Decision Tree vs Random Forest: Use Cases & Performance Metrics

Decision Trees and Random Forests are both powerful machine learning algorithms, but they differ significantly in their approach and performance. A decision tree is a simple, interpretable model that splits data based on feature thresholds, whereas a random forest creates an ensemble of multiple decision trees to enhance accuracy and prevent overfitting.

In this blog, you’ll explore decision tree vs random forest and examine their key differences and use cases. You’ll also learn how performance metrics help you evaluate the effectiveness of each model in solving practical problems like fraud detection, stock market prediction, and medical diagnosis.

Let's now analyze decision tree vs random forest, exploring the key factors that differentiate these two algorithms.

Decision Tree vs Random Forest: Key Differences

Decision Trees and Random Forests are both popular machine learning algorithms, but they differ significantly in terms of structure, performance, and complexity. Decision Trees are individual models that predict by splitting data into a tree-like structure, simple enough to understand with their clear if-then rules. They can sometimes overfit the data, making them less reliable for new information.

Random Forests, on the other hand, combine many decision trees, averaging their predictions to get a more accurate and stable result. This ensemble approach reduces overfitting and generally performs better, though the model becomes more complex and less straightforward to interpret than a single decision tree.

If you're looking to develop the essential skills in machine learning to understand algorithms like decision trees and random forests, the following upGrad courses can provide a solid foundation:

• Executive Diploma in Machine Learning and AI with IIIT-B
• Master’s Degree in Artificial Intelligence and Data Science
• Generative AI Mastery Certificate for Software Development

Comparison table of Decision Tree vs Random Forest

Also Read: Categories of Machine Learning: What Classes of Problems Do They Solve?

Now that you have a good understanding of the differences between Decision Tree vs Random Forest, let’s explore them each in more detail.

What is a Decision Tree? Key Components Explained

A Decision Tree in Machine Learning is a popular model used for classification and regression tasks. It follows a tree-like structure, where each internal node represents a decision or test on a specific feature, and each branch shows the outcome of that decision.

Finally, each leaf node provides the final prediction or class label. The model recursively splits the data based on the most informative feature at each step, aiming to make accurate predictions by following a series of decisions.

Key Components of Decision Tree

Understanding the key components of a Decision Tree in machine learning is essential to comprehend how it makes predictions. Each element plays a critical role in the recursive splitting of data to reach an accurate conclusion.

• Root Node: The topmost node in the tree, where the first decision is made. It represents the feature that is most informative in dividing the dataset. The choice of this feature is based on criteria like Gini Impurity or Entropy for classification tasks or variance reduction for regression tasks.
• Decision Nodes: These are the intermediate nodes in the tree that represent decisions based on a specific feature’s value. Each decision node tests the data against a feature, further splitting the dataset to reduce impurity or variance. These nodes are critical in determining the path followed by each data point in the tree.
• Branches: The edges or links between nodes, which represent the outcomes of a decision or test. Each branch corresponds to one of the possible outcomes (e.g., a specific range of feature values). Branches guide data points toward the next decision node or leaf node.
• Leaf Nodes: The terminal nodes of the tree that provide the final prediction or class label. In a classification task, each leaf node corresponds to a specific class label, while in a regression task, it provides a predicted numerical value. The leaf nodes represent the outcome of all prior decisions made along the path.

In Artificial Intelligence, decision trees are valued for their ability to create interpretable models that reveal the decision-making process, making them useful for applications where transparency and clarity are important.

Example Scenario: We want to predict if a person will play tennis based on the weather conditions. The decision tree splits the data based on the most informative features, and the final decision (whether to play tennis or not) is made based on a sequence of conditions.

Example Dataset:

Decision Tree Structure: The root node is the first decision, which checks if it's Sunny.

• If Yes, the next decision checks if it's Windy.
  • If Windy = Yes, the decision is Don’t Play Tennis (leaf node).
  • If Windy = No, the decision is Play Tennis (leaf node).
• If No, the next decision checks if it’s Rainy.
  • If Rainy = Yes, the decision is Don’t Play Tennis (leaf node).
  • If Rainy = No, the decision is Play Tennis (leaf node).

