Ways to Detect and Remove the Outliers
By: Natasha Sharma
Tags: Outliers, Data Science, Machine Learning, Data Analytics

While working on a Data Science project, what is it, that you look for? What is the most important part of the EDA phase? There are certain things which, if are not done in the EDA phase, can affect further statistical/Machine Learning modelling. One of them is finding “Outliers”. In this post we will try to understand what is an outlier? Why is it important to identify the outliers? What are the methods to outliers? Don’t worry, we won’t just go through the theory part but we will do some coding and plotting of the data too.

Meet the Outlier

Wikipedia definition,

In statistics, an outlier is an observation point that is distant from other observations.

The above definition suggests that outlier is something which is separate/different from the crowd. A lot of motivation videos suggest to be different from the crowd, specially Malcolm Gladwell. In respect to statistics, is it also a good thing or not? we are going to find that through this post.

Google Image — Wikihow

Do you see anything different in the above image? All the numbers in the 30’s range except number 3. That’s our outlier, because it is no where near to the other numbers.

Data Collection & Outliers

As we now know what is an outlier, but, are you also wondering how did an outlier introduce to the population?

The Data Science project starts with collection of data and that’s when outliers first introduced to the population. Though, you will not know about the outliers at all in the collection phase. The outliers can be a result of a mistake during data collection or it can be just an indication of variance in your data.

Let’s have a look at some examples. Suppose you have been asked to observe the performance of Indian cricket team i.e Run made by each player and collect the data.

Collected data

As you can see from the above collected data that all other players scored 300+ except Player3 who scored 10. This figure can be just a typing mistake or it is showing the variance in your data and indicating that Player3 is performing very bad so, needs improvements.

Now that we know outliers can either be a mistake or just variance, how would you decide if they are important or not. Well, it is pretty simple if they are the result of a mistake, then we can ignore them, but if it is just a variance in the data we would need think a bit further. Before we try to understand whether to ignore the outliers or not, we need to know the ways to identify them.

Finding Outliers

Most of you might be thinking, Oh! I can just have a peak of data find the outliers just like we did in the previously mentioned cricket example. Let’s think about a file with 500+ column and 10k+ rows, do you still think outlier can be found manually? To ease the discovery of outliers, we have plenty of methods in statistics, but we will only be discussing few of them. Mostly we will try to see visualization methods(easiest ones) rather mathematical.

So, Let’s get start. We will be using Boston House Pricing Dataset which is included in the sklearn dataset API. We will load the dataset and separate out the features and targets.

boston = load_boston()

x = boston.data

y = boston.target

columns = boston.feature_names #create the dataframe

boston_df = pd.DataFrame(boston.data)

boston_df.columns = columns

boston_df.head()

Boston Housing Data

Features/independent variable will be used to look for any outlier. Looking at the data above, it s seems, we only have numeric values i.e. we don’t need to do any data formatting.(Sigh!)

There are two types of analysis we will follow to find the outliers- Uni-variate(one variable outlier analysis) and Multi-variate(two or more variable outlier analysis). Don’t get confused right, when you will start coding and plotting the data, you will see yourself that how easy it was to detect the outlier. To keep things simple, we will start with the basic method of detecting outliers and slowly move on to the advance methods.

Discover outliers with visualization tools

Box plot-

Wikipedia Definition,

In descriptive statistics, a box plot is a method for graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points.

Above definition suggests, that if there is an outlier it will plotted as point in boxplot but other population will be grouped together and display as boxes. Let’s try and see it ourselves.

import seaborn as sns

sns.boxplot(x=boston_df['DIS'])

Boxplot — Distance to Employment Center

Above plot shows three points between 10 to 12, these are outliers as there are not included in the box of other observation i.e no where near the quartiles.

Here we analysed Uni-variate outlier i.e. we used DIS column only to check the outlier. But we can do multivariate outlier analysis too. Can we do the multivariate analysis with Box plot? Well it depends, if you have a categorical values then you can use that with any continuous variable and do multivariate outlier analysis. As we do not have categorical value in our Boston Housing dataset, we might need to forget about using box plot for multivariate outlier analysis.

Scatter plot-

Wikipedia Defintion

A scatter plot , is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.

As the definition suggests, the scatter plot is the collection of points that shows values for two variables. We can try and draw scatter plot for two variables from our housing dataset.

fig, ax = plt.subplots(figsize=(16,8))

ax.scatter(boston_df['INDUS'], boston_df['TAX'])

ax.set_xlabel('Proportion of non-retail business acres per town')

ax.set_ylabel('Full-value property-tax rate per $10,000')

plt.show()

Scatter plot — Proportion of non-retail business acres per town v/s Full value property tax

Looking at the plot above, we can most of data points are lying bottom left side but there are points which are far from the population like top right corner.

