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

Bivariate Feature Analysis in Python

r
rohit Last Updated : 07 Apr, 2022
7 min read

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

Introduction

Feature analysis is an important step in building any predictive model. It helps us in understanding the relationship between dependent and independent variables. In this article, we will look into a very simple feature analysis technique that can be used in cases such as binary classification problems. The underlying idea is to quantify the relationships between each independent variable and dependent variable at certain levels of values for each variable, this can help in identifying a subset of variables that are more important and also know about the important levels of particular feature values.

This knowledge about features can help us in deciding which features to include in the initial model. It can also help reduce the overall complexity of the predictive model by converting continuous numerical variables to categorical types by way of binning them. In particular, we will look at a supervised feature analysis approach also known as bivariate feature analysis.

Dataset

Wine Quality Dataset –

The dataset used in this article is publicly available from the UCI Machine Learning Repository,

Link: https://archive-beta.ics.uci.edu/ml/datasets/wine+quality

Attributes/Features List

 Source: Author

Output (Target) variable: quality (score between 0 and 10)

Let’s look at the distribution of target variable,

                                                       Source: Author

A higher score means better quality of the wine.

Let’s consider scores of 8 & 9 as an excellent quality group and the rest of the scores as a non-excellent quality group.

Source: Author

Thus, our problem statement now is to predict the quality of wine as Excellent or Non-Excellent based on the available features.

Note that the classes are imbalanced here, we have very few examples of Excellent quality wines as compared to Non-Excellent ones. These kinds of situations are often encountered in problems such as credit card fraud detection, insurance claim fraud identification or disease detection. Identifying the most relevant features in these kinds of situations can help businesses prioritize & focus on important features thereby significantly improving the predictive power of the underlying model while keeping it simple.

We will use feature analysis methods to see which of these are relevant variables for determining the excellent quality wine.

Feature Analysis

We will follow a supervised feature analysis approach. In particular, we will use the target variable along with independent variables to check their relationships.

Let’s split the data as train & test sets,

After splitting the dataset into train & test sets the target distribution will look as below,

Source: Author

In order to produce the same results/numbers as above refer to the data exploration code below and set the random_state=100

 

In this dataset, all the features are numeric. The values of these features are continuous in nature. In order to understand how these are related to the target variable, we need to look at the buckets/level of each variable value.

The helper function below will compute several statistics in order to analyse the relationship between each bucket of values and the target variable.

 

Comparing Train & Test Target Percentage

Using the feature_analysis helper function above we will get a feature analysis dataframe.

all_features_list = ['fixed acidity', 'volatile acidity', 'citric acid', 'residual sugar', 'chlorides', 'free sulfur dioxide', 'total sulfur dioxide', 'density', 'pH', 'sulphates', 'alcohol']
feature_analysis_df = feature_analysis(y='target', features=all_features_list, trn_df=trn_wine_data, tst_df=tst_wine_data, y_hat=None)feature_analysis_df = feature_analysis(y='target', features=all_features_list, trn_df=trn_wine_data, tst_df=tst_wine_data, y_hat=None) 

We can see that each feature is broken down into various levels.

Table 1: Feature analysis of feature – fixed acidity

feature analysis technique

Source: Author

Since we randomly sampled train and test datasets hence the overall target percentages of train and test splits are nearly the same.

The overall target percentage is like a benchmark against which each of the levels can be compared.

The objective of this analysis is to know,

  1. Whether there is a trend between levels and target percentage.
  2. On average, how does a feature is relevant based on the presence of the target as compared to the overall target percentage

Let’s look at each feature individually,

For feature fixed acidity we see that (Refer Table 1),

  1. As the levels are increasing the target percentage is getting lower
  2. This suggests that the more acidic nature of the wine makes it poor
  3. Although values between the range 3.8-5.9 have a good correlation with the target it’s not the case for the corresponding train target percentage
  4. This feature may not be that relevant or important for predicting the quality of wine

For feature alcohol, we see that

  1. There is a clear increasing trend here, as the levels are increasing we see the target percentage improves
  2. This suggests that wine with more alcohol improves its quality
  3. Also, note that the last levels have significantly more target percentage as compared to the overall target percentage
  4. This feature could be most relevant or important for predicting the quality of wine