Each decision node tests a condition (e.g., "Is it sunny?" or "Is it windy?"), and each leaf node provides the final outcome based on the sequence of decisions. The branches represent the paths leading to the next node or final prediction.

Python Code Example:

import pandas as pd
from sklearn.tree import DecisionTreeClassifier, export_text
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# Sample data for weather conditions and play tennis decision
data = {
    'Sunny': ['Yes', 'Yes', 'No', 'No', 'Yes', 'No', 'Yes', 'No'],
    'Windy': ['No', 'Yes', 'No', 'No', 'Yes', 'Yes', 'No', 'Yes'],
    'Rainy': ['No', 'No', 'Yes', 'No', 'Yes', 'Yes', 'No', 'No'],
    'Play_Tennis': ['Yes', 'No', 'No', 'Yes', 'No', 'No', 'Yes', 'Yes']
}

# Convert categorical data to numerical values (Yes = 1, No = 0)
df = pd.DataFrame(data)
df['Sunny'] = df['Sunny'].map({'Yes': 1, 'No': 0})
df['Windy'] = df['Windy'].map({'Yes': 1, 'No': 0})
df['Rainy'] = df['Rainy'].map({'Yes': 1, 'No': 0})
df['Play_Tennis'] = df['Play_Tennis'].map({'Yes': 1, 'No': 0})

# Features (X) and target (y)
X = df[['Sunny', 'Windy', 'Rainy']]  # Features
y = df['Play_Tennis']  # Target

# Split into training and test data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)

# Create and train the Decision Tree model
clf = DecisionTreeClassifier(random_state=42)
clf.fit(X_train, y_train)

# Make predictions
y_pred = clf.predict(X_test)

# Calculate accuracy
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")

# Print the decision tree structure
tree_rules = export_text(clf, feature_names=['Sunny', 'Windy', 'Rainy'])
print("\nDecision Tree Structure:\n")
print(tree_rules)

# Predictions on test data
print("Predicted Play Tennis:", y_pred)

Code Explanation:

• Data Preprocessing: The categorical features (Sunny, Windy, Rainy, Play_Tennis) are mapped to numerical values (1 for "Yes", 0 for "No").
• Model Training: A Decision Tree is trained using DecisionTreeClassifier on the features (Sunny, Windy, Rainy) to predict whether to play tennis.
• Prediction & Evaluation: The model makes predictions on the test set and calculates the accuracy. The decision tree structure is printed, showing how splits are made based on weather conditions.

Output: The model has 100% accuracy, meaning it correctly predicts whether to play tennis for all instances in the test set.

Accuracy: 100.00%

Decision Tree Structure:

|--- Sunny <= 0.50

|   |--- Rainy <= 0.50

|   |   |--- class: 1

|   |   |--- class: 0

|   |--- class: 1

|--- Windy <= 0.50

|   |--- class: 0

|--- class: 1

Predicted Play Tennis: [1 0]

• Decision Tree Structure: The decision tree structure printed shows how the tree splits based on the features:
• Root Node: The tree first checks if Sunny <= 0.50 (Sunny = No).
  • If Yes (Sunny = No), the decision is based on Rainy.
  • If No (Sunny = Yes), the tree checks if Windy <= 0.50 (Windy = Yes).
  • This decision-making continues recursively, splitting the data based on the conditions for Sunny, Windy, and Rainy.
• Predictions: The model predicts 1 (Play Tennis) for the first test instance and 0 (Don't Play Tennis) for the second test instance.

A Decision Tree starts by splitting the data based on features like Sunny, Windy, and Rainy, recursively dividing it into smaller subsets. The tree reaches leaf nodes where the final decision to play tennis is made based on these conditions.

Also Read: Decision Tree Example: A Comprehensive Guide to Understanding and Implementing Decision Trees

Let's now explore how a decision tree makes predictions by recursively splitting the data and selecting the best features at each step.

How a Decision Tree Makes Predictions?

A Decision Tree Algorithm recursively splits data based on the feature that best separates the target variable (for classification) or minimizes variance (for regression). The process follows a criteria-based approach to determine the feature and threshold for splitting.

1. Classification Criteria

To split the data for classification tasks, the following metrics are commonly used. These criteria help determine the most informative feature for each split in a Decision Tree, optimizing the model's performance.

