An Outlier is a data-item/object that deviates significantly from the rest of the [so-called normal]objects. They can be caused by measurement or execution errors. The analysis for outlier detection is referred to as outlier mining. There are many ways to detect the outliers, and the removal process is the data frame same as removing a data item from the panda’s data frame.
Here pandas data frame is used for a more realistic approach as in real-world project need to detect the outliers arouse during the data analysis step, the same approach can be used on lists and series-type objects.
Dataset:
Dataset used is Boston Housing dataset as it is preloaded in the sklearn library.
Python3
import sklearn
from sklearn.datasets import load_boston
import pandas as pd
import matplotlib.pyplot as plt
bos_hou = load_boston[]
column_name = bos_hou.feature_names
df_boston = pd.DataFrame[bos_hou.data]
df_boston.columns =
column_name
df_boston.head[]
Output:
part of the dataset
Detecting the outliers
Outliers can be detected using visualization, implementing mathematical formulas on the dataset, or using the statistical approach. All of these are discussed below.
1. Visualization
Example 1: Using Box Plot
It captures the summary of the data effectively and efficiently with only a simple box and whiskers. Boxplot summarizes sample data using 25th, 50th, and 75th percentiles. One can just get insights[quartiles, median, and outliers] into the dataset by just looking at its boxplot.
Python3
import seaborn as sns
sns.boxplot[df_boston['DIS']]
Output:
Boxplot- DIS column
In the above graph, can clearly see that values above 10 are acting as the outliers.
Python3
print[np.where[df_boston['DIS']>10]]
Output:
Outlier’s Index
Example 2: Using ScatterPlot.
It is used when you have paired numerical data, or when your dependent variable has multiple values for each reading independent variable, or when trying to determine the relationship between the two variables. In the process of utilizing the scatter plot, one can also use it for outlier detection.
To plot the scatter plot one requires two variables that are somehow related to each other. So here, ‘Proportion of non-retail business acres per town’ and ‘Full-value property-tax rate per $10,000’ are used whose column names are “INDUS” and “TAX” respectively.
Python3
fig, ax = plt.subplots[figsize = [18,10]]
ax.scatter[df_boston['INDUS'], df_boston['TAX']]
ax.set_xlabel['[Proportion non-retail business acres]/[town]']
ax.set_ylabel['[Full-value property-tax rate]/[ $10,000]']
plt.show[]
Output:
Scatter Plot
Looking at the graph can summarize that most of the data points are in the bottom left corner of the graph but there are few points that are exactly;y opposite that is the top right corner of the graph. Those points in the top right corner can be regarded as Outliers.
Using approximation can say all those data points that are x>20 and y>600 are outliers. The following code can fetch the exact position of all those points that satisfy these conditions.
Python3
print[np.where[[df_boston['INDUS']>20] & [df_boston['TAX']>600]]]
Output:
Outlier’s Index
2. Z-score
Z- Score is also called a standard score. This value/score helps to understand that how far is the data point from the mean. And after setting up a threshold value one can utilize z score values of data points to define the outliers.
Zscore = [data_point -mean] / std. deviation
Python3
from scipy import stats
import numpy as np
z = np.abs[stats.zscore[df_boston['DIS']]]
print[z]
Output:
part of the list[z]
The above output is just a snapshot of part of the data; the actual length of the list[z] is 506 that is the number of rows. It prints the z-score values of each data item of the column
Now to define an outlier threshold value is chosen which is generally 3.0. As 99.7% of the data points lie between +/- 3 standard deviation [using Gaussian Distribution approach].
Python3
threshold = 3
print[np.where[z > 3]]
Output:
Outlier’s Index
3. IQR [Inter Quartile Range]
IQR [Inter Quartile Range] Inter Quartile Range approach to finding the outliers is the most commonly used and most trusted approach used in the research field.
IQR = Quartile3 – Quartile1
Python3
Q1 = np.percentile[df_boston['DIS'], 25,
interpolation = 'midpoint']
Q3 = np.percentile[df_boston['DIS'], 75,
interpolation = 'midpoint']
IQR = Q3 - Q1
Output:
To define the outlier base value is defined above and below datasets normal range namely Upper and Lower bounds, define the upper and the lower bound [1.5*IQR value is considered] :
upper = Q3 +1.5*IQR
lower = Q1 – 1.5*IQR
In the above formula as according to statistics, the 0.5 scale-up of IQR [new_IQR = IQR + 0.5*IQR] is taken, to consider all the data between 2.7 standard deviations in the Gaussian Distribution.
Python3
upper = df_boston['DIS'] >= [Q3+1.5*IQR]
print["Upper bound:",upper]
print[np.where[upper]]
lower = df_boston['DIS'] =
[Q3+1.5*IQR]]
lower = np.where[df_boston['DIS']