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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

Confusion Matrix: Detailed intuition and trick to learn

prayas.singh@outlook.com
[email protected] Last Updated : 22 Apr, 2021
6 min read
This article was published as a part of the Data Science Blogathon.

Introduction

What is the first measure coming into your mind when you must test your classification model? Do you always check accuracy? Is accuracy enough to test the model?

In this read, you will get to know that accuracy is not the best measure to test your classification model, how can you draw more insight from your model, and can get a sense of how you can improve it. And, I will tell you one great trick to remember the mighty confusion Matrix, so that next time you won’t find it confusing. So, without further ado, let’s start!

We will be covering items here:

  • Confusion Matrix: a simple definition
    • TP and TPR
    • TN and TNR
    • FP and FPR
    • FN and FNR
    • Accuracy
    • Error Rate
    • General Understanding
  • Why is the confusion matrix better than accuracy?
  • Precision and Recall
  • F1 Score
  • Trick to remember confusion matrix

 

Confusion Matrix: a simple definition

As the name suggests, it is a matrix. A matrix of predicted and actual target values. This matrix compares the predicted target values with the actual target values. And it cannot process probability scores.

Let’s understand it with the help of a small dataset:

Data points Actual Class Labels Predicted class labels
x1 y1 Y1
x2 y2 Y2
x3 y3 Y3
. . .
. . .
. . .
xn yn Yn

 

Here, x1,x2,x3……xn is the independent data points, y1,y2,y3…..yn are the actual target values or actual class labels, and Y1, Y2, Y3…..Yn has predicted class labels. Because the confusion matrix cannot process probability scores, all these class labels are binary.

Here every class label is either 0 or 1 (0 represents negative and 1 represents positive labels). So, the confusion matrix for a binary classification will be:

N = total negative

P = total positive

Here we can see how a confusion matrix looks like for a binary classification model. Now let’s understand TN, TP, FN, FP further.

 

True Positive (TP) and True Positive Rate (TPR):

True Positive – The predicted value as well as the actual value both are positive, i.e., the model correctly predicts the class label to be positive.

True Positive Rate – The ratio of true positive and totally positive, i.e.,

TPR = TP / P

TPR = TP / (FN+TP)

 

True Negative (TN) and True Negative Rate (TNR):

True Negative – The predicted value as well as the actual value both are negative, i.e., the model correctly predicts the class label to be negative.

True Negative Rate – The ratio of true negative and total negative, i.e.,

TNR = TN / N

TNR = TN / (TN+FP)

 

False Positive (FP) and False Positive Rate (FPR):

False Positive – The predicted value is positive, but the actual value was negative, i.e., the model falsely predicted these negative class labels to be positive.

False Positive Rate – The ratio of false-positive and total negative, i.e.,

FPR = FP / N

FPR = FP / (TN+FP)

NOTE: False positive (FP) is also called ‘type-1 error’.

 

False Negative (FN) and False Negative Rate (FNR):

False Negative – The predicted value is negative, but the actual value is positive, i.e., the model falsely predicted the positive class labels to be negative.

False Negative Rate – The ratio of false-negative and totally positive, i.e.,

FNR = FN / P

FNR = FN / (FN+TP)

NOTE: False negative (FN) is also called ‘type-2 error’.

Accuracy – The ratio of correctly predicted class labels to all class labels. It tells us how much our model is correct.

Accuracy = (TN+TP) / (N+P)

Error rate – The ratio of incorrectly predicted class labels to all class labels. It tells us how much our model has errored.

Error rate = (FN + FP) / (N+P)

 

General Understanding:

If the model is sensible and not dumb then,

Confusion Matrix General Understanding

i.e., the elements in the principal diagonal in the matrix will be high and the rest of the off-diagonal elements will be small if the model is good or sensible.

So, by looking at the rates we have discussed above, we can conclude whether the model is dumb or sensible regardless it is balanced or imbalanced.

 

Why is the confusion matrix better than accuracy?

Let’s take a very simple example and understand it more deeply.

Suppose we have an imbalanced dataset that is 95% negative and 5% positive. So in this dataset, for any given ‘x’ we will have a negative ‘Y’ 95% of the time.

Let’s say after fitting the model our different rates are like this:

TP = 70, TN = 880, FP = 30, FN = 20

So, our accuracy will be:

Accuracy = (880+70) / (70+880+30+20)

Accuracy = 950 / 1000 = 0.95

i.e., 95%

We will think that the model is 95% accurate, i.e., it will predict accurately 95% of the time. But we can see here that it is a dumb model and 95% of the time it will say that the predicted value is negative.

We can overcome this problem by using precision and recall which are derived from the confusion matrix.

Now, I believe, you get my point, why accuracy is not the best matrix to measure our model performance.

 

Precision and Recall

Precision: Of all the points that the model predicted to be positive, how much percentage of them are truly positive?

Precision = TP / (FP+TP)

Recall: Of all the actually positive points how much percentage of them are predicted positive points?

Recall = TP / (FN+TP)

In most cases, we want both our precision and recall being high, but it is not possible. When our precision will be high our recall will be low and vice versa. So to balance these we have another matric called F1 Score.

F1 Score: It is the harmonic mean of precision and recall values. It is maximum when precision is equal to recall.

Trick to remember confusion matrix

Here is our confusion matrix:

confusion matrix trick

2 steps to remember:

  1. What is the predicted label? (the 2nd part)
  2. Are we correct? (the first part)

Let me elaborate. If we need to find (a) in the above matrix, we will ask ourselves what if the predicted label and write it in the 2nd place:

Actual values

Now, we will ask the second question, i.e., are we correct? If yes, then we will write true (T) and if no, we will write false (F) and write it in the first place:

Predicted Values

 

Similarly for (b), what is the predicted value? – N. Are we correct? – F. So in place of (b) we can write – FN:

confusion matrix Fn

Similarly, we can fill (c) and (d) also:

PV

Now how we can remember formulae for TPR, FPR, TNR, FNR:

TPR = number of true positives / total number of positives

So, the number of true positive points is – TP and the total number of positive points is – the sum of the column in which TP is present which is – P.

i.e.,

TPR = TP / P

TPR = TP / (FN+TP)

Similarly, we can see that,

TNR = TN / N

TNR = TN / (TN+FP)

Using the same trick, we can write FPR and FNR formulae.

So now, I believe you can understand the confusion matrix and different formulae related to it. How and why is it used and how it is better than accuracy? See, the confusion matrix is not very confusing anymore!

We will soon come with another article with some other tricks and in-depth intuition.

Stay Well!

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

prayas.singh@outlook.com
[email protected]

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