Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Exploratory Data Analysis with an Example

A
Alifia Ghantiwala Last Updated : 06 Apr, 2022
7 min read

This article was published as a part of the Data Science Blogathon.

Introduction

Exploratory Data Analysis helps in identifying any outlier data points, understanding the relationships between the various attributes and structure of the data, recognizing the important variables. It helps in framing questions and visualizing the results, paving the way to make an informed choice of the machine learning algorithm for the problem at hand.

While working on performing Exploratory Data Analysis, it is important that we keep our objective in mind. Plotting fancy graphs is not the aim but deriving useful insights is.

Keeping that in mind, in this article we would look into an example of Exploratory Data Analysis performed on Haberman’s survival dataset which is available on Kaggle.

The objective of this analysis is To find patterns within the dataset to gain further understanding of the data and leverage it to choose a machine learning algorithm for predicting the survival rates of patients who undergo the surgery.

The dataset contains cases from a study that was conducted between 1958 and 1970 at the University of Chicago’s Billings Hospital on the survival of patients who had undergone surgery for breast cancer.

Data attributes:-

Age of patient at the time of operation (numerical)

Patient’s year of operation (year — 1900, numerical)

Number of positive axillary nodes detected (numerical)

Survival status (class attribute) 1 = the patient survived 5 years or longer, 2 = the patient died within 5 year

We start by loading the data into a data frame

df = pd.read_csv("/kaggle/input/habermans-survival-data-set/haberman.csv")
df.shape

df.info()

Exploratory Data Analysis

The data has 305 rows and 4 columns with no NULL values. The columns do not have a heading/title, hence we provide a meaningful title to the columns in our dataset.

df.columns = ["age",'year','nodes','status']

df.describe()

Exploratory Data Analysis

Observations

  • The data includes patients whose ages are ranging from 30 to 83 years.
  • The operation has been performed for years 1958 to 1969
  • The maximum number of lymph nodes in the dataset is 52, with an approximate mean value of 4

Let’s Look at the Data!

A quick look at the count of records for the attributes “age” and “year”(when the operation was performed) gives us the following insights.

  • We have more patients with a survival status of 1(those who survived for more than 5 years or longer) than patients with a survival status of 2(those who died within 5 years)
  • As the number of records existing for both survival rates has a major difference, our data is imbalanced.
  • In the year 1958, most of the operations were performed and the least operations were performed in 1969
print(df["status"].value_counts())
print(df["year"].value_counts())

Exploratory Data Analysis

Univariate Analysis

It is the simplest form of analyzing data, it uses only one variable hence the name, Univariate.

We would use Probability Density Function, Cumulative Distribution Function, Box Plots, and Violin Plots for our analysis

Probability Density Function

The probability density function(PDF) provides the probability of a random variable falling in the range of values.

We have plotted below the PDF of the age

Univariate Analysis

Observations

  • Patients between the ages of 30–34 have survived for 5 years or longer.
  • Patients whose age is more than 75 died within 5 years of the operation.
  • The number of patients between the age of 40–50 is more for status 2(i.e those who died within 5 years)
  • The number of patients between the age of 35–40 is more for status 1(i.e who have survived for 5 years or more), patients within this age group have a good chance of survival post the operation.

PDF of Number of Nodes

Number of Nodes | Exploratory Data Analysis

Observations

We see that the data is overlapping but we can note that the survival rate is better in patients who have 0–2 nodes and the survival rate decreases as there is an increase in the number of nodes.

PDF of the year of operation

Observations

The data is overlapping but we can see that between 1963 and 1966 we have more survival data and between 1958–1961 we have more data on patients who died within 5 years of the operation.

Cumulative Distribution Function

It describes the probability that a random variable will be found at a value less than or equal to the point at which the CDF is calculated.

CDF of number of nodes

 

Observations

  • 80% of the patients who survived had nodes less than 5.
  • Whereas 80% of the patients who could not survive had greater than 10 nodes.

CDF of Age

 

CDF of Age

Observations

  • The CDF curve is highly overlapping but we can observe that 20% of surviving patients had an approximate age of 38, while 20% of patients who could not survive have an approximate age of 45

Box Plots

Help us in visualizing the distribution of data based on the quartiles and provide some indication of the data’s symmetry and skewness. Unlike many other methods of data display, boxplots show outliers.

