- Machine Learning Basics
- Machine Learning - Home
- Machine Learning - Getting Started
- Machine Learning - Basic Concepts
- Machine Learning - Python Libraries
- Machine Learning - Applications
- Machine Learning - Life Cycle
- Machine Learning - Required Skills
- Machine Learning - Implementation
- Machine Learning - Challenges & Common Issues
- Machine Learning - Limitations
- Machine Learning - Reallife Examples
- Machine Learning - Data Structure
- Machine Learning - Mathematics
- Machine Learning - Artificial Intelligence
- Machine Learning - Neural Networks
- Machine Learning - Deep Learning
- Machine Learning - Getting Datasets
- Machine Learning - Categorical Data
- Machine Learning - Data Loading
- Machine Learning - Data Understanding
- Machine Learning - Data Preparation
- Machine Learning - Models
- Machine Learning - Supervised
- Machine Learning - Unsupervised
- Machine Learning - Semi-supervised
- Machine Learning - Reinforcement
- Machine Learning - Supervised vs. Unsupervised
- Machine Learning Data Visualization
- Machine Learning - Data Visualization
- Machine Learning - Histograms
- Machine Learning - Density Plots
- Machine Learning - Box and Whisker Plots
- Machine Learning - Correlation Matrix Plots
- Machine Learning - Scatter Matrix Plots
- Statistics for Machine Learning
- Machine Learning - Statistics
- Machine Learning - Mean, Median, Mode
- Machine Learning - Standard Deviation
- Machine Learning - Percentiles
- Machine Learning - Data Distribution
- Machine Learning - Skewness and Kurtosis
- Machine Learning - Bias and Variance
- Machine Learning - Hypothesis
- Regression Analysis In ML
- Machine Learning - Regression Analysis
- Machine Learning - Linear Regression
- Machine Learning - Simple Linear Regression
- Machine Learning - Multiple Linear Regression
- Machine Learning - Polynomial Regression
- Classification Algorithms In ML
- Machine Learning - Classification Algorithms
- Machine Learning - Logistic Regression
- Machine Learning - K-Nearest Neighbors (KNN)
- Machine Learning - Naïve Bayes Algorithm
- Machine Learning - Decision Tree Algorithm
- Machine Learning - Support Vector Machine
- Machine Learning - Random Forest
- Machine Learning - Confusion Matrix
- Machine Learning - Stochastic Gradient Descent
- Clustering Algorithms In ML
- Machine Learning - Clustering Algorithms
- Machine Learning - Centroid-Based Clustering
- Machine Learning - K-Means Clustering
- Machine Learning - K-Medoids Clustering
- Machine Learning - Mean-Shift Clustering
- Machine Learning - Hierarchical Clustering
- Machine Learning - Density-Based Clustering
- Machine Learning - DBSCAN Clustering
- Machine Learning - OPTICS Clustering
- Machine Learning - HDBSCAN Clustering
- Machine Learning - BIRCH Clustering
- Machine Learning - Affinity Propagation
- Machine Learning - Distribution-Based Clustering
- Machine Learning - Agglomerative Clustering
- Dimensionality Reduction In ML
- Machine Learning - Dimensionality Reduction
- Machine Learning - Feature Selection
- Machine Learning - Feature Extraction
- Machine Learning - Backward Elimination
- Machine Learning - Forward Feature Construction
- Machine Learning - High Correlation Filter
- Machine Learning - Low Variance Filter
- Machine Learning - Missing Values Ratio
- Machine Learning - Principal Component Analysis
- Machine Learning Miscellaneous
- Machine Learning - Performance Metrics
- Machine Learning - Automatic Workflows
- Machine Learning - Boost Model Performance
- Machine Learning - Gradient Boosting
- Machine Learning - Bootstrap Aggregation (Bagging)
- Machine Learning - Cross Validation
- Machine Learning - AUC-ROC Curve
- Machine Learning - Grid Search
- Machine Learning - Data Scaling
- Machine Learning - Train and Test
- Machine Learning - Association Rules
- Machine Learning - Apriori Algorithm
- Machine Learning - Gaussian Discriminant Analysis
- Machine Learning - Cost Function
- Machine Learning - Bayes Theorem
- Machine Learning - Precision and Recall
- Machine Learning - Adversarial
- Machine Learning - Stacking
- Machine Learning - Epoch
- Machine Learning - Perceptron
- Machine Learning - Regularization
- Machine Learning - Overfitting
- Machine Learning - P-value
- Machine Learning - Entropy
- Machine Learning - MLOps
- Machine Learning - Data Leakage
- Machine Learning - Resources
- Machine Learning - Quick Guide
- Machine Learning - Useful Resources
- Machine Learning - Discussion
Machine Learning - Entropy
Entropy is a concept that originates from thermodynamics and was later applied in various fields, including information theory, statistics, and machine learning. In machine learning, entropy is used as a measure of the impurity or randomness of a set of data. Specifically, entropy is used in decision tree algorithms to decide how to split the data to create a more homogeneous subset. In this article, we will discuss entropy in machine learning, its properties, and its implementation in Python.
