analysis with Python

Statistics with Panda DataFrame

Below are the Pandas DataFrame statistical methods with their description:

Method	Description	Example
describe	This method returns a small table with descriptive statistics	print("Describe", sunspots.describe(),"\n") #out Describe Yearly Mean Total Sunspot Number Yearly Mean Standard Deviation \ count 317.000000 199.000000 mean 79.378233 8.009548 std 61.998961 3.808942 min 0.000000 1.700000 25% 25.100000 4.700000 50% 66.700000 7.700000 75% 116.300000 10.450000 max 269.300000 19.100000 Number of Observations Definitive/Provisional Indicator count 199.000000 317.0 mean 1467.678392 1.0 std 2463.925956 0.0 min 150.000000 1.0 25% 365.000000 1.0 50% 365.000000 1.0 75% 366.000000 1.0 max 9940.000000 1.0
count	This method returns the number of non-NaN items	`print("Non NaN observations", sunspots.count(),"\n") #out Non NaN observations Yearly Mean Total Sunspot Number 317 Yearly Mean Standard Deviation 199 Number of Observations 199 Definitive/Provisional Indicator 317 dtype: int64`
mad	This method calculates the mean absolute deviation, which is a robust measure similar to the standard deviation	`print("MAD", sunspots.mad(),"\n") #out MAD Yearly Mean Total Sunspot Number 50.931061 Yearly Mean Standard Deviation 3.128860 Number of Observations 1838.628924 Definitive/Provisional Indicator 0.000000 dtype: float64`
median	This method returns the median. This is equivalent to the value at the 50^th percentile	`print("Median", sunspots.median(),"\n") #out Median Yearly Mean Total Sunspot Number 66.7 Yearly Mean Standard Deviation 7.7 Number of Observations 365.0 Definitive/Provisional Indicator 1.0 dtype: float64`
min	This method returns the lowest value	`print("Min", sunspots.min(),"\n") #out Min Yearly Mean Total Sunspot Number 0.0 Yearly Mean Standard Deviation 1.7 Number of Observations 150.0 Definitive/Provisional Indicator 1.0 dtype: float64`
max	This method returns the highest value	`print("Max", sunspots.max(),"\n") #out Max Yearly Mean Total Sunspot Number 269.3 Yearly Mean Standard Deviation 19.1 Number of Observations 9940.0 Definitive/Provisional Indicator 1.0 dtype: float64`
mode	This method returns the mode, which is the most frequently occurring value	`print("Mode", sunspots.mode(),"\n") #out Mode Yearly Mean Total Sunspot Number Yearly Mean Standard Deviation \ 0 18.3 9.2 Number of Observations Definitive/Provisional Indicator 0 365.0 1.0`
std	This method returns the standard deviation, which measures dispersion. It is the square root of the variance	`print("Standard Deviation", sunspots.std(),"\n") #out Standard Deviation Yearly Mean Total Sunspot Number 61.998961 Yearly Mean Standard Deviation 3.808942 Number of Observations 2463.925956 Definitive/Provisional Indicator 0.000000 dtype: float64`
var	This method returns the variance	`print("Variance", sunspots.var(),"\n") #out Variance Yearly Mean Total Sunspot Number 3.843871e+03 Yearly Mean Standard Deviation 1.450804e+01 Number of Observations 6.070931e+06 Definitive/Provisional Indicator 0.000000e+00 dtype: float64`
skew	This method returns skewness. Skewness is indicative of the distribution symmetry	`print("Skewness", sunspots.skew(),"\n") #out Skewness Yearly Mean Total Sunspot Number 0.804414 Yearly Mean Standard Deviation 0.561530 Number of Observations 1.871952 Definitive/Provisional Indicator 0.000000 dtype: float64`
kurt	This method returns kurtosis. Kurtosis is indicative of the distribution shape	`print("Kurtosis", sunspots.kurt(),"\n") #out Kurtosis Yearly Mean Total Sunspot Number -0.135040 Yearly Mean Standard Deviation -0.243958 Number of Observations 1.850223 Definitive/Provisional Indicator 0.000000 dtype: float64`

Querying Data in Pandas

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A Pandas DataFrame is structured very similar to a relational database. We can view operations that read data from a DataFrame as a query. We are going to retrieve the annual sunspot data from Quandl.

We can use the Quandl API or we can download the data manually as a CSV file from Quandl website. To download the data you have to sign up. I will install the API by running the following command in the terminal:

pip3 install Quandl

Note:
Using the API is limited to 50 API calls per day.

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Pandas Series

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The Pandas Series is a one-dimensional, heterogeneous array with labels. We can create a Pandas Series data structure in three different ways:

Note:
When creating a Series, we can hand the constructor a list of axis labels (index). The index is an optional parameter.

With a Python dictionary – the sorted dictionary keys will become the index
With a NumPy array – the index values will be incremented starting from 0
With a single scalar value – we have to supply the index

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The Pandas DataFrames

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A Pandas DataFrame is a labeled two-dimensional data structure similar to a worksheet or a relational database table. The columns in Pandas DataFrame can be of different types.