Discover outliers with mathematical function

Z-Score-

Wikipedia Definition

The Z-score is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured.

The intuition behind Z-score is to describe any data point by finding their relationship with the Standard Deviation and Mean of the group of data points. Z-score is finding the distribution of data where mean is 0 and standard deviation is 1 i.e. normal distribution.

You must be wondering that, how does this help in identifying the outliers? Well, while calculating the Z-score we re-scale and center the data and look for data points which are too far from zero. These data points which are way too far from zero will be treated as the outliers. In most of the cases a threshold of 3 or -3 is used i.e if the Z-score value is greater than or less than 3 or -3 respectively, that data point will be identified as outliers.

We will use Z-score function defined in scipy library to detect the outliers.

from scipy import stats

import numpy as np z = np.abs(stats.zscore(boston_df))

print(z)

Z-score of Boston Housing Data

Looking the code and the output above, it is difficult to say which data point is an outlier. Let’s try and define a threshold to identify an outlier.

threshold = 3

print(np.where(z > 3))

This will give a result as below -

Data points where Z-scores is greater than 3

Don’t be confused by the results. The first array contains the list of row numbers and second array respective column numbers, which mean z[55][1] have a Z-score higher than 3.

print(z[55][1]) 3.375038763517309

So, the data point — 55th record on column ZN is an outlier.

IQR score -

Box plot use the IQR method to display data and outliers(shape of the data) but in order to be get a list of identified outlier, we will need to use the mathematical formula and retrieve the outlier data.

Wikipedia Definition

The interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q3 − Q1. In other words, the IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data. It is a measure of the dispersion similar to standard deviation or variance, but is much more robust against outliers.

IQR is somewhat similar to Z-score in terms of finding the distribution of data and then keeping some threshold to identify the outlier.

Let’s find out we can box plot uses IQR and how we can use it to find the list of outliers as we did using Z-score calculation. First we will calculate IQR,

Q1 = boston_df_o1.quantile(0.25)

Q3 = boston_df_o1.quantile(0.75)

IQR = Q3 - Q1

print(IQR)

Here we will get IQR for each column.

IQR for each column

As we now have the IQR scores, it’s time to get hold on outliers. The below code will give an output with some true and false values. The data point where we have False that means these values are valid whereas True indicates presence of an outlier.

print(boston_df_o1 < (Q1 - 1.5 * IQR)) |(boston_df_o1 > (Q3 + 1.5 * IQR))

Detecting outlier with IQR

Now that we know how to detect the outliers, it is important to understand if they needs to be removed or corrected. In the next section we will consider a few methods of removing the outliers and if required imputing new values.

Working with Outliers: Correcting, Removing

During data analysis when you detect the outlier one of most difficult decision could be how one should deal with the outlier. Should they remove them or correct them? Before we talk about this, we will have a look at few methods of removing the outliers.

Z-Score

In the previous section, we saw how one can detect the outlier using Z-score but now we want to remove or filter the outliers and get the clean data. This can be done with just one line code as we have already calculated the Z-score.

boston_df_o = boston_df_o[(z < 3).all(axis=1)]

With and without outlier size of the dataset

So, above code removed around 90+ rows from the dataset i.e. outliers have been removed.

IQR Score -

Just like Z-score we can use previously calculated IQR score to filter out the outliers by keeping only valid values.

boston_df_out = boston_df_o1[~((boston_df_o1 < (Q1 - 1.5 * IQR)) |(boston_df_o1 > (Q3 + 1.5 * IQR))).any(axis=1)] boston_df_out.shape

The above code will remove the outliers from the dataset.

There are multiple ways to detect and remove the outliers but the methods, we have used for this exercise, are widely used and easy to understand.

Whether an outlier should be removed or not. Every data analyst/data scientist might get these thoughts once in every problem they are working on. I have found some good explanations -

To summarize their explanation- bad data, wrong calculation, these can be identified as Outliers and should be dropped but at the same time you might want to correct them too, as they change the level of data i.e. mean which cause issues when you model your data. For ex- 5 people get salary of 10K, 20K, 30K, 40K and 50K and suddenly one of the person start getting salary of 100K. Consider this situation as, you are the employer, the new salary update might be seen as biased and you might need to increase other employee’s salary too, to keep the balance. So, there can be multiple reasons you want to understand and correct the outliers.

Summary

Throughout this exercise we saw how in data analysis phase one can encounter with some unusual data i.e outlier. We learned about techniques which can be used to detect and remove those outliers. But there was a question raised about assuring if it is okay to remove the outliers. To answer those questions we have found further readings(this links are mentioned in the previous section). Hope this post helped the readers in knowing Outliers.

Note- For this exercise, below tools and libaries were used.

Framework- Jupyter Notebook, Language- Python, Libraries- sklearn library, Numpy, Panda and Scipy, Plot Lib- Seaborn and Matplot.

Refernces