Gini Impurity: Measures the impurity or disorder of a dataset

where pi​ is the proportion of class i in the dataset D.

Entropy: Measures the uncertainty or disorder of a dataset.

where pi​ is the class probability in dataset D.

2. Regression Criteria

For regression tasks, the goal is to minimize variance within the subsets after the split. The metric used is:

Variance Reduction:

where yi​  is the actual value, and y​ is the predicted value and N is the total number of observations.

3. Stopping Criteria:

The splitting continues recursively until one of the following stopping conditions is met:

• Maximum Tree Depth: Prevents the tree from growing too deep.
• Minimum Samples Per Leaf Node: Ensures there are enough samples in each leaf.
• Minimum Impurity or Variance: Stops splitting when the impurity or variance is sufficiently low.

Also Read: Understanding Decision Tree In AI: Types, Examples, and How to Create One

Let's explore some of the key areas where decision trees are widely applied.

Where Are Decision Trees Used?

Decision Trees are versatile models used across various domains for both classification and regression tasks. Their interpretability and ability to handle both categorical and numerical data make them popular in machine learning applications.

1. Classification Tasks:

• Medical Diagnosis: Decision Trees are used to classify diseases based on patient attributes (e.g., age, blood pressure, symptoms). They can handle complex feature interactions, making them useful for medical prediction models, but care must be taken to avoid overfitting with noisy data.
• Credit Scoring: In finance, Decision Trees are used to classify loan applicants as "high risk" or "low risk" based on financial history, credit score, and other attributes. The model helps financial institutions make lending decisions, and it's often used for its interpretability to explain decisions.
• Image Recognition: Decision Trees, combined with feature extraction techniques, can be used for image classification tasks, particularly in low-complexity cases, where pixel-level data is directly processed.

2. Regression Tasks:

• Stock Price Prediction: Predicting the future price of stocks or commodities based on historical data and market indicators.
• Real Estate Pricing: Estimating the price of properties based on features like location, square footage, and amenities.
• Energy Demand Forecasting: Used in predicting the energy demand of households or industries based on features such as weather patterns, seasonal trends, and historical consumption data.

3. Feature Selection: Decision Trees can be used for feature importance ranking, helping identify which features contribute most to predictions, used in preprocessing pipelines.

4. Business Decision-Making: Used in strategic planning, sales forecasting, and customer segmentation by learning patterns in business data and providing actionable insights.

5. Risk Management:  Applied in assessing risks for insurance companies by evaluating client data, including age, location, and claim history, to predict future claims or financial exposure.

6. Environmental Modeling: Decision Trees are used in environmental science to model the impact of various factors (e.g., temperature, pollution levels) on ecosystems. Their interpretability is crucial for understanding how different environmental conditions affect ecological balance.

Also Read: Decision Tree Classification: Everything You Need to Know

Next, let’s explore Random Forests, an ensemble method that builds upon Decision Trees to enhance your model's performance and stability.

What is a Random Forest? Key Components Explained

A Random Forest Algorithm is an ensemble learning method used for both classification and regression tasks. It constructs a collection of Decision Trees during training, where each tree independently makes a prediction.

The final output is determined by aggregating the predictions of individual trees, either through majority voting (for classification) or averaging (for regression). The goal is to improve model accuracy, reduce variance, and mitigate overfitting, which a single Decision Tree might be prone to.

Key Components of Random Forest

Understanding the key components of a random forest in machine learning  is essential to comprehend how it makes predictions. Each element plays a critical role in the splitting of data to reach an accurate conclusion.

• Ensemble of Trees: A Random Forest is made up of multiple Decision Trees, each trained on a random subset of the training data. This allows each tree to learn different patterns, improving the overall model’s performance.
• Leaf Nodes: Similar to individual Decision Trees, each tree in the Random Forest ends in leaf nodes, which provide the final prediction. For classification tasks, each leaf corresponds to a class label, while for regression, it provides a numerical value.

Example Scenario: In a Random Forest, we use multiple decision trees, each trained on a random subset of the data and possibly using random subsets of features at each split.