Boxplot on Age

Boxplot of Age

Observations

  • The 25th percentile of patients who have survived are of age approximate 42 years
  • The 25th percentile of patients who died are of age approximate 46 years
  • The 50th percentile of patients who have survived are of age approximate 52 years
  • The 50th percentile of patients who died are of age approximate 55 years
  • 75th percentile of patients who have survived are of age approximate 60 years
  • 75th percentile of patients who died are of age approximate 61 years

As we have noted before the data is overlapping to a great extent and hence we would not be able to draw an accurate conclusion on the basis of just the age of the patient.

Boxplot on Nodes

 

Bloxplot of Nodes | Exploratory Data Analysis

Observations

We can see that for the nodes attribute we have some outlier points.

  • 75 percentile of patients who survived have less than 4 nodes whereas 50 percentile of patients who could not survive have 5 nodes
  • Having a low count of active nodes is definitely a contributing factor to the survival of a patient.

Bivariate Analysis

The aim is to find patterns/relationships within the dataset using two attributes. It is useful in testing simple associations.

One plot which can be used for the analysis is the pair plot.

Pair plots are an easy way to visualize relationships within your data. A matrix of each variable associated with another variable is produced for our analysis.

 Example of Pair Plots

Bivariate Analysis

Observations

Plot 2:- attributes:- age and year

The points are overlapping, due to which all points are not clearly visible on the plot, which makes it difficult to conclude.

Plot 3:- attributes:- age and nodes

The points are overlapping, due to which all points are not clearly visible on the plot, which makes it difficult to conclude. We can however see that patients with more number of nodes and high age are generally of status 2(who could not survive)

Plot 6:- attributes:- year and nodes

The points are overlapping, due to which all points are not clearly visible on the plot, which makes it difficult to conclude.

Multivariate Analysis

Contour plots can be used for multivariate analysis. They are used to represent a three-dimensional surface on a two-dimensional plane. One variable is represented on the horizontal axis and a second variable is represented on the vertical axis. The third variable is represented by a colour gradient.

A contour plot on attributes, age on the Y axis, year on the X-axis, and the third variable is status = 1(successful survival post 5 years of operation)

Multivariate Analysis

Observations

The patients who survived are mostly in the approximate age group of 45–55 within the years 1962–1964

A contour plot on attributes, age on the Y axis, year on the X-axis, and the third variable is status = 2(could not survive)

Multivariate Analysis 2

Observations

The patients who could not survive were in the approximate age group of 45–50 between the years 1962 and 1965

Conclusion

  • The dataset is imbalanced.
  • The data is highly overlapping for both the status which makes it difficult to implement a simple decision-making algorithm.
  • Less number of nodes is a contributing factor to the survival status of a patient.
  • Through our exploratory data analysis, we can deduce that since our dataset has highly overlapping attributes we would need to use a powerful machine learning algorithm for our objective of predicting the survival rates.

Hope you liked reading my article on Exploratory Data Analysis. Read the latest articles on our blog!

About the Author

I am currently working as an analyst. By writing these articles I try to deepen my understanding of applied machine learning. Click here and get in touch with me!

The media shown in this article is not owned by Analytics Vidhya and are used at the Author’s discretion. 

blogathondata visualisationexploratory data analysismachine learningMultivariate Analysis
A
Alifia Ghantiwala

I investigate data on a daily basis to find insights! I write so that I can understand more clearly. Have completed my graduation in Computer Engineering, and won my first public data science competition last month, March 2021, hosted on Kaggle by Google Developers.

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag
Congratulations, You Did It!
Well Done on Completing Your Learning Journey. Stay curious and keep exploring!
Walk Through of Haberman Cancer Survival Dataset Exploratory Data Analysis
Walk Through of Haberman Cancer Survival Dataset Exploratory Data Analysis
What is Exploratory Data Analysis (EDA) and How Does it Work?
What is Exploratory Data Analysis (EDA) and How Does it Work?

We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.

Show details