PCA in Machine Learning: A Complete Guide for 2025

Principal Component Analysis (PCA) is a dimensionality reduction technique used in machine learning and statistics to simplify large datasets. These ‘principal’ components retain the most important information from the original data while reducing redundancy and noise. 

As data continues to grow in both size and complexity, this dimensionality reduction technique has become increasingly relevant in 2025.For example, in facial recognition systems, PCA in machine learning is used to reduce the number of features needed to represent an image, making the model faster and more efficient without sacrificing accuracy.

In this blog, we’ll dive into how PCA in machine learning works and its key applications. You'll learn how it can help streamline data, enhance model performance, and make complex datasets more manageable.

If you want to build AI and ML skills to improve your data modelling skills, upGrad’s online AI and ML courses can help you. By the end of the program, participants will be equipped with the skills to build AI models, analyze complex data, and solve industry-specific challenges.

What is Principal Component Analysis or PCA in Machine Learning?

ML models with many input variables or higher dimensionality tend to fail when operating on a higher input dataset. PCA in machine learning helps in identifying relationships among different variables & then coupling them. PCA works on some assumptions which are to be followed and it helps developers maintain a standard.

PCA involves the transformation of variables in the dataset into a new set of variables which are called PCs (Principal Components). The principal components would be equal to the number of original variables in the given dataset.

Machine learning professionals skilled in techniques like PCA are in high demand due to their ability to handle complex data. If you're looking to develop skills in AI and ML, here are some top-rated courses to help you get there:

• Masters in Artificial Intelligence and Machine Learning
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Here are some of the most commonly used terms for PCA in machine learning:

• Dimensionality: It basically refers to the number of features or variables that you can find in a dataset. To put it simply, dimensionality refers to the number of columns that are present in the dataset. 
• Correlation: The second most commonly used term in PCA machine learning is correlation. Correlation means how strongly two variables are related to each other. 
• Orthogonal: Yet another commonly used term of PCA algorithm in machine learning is orthogonal. It states that variables are not co-related to each other. This automatically means that the correlation between the two variables is basically zero. 
• Covariance Matrix: Last but not least, the covariance matrix is one of the most commonly used terms that is used in the principal component analysis in machine learning. It basically refers to a matrix that contains covariance between the pair of variables.

Also Read: 15 Key Techniques for Dimensionality Reduction in Machine Learning 

What is PCA Used for?

PCA in machine learning is primarily used to reduce the dimensionality of large datasets while preserving as much variance as possible, making it easier to analyze and visualize complex data. It is widely applied in areas like image processing, speech recognition, and feature extraction for machine learning models, improving computational efficiency and accuracy.

Let us go through the various usages of principal component analysis in machine learning:

• Data Slimming Down: PCA is like a Marie Kondo for your data, helping you toss out the unnecessary and keep only what sparks joy, making it more manageable.
• Picking the VIPs: It’s your personal red-carpet event for data features. PCA selects the real stars, discarding the extras, so your analysis focuses on the A-listers. 
• Spotting Trends: Ever feel lost in a sea of numbers? PCA in machine learning acts like a trend-spotter, simplifying your data jungle and pointing out the big trends you might have missed. 
• Filtering Out Noise: Think of PCA as your noise-canceling headphones for data. It tunes out the irrelevant bits, leaving you with a clearer signal. 
• Data Face-lift: When your data needs a makeover, PCA is the go-to stylist. It transforms your dataset, giving it a fresh look in a new, more stylish dimension. 
• Helping Machines Learn Better: In the world of machines, PCA is the tutor. It preps the data, making it easier for machines to learn the important stuff without getting distracted by the noise. 

Also Read: Curse of Dimensionality in Machine Learning: A Complete Guide

Key Assumptions of PCA In Machine Learning

For PCA in machine learning to work effectively in machine learning, certain assumptions must be followed. These assumptions ensure the algorithm functions accurately and efficiently.