Example Dataset:

Steps for Random Forest:

1. Multiple Trees: In a Random Forest, instead of a single decision tree, we create multiple trees. For example, let’s say we use 3 trees in our Random Forest.
2. Bootstrapping: Each tree is trained on a random subset of the data (with replacement). For instance, Tree 1 might train on rows 1, 3, 5, and 7; Tree 2 on rows 2, 4, 6, and 8; and so on.
3. Random Feature Selection: At each split in a tree, a random subset of features is selected. For instance, one tree may decide on the "Sunny" feature at the root node, while another tree might look at "Windy" first.

Lets take a closer look:

Tree 1: Root Node: "Is it Sunny?"

• If Yes → Go to "Is it Windy?"
  • If Yes → Don't play tennis (leaf node).
  • If No → Play tennis (leaf node).
• If No → Go to "Is it Rainy?"
  • If Yes → Don't play tennis (leaf node).
  • If No → Play tennis (leaf node).

Tree 2: Root Node: "Is it Windy?"

• If Yes → Don't play tennis (leaf node).
• If No → Go to "Is it Sunny?"
  • If Yes → Play tennis (leaf node).
  • If No → Go to "Is it Rainy?"
    • If Yes → Don't play tennis (leaf node).
    • If No → Play tennis (leaf node).

Tree 3: Root Node: "Is it Rainy?"

• If Yes → Don't play tennis (leaf node).
• If No → Go to "Is it Windy?"
  • If Yes → Don't play tennis (leaf node).
  • If No → Play tennis (leaf node).

Final Prediction: After all three trees have made their predictions, the final decision is made by majority voting:

• Tree 1 might predict: Play tennis
• Tree 2 might predict: Don't play tennis
• Tree 3 might predict: Play tennis

So, the majority vote is to play tennis.

Python Code Example for Random Forest:

import pandas as pd
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# Sample dataset
data = {
    'Sunny': ['Yes', 'Yes', 'No', 'No', 'Yes', 'No', 'Yes', 'No'],
    'Windy': ['No', 'Yes', 'No', 'No', 'Yes', 'Yes', 'No', 'Yes'],
    'Rainy': ['No', 'No', 'Yes', 'No', 'Yes', 'Yes', 'No', 'No'],
    'Play_Tennis': ['Yes', 'No', 'No', 'Yes', 'No', 'No', 'Yes', 'Yes']
}

# Convert categorical data to numerical values
df = pd.DataFrame(data)
df['Sunny'] = df['Sunny'].map({'Yes': 1, 'No': 0})
df['Windy'] = df['Windy'].map({'Yes': 1, 'No': 0})
df['Rainy'] = df['Rainy'].map({'Yes': 1, 'No': 0})
df['Play_Tennis'] = df['Play_Tennis'].map({'Yes': 1, 'No': 0})

# Features and target
X = df[['Sunny', 'Windy', 'Rainy']]  # Features
y = df['Play_Tennis']  # Target

# Split into training and test data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)

# Create Random Forest model
rf = RandomForestClassifier(n_estimators=3, random_state=42)  # Using 3 trees in the forest
rf.fit(X_train, y_train)

# Make predictions
y_pred = rf.predict(X_test)

# Accuracy
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")

# Predictions
print("Predicted Play Tennis: ", y_pred)

Code Explanation:

• Data Preparation: A sample dataset with weather conditions (Sunny, Windy, Rainy) and whether to Play_Tennis is created. Categorical values ('Yes', 'No') are mapped to numerical values (1, 0).
• Splitting Data: The dataset is split into training and test sets using train_test_split(), with 75% of the data for training and 25% for testing.
• Model Creation: A RandomForestClassifier with 3 trees (n_estimators=3) is trained on the training data (X_train, y_train).
• Prediction: The trained model predicts whether to play tennis (y_pred) based on the test data.
• Evaluation: The accuracy of the model is calculated by comparing predicted values (y_pred) with the actual test labels (y_test), and the result is printed.

Output:

• Accuracy: 100%: The model predicts the correct outcome (whether to play tennis) for all test instances.

Accuracy: 100.00%

Predicted Play Tennis:  [1 0]

• Predicted Play Tennis: [1 0]:
  • 1 means the model predicts "Play Tennis" for the first test instance.
  • 0 means the model predicts "Don't Play Tennis" for the second test instance.