A DataFrame can be created in the following ways:

Using another DataFrame
Using a NumPy array or a composite of arrays that has a two-dimensional shape
From another Pandas data structure called Series
From a file (a CSV file for example)
From a dictionary of one-dimensional structures (one-dimensional NumPy arrays, lists, dicts, or Pandas Series, for example)

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Pandas introduction

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Pandas is a very popular Python library and its name comes from Panel Data and Data Analysis.

The official documentation insists on naming pandas with lowercase letters and the import statement should be import pandas as pd.

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Broadcasting a NumPy array

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Broadcasting a NumPy array refers to a procedure executed on two operands even if they don’t have the same shape.

In this example we are going to multiply a scalar and an array. We will import a sound file and we will make it quieter.

import scipy.io.wavfile as sw
import matplotlib.pyplot as plt
import urllib
import numpy as np

request = urllib.request.Request('http://www.thesoundarchive.com/austinpowers/smashingbaby.wav')
response = urllib.request.urlopen(request)
print(response.info())
WAV_FILE = 'smashingbaby.wav'
filehandle = open(WAV_FILE, 'wb')
filehandle.write(response.read())
filehandle.close()
sample_rate, data = sw.read(WAV_FILE)
print("Data type", data.dtype, "Shape", data.shape)

plt.subplot(2, 1, 1)
plt.title("Original")
plt.plot(data)

plt.show()

newdata = data * 0.2
newdata = newdata.astype(np.uint8)
print("Data type", newdata.dtype, "Shape", newdata.shape)

sw.write("quiet.wav", sample_rate, newdata)

plt.subplot(2, 1, 2)
plt.title("Quiet")
plt.plot(newdata)

plt.show()

The output:

Content-Type: audio/wav
Last-Modified: Tue, 12 Aug 2014 15:53:38 GMT
Accept-Ranges: bytes
ETag: "ac20ba9445b6cf1:0"
Server: Microsoft-IIS/7.5
X-Powered-By: ASP.NET
Date: Tue, 26 Sep 2017 22:32:35 GMT
Connection: close
Content-Length: 43642


Data type uint8 Shape (43584,)
Data type uint8 Shape (43584,)

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Indexing NumPy arrays with Booleans

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Boolean indexing is a kind of fancy indexing therefor it works pretty much the same.

import scipy.misc 
import matplotlib.pyplot as plt
import numpy as np 

face = scipy.misc.face() 
xmax = face.shape[0] 
ymax = face.shape[1] 
face = face[:min(xmax,ymax),:min(xmax,ymax)]

def get_indices(size):
    arr = np.arange(size)
    return arr % 4 == 0

face1 = face.copy()
xindices = get_indices(face.shape[0])
yindices = get_indices(face.shape[1])
face1[xindices, yindices] = 0
plt.subplot(211)
plt.imshow(face1)
face2 = face.copy()
face2[(face > face.max()/4) & (face < 3 * face.max()/4)] = 0
plt.subplot(212)
plt.imshow(face2)
plt.show()

#out

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Indexing with a list of locations

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We are going to use again the Lena photo and apply the ix_() function to shuffle it.

import scipy.misc
import matplotlib.pyplot as plt
import numpy as np

face = scipy.misc.face() 
xmax = face.shape[0]
ymax = face.shape[1]

def shuffle_indices(size):
    arr = np.arange(size)
    np.random.shuffle(arr)

    return arr

xindices = shuffle_indices(xmax)
np.testing.assert_equal(len(xindices), xmax)
yindices = shuffle_indices(ymax)
np.testing.assert_equal(len(yindices), ymax)
plt.imshow(face[np.ix_(xindices, yindices)])
plt.show()

#out

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Fancy indexing

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Fancy indexing is not conventional indexing that involves integers and slicing. If we take the Lena photo again we could draw two black diagonal lines on the photo by setting the diagonal values to 0.

import scipy.misc
import matplotlib.pyplot as plt

face = scipy.misc.face()

xmax = face.shape[0]
ymax = face.shape[1]

face = face[:min(xmax,ymax),:min(xmax,ymax)]

xmax = face.shape[0]
ymax = face.shape[1]

face[range(xmax),range(ymax)] = 0
face[range(xmax-1,-1,-1), range(ymax)] = 0

plt.imshow(face)
#out


plt.show()
#out

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Creating array views and copies

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You might think that views means just to view something and nothing more, like the ravel() example on an array. In NumPy, views are NOT read-only!

That’s why, having a replica of the shared array view is very important. A slice of an array will produce a view; if you assign the slice to a variable and alter the underlying array then the value of the variable will change.

Example:

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Dan Dumitrache

Web Developer

Category Archives: Python Data Analysis

Statistics with Panda DataFrame

Querying Data in Pandas

Pandas Series

The Pandas DataFrames

Pandas introduction

Broadcasting a NumPy array

Indexing NumPy arrays with Booleans

Indexing with a list of locations

Fancy indexing

Creating array views and copies