Here’s a breakdown:

• Linearity: PCA assumes that the data follows a linear relationship, meaning the variables combine in a linear fashion to form the dataset. This ensures that the principal components (PCs) capture the underlying patterns in the data effectively.
• Variance Emphasis: PCA gives more importance to the principal components with higher variance, as they carry the most significant information. Components with lower variance are often dismissed as noise. This assumption stems from the Pearson correlation coefficient framework, which emphasizes the axes with high variance.
• Consistent Measurement Levels: All variables should be measured at the same ratio level. Ideally, the sample size should be at least 150 observations, with a ratio of 5:1 between observations and features to ensure the stability of PCA results.
• Outliers: Extreme values, or outliers, should be minimized. A high number of outliers can lead to experimental errors, negatively impacting the effectiveness of the PCA model and the overall machine learning algorithm.
• Correlation Between Features: The features in the dataset must be correlated. After applying PCA, the reduced set of features should still represent the original dataset, but with fewer dimensions, allowing for more efficient analysis and model training.

By adhering to these assumptions, PCA can significantly enhance the efficiency and performance of machine learning models.

Also Read: Top 5 Machine Learning Models Explained For Beginners

Next, let’s look at how PCA in Machine Learning works.

How Does PCA in Machine Learning Work? Step-By-Step Process

Each step of PCA plays a crucial role in reducing dimensionality while retaining key data patterns. Normalization ensures features contribute equally, preventing dominance by larger values. Covariance calculation helps identify relationships between variables. 

Eigenvalue and eigenvector computations capture the directions of maximum variance, while sorting and selecting the top eigenvalues ensures only the most significant components are retained. Finally, using the principal components transforms the data into a lower-dimensional space, preserving essential information for more efficient analysis.

Below are the key steps to apply PCA effectively in any machine learning model or algorithm:

Step 1: Normalization of Data

The first step in applying PCA is normalizing the data. Unscaled data can skew the relative comparison of features, especially when they have different units or scales. For instance, in a 2D dataset, you subtract the mean from each data point to standardize it. This step ensures that each feature contributes equally to the analysis.

Example: Suppose you have a dataset with Height (ranging from 150 cm to 190 cm) and Weight (ranging from 50 kg to 100 kg). Without normalization, Weight could dominate due to its larger range. To normalize, subtract the mean of each feature from the values and divide by their standard deviations. This makes both Height and Weight comparable in terms of variance.

Also Read: Normalization in SQL: Benefits and Concepts

Step 2: Calculate Covariance Matrix

Once the data is normalized, the next step is to calculate the covariance between different dimensions. The covariance matrix will capture how each pair of variables in the dataset varies together. The diagonal elements represent the variances of individual variables, while the off-diagonal elements capture the covariances between pairs of variables.

A covariance matrix is symmetric, and it provides insight into the relationships between the features and the variance in each principal component.

Example: After normalizing Height and Weight, calculate the covariance matrix. If taller people generally weigh more, the covariance between Height and Weight will be positive, indicating a direct relationship. This covariance matrix allows PCA to understand how the features are related and how much variance each feature contributes to the dataset.

Also Read: Difference Between Covariance and Correlation

Step 3: Eigenvalue and Eigenvector Calculation

To understand the amount of variance captured by each principal component, you need to calculate the eigenvalues and eigenvectors of the covariance matrix. Eigenvalues represent the variance of the data along the direction of the corresponding eigenvector.

The equation for eigenvalue calculation is: det(EI - C) = 0, where E is the eigenvalue matrix, I is the identity matrix, and C is the covariance matrix. Eigenvectors indicate the direction in which maximum variance occurs.

Example: After calculating the covariance matrix, find the eigenvalues and eigenvectors. The eigenvalue corresponding to the largest eigenvector represents the axis where most variance occurs (e.g., from shorter, lighter individuals to taller, heavier individuals). This eigenvector becomes the first principal component, which explains the greatest variability in the data.

Step 4: Sort Eigenvalues and Select Components

After calculating the eigenvalues, arrange them in either ascending or descending order. Select the higher eigenvalues, which correspond to the most significant principal components. Although some information will be lost by ignoring smaller eigenvalues, they typically have minimal impact on the final result.

The selected eigenvalues will define the reduced dimensions for your new feature set, and the corresponding eigenvectors will form the feature vector.

Example: After calculating the eigenvalues, you find that the first principal component has an eigenvalue of 5 (capturing most of the variance), and the second component has an eigenvalue of 1 (capturing less variance). You decide to retain the first principal component, as it explains the majority of the data's variance, reducing the data from 2D to 1D.