A Random Forest is an ensemble of decision trees, each trained on random subsets of data and features. Each tree makes a prediction, and the final output is determined by majority voting. This method reduces overfitting and enhances the model's generalization compared to a single decision tree.

Also Read: Random Forest Algorithm: When to Use & How to Use? [With Pros & Cons]

Let's now explore how Random Forest makes predictions by utilizing the aggregated outputs of multiple decision trees. 

How Random Forest Makes Predictions?

Random Forest makes predictions by aggregating the outputs of multiple decision trees. Each tree independently predicts a class label (for classification) or a numerical value (for regression). The final output is determined by combining the predictions from all trees, ensuring the model is more robust and generalizes better than a single decision tree.

1. Bootstrap Aggregating (Bagging)

Random Forest builds multiple trees using bootstrap sampling (sampling with replacement) from the training data. Each tree is trained on a different subset of the data, introducing variability among trees and reducing model variance.

2. Random Feature Selection

At each node of every tree, a random subset of features is considered for the best split. This prevents trees from becoming too similar and improves model diversity, helping reduce overfitting.

3. Model Training

Each tree is trained independently, using different bootstrapped samples and feature subsets. After training, each tree makes a prediction (class label for classification or value for regression).

4. Final Prediction

• Majority Voting (for Classification):  In classification tasks, the final prediction is made by majority voting, where the class predicted by most trees is selected as the final output.

• Averaging (for Regression): For regression tasks, the final prediction is the average of all tree predictions, reducing noise and making the overall prediction more reliable.

where yi​ represents the prediction from the i-th tree, and N is the total number of trees.

5. Out-of-Bag (OOB) Error Estimation

Since each tree is trained on a random bootstrap sample of data, approximately one-third of the data is left out for each tree. These out-of-bag samples are used for error estimation, providing an unbiased estimate of model performance without needing a separate validation set.

Where Are Random Forests Used?

Random Forest algorithms are widely used in various domains due to their versatility and accuracy. Some of the key areas where they are applied include:

1. Classification

• Medical Diagnosis: Random Forest is used for classifying different types of diseases (e.g., cancer diagnosis) based on patient data, such as age, gender, medical history, and test results.
• Image Classification: It's applied to classify images based on pixel values. For example, in facial recognition, traffic sign detection, or medical imaging.
• Customer Segmentation: In marketing and customer analytics, Random Forest is used to classify customers into different groups based on purchase history, demographics, or behavior.

2. Regression

• House Price Prediction: Random Forest is used to predict continuous outcomes, like predicting house prices based on features like size, location, age of the property, etc.
• Sales Forecasting: It is applied to predict future sales in retail or e-commerce based on historical data and other business-related factors.
• Stock Price Prediction: While not always the best model for this complex domain, Random Forest can be used to predict stock prices or financial metrics by analyzing patterns in financial time series data.

3. Anomaly Detection

• Fraud Detection: Random Forest is used in identifying fraudulent transactions in banking, insurance, or online payment systems.
• Network Security: It is applied for detecting network intrusions or unusual patterns in network traffic that might indicate a security breach.

4. Feature Selection

• Identifying Important Features: In high-dimensional datasets, Random Forest can help identify which features (variables) are the most important for making predictions. This is particularly useful in genomics or text analysis.

5. Natural Language Processing (NLP)

• Sentiment Analysis: Random Forest can be used for classifying the sentiment of a piece of text (positive, negative, neutral) based on various linguistic features.
• Text Classification: It’s also applied to categorize text into different topics (e.g., spam detection in emails).

6. Bioinformatics

• Gene Expression Analysis: In genomics, Random Forest is applied to classify and predict gene expression patterns, identifying relationships between genes and diseases.
• Protein Structure Prediction: It is used to predict protein structures or functions from biological sequences.

7. Ecology and Environmental Science

• Species Classification: Random Forest is used to classify species based on environmental data like temperature, precipitation, and other geographic factors.
• Weather Prediction: It is used in forecasting certain weather patterns by analyzing historical data and environmental variables.

8. Robotics and Control Systems

• Autonomous Vehicles: Random Forest is used in various aspects of autonomous driving, such as object detection, lane detection, and predicting potential hazards in the environment.
• Industrial Automation: It’s applied in predictive maintenance and optimizing processes in manufacturing by analyzing data from sensors and other devices.