Table 2: Feature analysis of feature – alcohol

feature analysis technique

Source: Author

For feature sulphates, we see that

  1. On average, the levels have less than the overall target percentage
  2. Only the third level has the percentage of the targets slightly more than the overall train target percentage
  3. This feature may not be that relevant or important for predicting the quality of wine

Table 3: Feature analysis for feature – sulphates

Feature Analysis for Feature

Source: Author

For feature pH, we see that

  1. There is a slight trend
  2. As the levels are increasing the target percentage is also increasing but the increase is not much compared to the overall target percentage
  3. This suggests that this feature is slightly important for predicting the quality of wine

Table 4: Feature analysis for feature – pH

Feature Analysis for Ph

Source: Author

For feature volatile acidity, we see that

  1. The percentage of the target in each level is only slightly better than the overall target percentage
  2. This suggests, this feature may not be that relevant or important for predicting the quality of wine

Table 5: Feature analysis for feature – volatile acidity

Volatile acidity

Source: Author

For feature citric acid, we see that

  1. There is no uniform trend between increasing levels & target percentage
  2. We do see a slight increase in the target percentage in the mid-levels
  3. This suggests that this could be a somewhat important feature and a mild level of citric acid helps to improve the quality of wine

Table 6: Feature analysis for feature – citric acid

 

feature analysis technique | citric acid

Source: Author

For feature residual sugar, we see that

  1. Similar to the observation made for the citric acid feature here also we see that the mid-level values are more suitable for good quality wine
  2. Also, note that compared to citric acid here the mid-level values show a higher target percentage
  3. This suggests that this feature could be a somewhat important feature – better than citric acid – for predicting the quality of wine

Table 7: Feature analysis for feature – residual sugar

Residual Sugar | feature analysis technique

Source: Author

For feature chlorides, we see that

  1. Here the first few levels have a higher target percentage compared to the overall target percentage
  2. This suggests that this could be a slightly important variable

Table 8: Feature analysis technique for feature – chlorides

 

Chlorides | feature analysis technique

Source: Author

For feature free sulphur dioxide, we see that

  1. On average, the train target percentage is not that higher than the corresponding overall target percentage for different levels
  2. This suggests that this feature may not be much relevant or important for predicting the quality of wine

Table 9: Feature analysis technique for feature-free sulphur dioxide

Source: Author

For feature total sulphur dioxide, we see that

  1. The Mid-level values do have a higher test target percentage than the overall target percentage but corresponding train target percentages are just slightly better than the overall target percentage
  2. This suggests that if this feature is included in the model will introduce somewhat of variance as the test data is seeing slightly different target percentage compared to train data

Table 10: Feature analysis technique for feature total sulphur dioxide

feature analysis technique

Source: Author

For feature density, we see that

  1. Similar to chlorides here also we see initial levels show a higher train target percentage compared to the overall train target percentage
  2. This suggests that this could be a slightly important variable

Table 11: Feature analysis for feature density

Feature analysis

Source: Author

Great, we covered all the features!

The above analysis is very simple in nature but greatly helps us in giving a first-hand overview of the nature of the individual features & also the important levels too!

Conclusion

  • A simple yet effective way to do the initial level of feature analysis is by simply analysing the key stats at each level of feature values.
  • A supervised feature analysis approach described here can be applied to a variety of binary classification problems with all kinds of features – be it numeric or categorical.
  • This simple feature analysis technique outlined here can complement the feature selection process and describes a very easy & visual way to look at the relationships between dependent & independent variables.

In particular, this simple analysis of comparing the target percentages in each level of feature values gave us a lot of insights. It helped us identify important features such as high alcohol value, it also helped us identify the important levels of certain features such as initial level of values for features chlorides and sulphates. 

This analysis can further help in compressing the levels and bin the features to only include important levels thereby converting the continuous feature into a categorical type thereby reducing the overall complexity of the model.

Hope you will find this feature analysis technique useful in your work! Read the latest articles on our blog.

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

blogathonfeature analysis techniquemachine learningpython
r
rohit

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

Rose
Rose

Hi, sir. I found this article very helpful. I'm new to python and there are no resources using the feature analysis function and i love how you explained it. do you mind sharing the complete code? Hope you can help me with this request, sir.

123

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!
Top 100 Data Science Interview Questions & Answers 2024
Top 100 Data Science Interview Questions & Answers 2024
Wine Quality Prediction Using Machine Learning
Wine Quality Prediction Using Machine Learning

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