Entropy is defined as a measure of disorder or randomness in a system. In the context of decision trees, entropy is used as a measure of the impurity of a node. A node is considered pure if all the examples in it belong to the same class. In contrast, a node is impure if it contains examples from multiple classes.
To calculate entropy, we need to first define the probability of each class in the data set. Let p(i) be the probability of an example belonging to class i. If we have k classes, then the total entropy of the system, denoted by H(S), is calculated as follows −
$$H\left ( S \right )=-sum\left ( p\left ( i \right )\ast log_{2}\left ( p\left ( i \right ) \right ) \right )$$
where the sum is taken over all k classes. This equation is called the Shannon entropy.
For example, suppose we have a dataset with 100 examples, of which 60 belong to class A and 40 belong to class B. Then the probability of class A is 0.6 and the probability of class B is 0.4. The entropy of the dataset is then −
$$H\left ( S \right )=-(0.6\times log_{2}(0.6)+ 0.4\times log_{2}(0.4)) = 0.971$$
If all the examples in the dataset belong to the same class, then the entropy is 0, indicating a pure node. On the other hand, if the examples are evenly distributed across all classes, then the entropy is high, indicating an impure node.
In decision tree algorithms, entropy is used to determine the best split at each node. The goal is to create a split that results in the most homogeneous subsets. This is done by calculating the entropy of each possible split and selecting the split that results in the lowest total entropy.
For example, suppose we have a dataset with two features, X1 and X2, and the goal is to predict the class label, Y. We start by calculating the entropy of the entire dataset, H(S). Next, we calculate the entropy of each possible split based on each feature. For example, we could split the data based on the value of X1 or the value of X2. The entropy of each split is calculated as follows −
$$H\left ( X_{1} \right )=p_{1}\times H\left ( S_{1} \right )+p_{2}\times H\left ( S_{2} \right )H\left ( X_{2} \right )=p_{3}\times H\left ( S_{3} \right )+p_{4}\times H\left ( S_{4} \right )$$
where p1, p2, p3, and p4 are the probabilities of each subset; and H(S1), H(S2), H(S3), and H(S4) are the entropies of each subset.
We then select the split that results in the lowest total entropy, which is given by −
$$H_{split}=H\left ( X_{1} \right )\, if\, H\left ( X_{1} \right )\leq H\left ( X_{2} \right );\: else\: H\left ( X_{2} \right )$$
This split is then used to create the child nodes of the decision tree, and the process is repeated recursively until all nodes are pure or a stopping criterion is met.
Example
Let's take an example to understand how it can be implemented in Python. Here we will use the "iris" dataset −
from sklearn.datasets import load_iris
import numpy as np
# Load iris dataset
iris = load_iris()
# Extract features and target
X = iris.data
y = iris.target
# Define a function to calculate entropy
def entropy(y):
n = len(y)
_, counts = np.unique(y, return_counts=True)
probs = counts / n
return -np.sum(probs * np.log2(probs))
# Calculate the entropy of the target variable
target_entropy = entropy(y)
print(f"Target entropy: {target_entropy:.3f}")
The above code loads the iris dataset, extracts the features and target, and defines a function to calculate entropy. The entropy() function takes a vector of target values and returns the entropy of the set.
The function first calculates the number of examples in the set and the count of each class. It then calculates the proportion of each class and uses these to calculate the entropy of the set using the entropy formula. Finally, the code calculates the entropy of the target variable in the iris dataset and prints it to the console.
Output
When you execute this code, it will produce the following output −
Target entropy: 1.585