Also Read: Feature Engineering for Machine Learning: Process, Techniques, and Examples

Let's now explore specific use cases to understand when a decision tree and random forest is the better choice for your problem.

Use Cases: When to Use Decision Tree vs Random Forest? 

Both decision trees and random forests are powerful machine learning algorithms, but they are suited for different types of problems depending on the complexity, interpretability, and accuracy requirements. Here’s when you should use one over the other:

When to Use Decision Tree

1. Simple, Interpretable Models:

• Decision Trees are easy to understand and interpret. If you need a model that can be easily explained (e.g., for regulatory purposes or to present to non-technical stakeholders), a Decision Tree is a good choice.
• The tree structure helps visualize decisions, making it easy to trace how the model arrives at a particular prediction.

2. Small to Medium-Sized Datasets: For small datasets, a Decision Tree might perform well without needing complex computations. A well-tuned decision tree on smaller datasets can be highly effective.

3. Handling Non-linear Data: Decision Trees are capable of capturing non-linear relationships, so if your data has complex non-linear decision boundaries, a single tree may be able to model this well, especially for simpler problems.

4. Faster Training Time: Decision Trees are relatively quick to train compared to Random Forests, making them ideal when computational resources or time is limited.

5. Low Noise in Data: If your dataset is relatively clean (i.e., not too noisy), a Decision Tree might perform adequately without overfitting. However, Decision Trees are prone to overfitting if the data is noisy or has many outliers.

When to Use Random Forest

1. Improved Accuracy (Ensemble Learning):

• Random Forests typically outperform Decision Trees because they combine multiple trees (ensemble learning). They reduce overfitting by averaging predictions across many trees, resulting in better generalization to unseen data.
• When accuracy is more important than interpretability, Random Forests tend to be the better choice.

2. Handling Large, Complex Datasets:

• Random Forests are more robust to overfitting and can handle large datasets with many features and observations better than a single Decision Tree.
• They also handle missing data, outliers, and noisy data better, so if your data is complex, Random Forests will likely provide superior performance.

3. Dealing with Overfitting: Decision Trees often overfit when they are too deep or when the data is noisy. Random Forests mitigate this problem by averaging predictions across multiple trees, effectively reducing variance and preventing overfitting.

4. High Dimensionality (Many Features): Random Forests are great when the data has many features, and you want to reduce the dimensionality through feature selection or want to capture more complex patterns in the data.

5. When Robustness is Key: If you're working in an application where robustness is critical (e.g., healthcare, finance), Random Forests are typically more reliable and stable than a single Decision Tree.Use a Decision Tree for simple, interpretable models with quick training on small, clean datasets. On the other hand, choose Random Forest when you need better accuracy and reliability on larger, more complex datasets or when you want to avoid overfitting through the use of ensemble learning.

To gain a comprehensive understanding of algorithms, their significance, and their functionality, enroll in upGrad’s Data Structures & Algorithms Course. This 50-hour program will help you develop expertise in runtime analysis, algorithm design, and more, with a focus on advanced machine learning operations.

Also Read: How to Learn Machine Learning – Step by Step

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The key difference in decision tree vs random forest lies in their model construction. A Decision Tree uses a single tree for predictions, while a Random Forest aggregates multiple trees to improve accuracy and reduce overfitting. Decision Trees are useful in areas requiring interpretability, like credit scoring and medical diagnosis, while Random Forests excel in fields like finance, marketing, and bioinformatics, where accuracy and handling complex data are crucial.

As you explore these models, upGrad offers specialized courses to support your growth in data mining and machine learning, equipping you with the skills needed to excel in today’s data-driven world.

Here are some relevant upGrad courses to help you get started:

• Artificial Intelligence in the Real World
• Introduction to Data Analysis using Excel
• Advanced Generative AI Certification Course

Not sure which course is the best fit to learn machine learning algorithms? Contact upGrad for personalized counseling and valuable insights. For more details, you can also visit your nearest upGrad offline center.

Also Read: Classification in Data Mining: A Complete Guide to Types, Algorithms & Model Building in 2025

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Reference:
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