Also Read: Linear Algebra for Machine Learning: Critical Concepts, Why Learn Before ML

Step 5: Compute the Principal Components

Multiply the transpose of the feature vector with the transpose of the normalized data to obtain the principal components. These components represent the transformed data in a lower-dimensional space while retaining the most critical variance in the dataset.

In practice, the highest eigenvalue will typically correspond to the most significant principal component, and other components will provide less information. This proves that PCA reduces the dataset’s dimensions without losing significant data, but rather by representing it more effectively.

Example: With your Height and Weight dataset, multiply the transpose of the feature vector (containing the selected eigenvectors) by the transpose of the normalized data. This operation will produce a new dataset where the first principal component (e.g., a combination of Height and Weight) explains most of the variance, reducing the dataset’s dimensions without significant information loss.

These steps effectively reduce the dimensionality of your dataset in PCA, ensuring that the most significant features are retained while eliminating noise and redundancy. 

Also Read: Linear Discriminant Analysis for Machine Learning: A Comprehensive Guide (2025)

Next, let’s look at some of the applications of PCA in Machine Learning.

Applications of PCA in Machine Learning

PCA in machine learning is widely used in data analysis due to its ability to reduce the dimensionality of complex datasets while retaining important features. By focusing on the most significant components, PCA makes it easier to interpret and visualize data.

Below are some key applications of PCA in machine learning:

1. Dimensionality Reduction for Improved Model Performance

One of the most common uses of PCA in machine learning is to reduce the number of features in a dataset without sacrificing much information. By eliminating less important features, models become faster to train and require less memory. This is especially important when working with high-dimensional datasets like image or text data.

Example: In image classification, each image might have thousands of pixels (features), but not all of them are necessary to recognize the object in the image. PCA can reduce these features to a smaller set of principal components, making the classification task more efficient while retaining key details of the image.

2. Noise Reduction and Data Cleaning

PCA helps filter out noise in data by focusing on the principal components that explain the most variance. This helps eliminate less important features (or noise) that might negatively impact machine learning algorithms, making the data cleaner and more reliable.

Example: In a dataset with sensor readings, PCA can help reduce noise from less informative features, allowing a predictive model to focus on the most relevant patterns, which leads to improved accuracy.

3. Feature Extraction in Unsupervised Learning

PCA is widely used in unsupervised learning tasks to identify patterns and structure in data. By reducing dimensionality, PCA helps uncover hidden patterns or clusters in the data, which can be useful for tasks like clustering and anomaly detection.

Example: In customer segmentation, PCA can reduce the dimensionality of customer data (e.g., age, income, purchase history) to a smaller set of features that still capture key differences, enabling more effective clustering and marketing strategies.

Also Read: Top 6 Techniques Used in Feature Engineering [Machine Learning]

4. Data Visualization

PCA makes it easier to visualize high-dimensional data by reducing it to 2 or 3 dimensions. This enables data scientists to explore and understand complex datasets through 2D or 3D plots, which would be otherwise difficult to interpret in higher dimensions.

Example: In a dataset with many features (e.g., gene expression data with thousands of genes), PCA can reduce it to two or three principal components, allowing for easy visualization of patterns, clusters, or outliers in the data.

5. Preprocessing for Machine Learning Models

PCA is often used as a preprocessing step before applying machine learning algorithms, especially for algorithms that are sensitive to the number of features, such as linear regression or support vector machines (SVM). By reducing the dimensionality, PCA can improve the performance and reduce overfitting of the model.

Example: When using SVM for text classification, applying PCA to reduce the number of features (such as terms in a document) can lead to better generalization and faster model training.

Also Read: Data Preprocessing in Machine Learning: A Practical Guide

6. Face Recognition

PCA is frequently used in face recognition tasks, where it helps reduce the high-dimensional feature set of facial images to a smaller number of principal components. These components capture the most important variations in faces, making the recognition process more efficient.

Example: In facial recognition systems like those used for security or authentication, PCA is applied to image datasets to extract features such as the shape and position of facial features. The reduced dataset is then used to train a recognition algorithm.

7. Improving Algorithm Efficiency in Large Datasets

PCA can improve the efficiency of machine learning algorithms when working with large-scale datasets. Reducing the dimensionality speeds up training times, decreases computational costs, and makes algorithms more scalable, especially in big data scenarios.

Example: In natural language processing (NLP), text data is often represented as a bag of words, resulting in a large number of features. PCA can reduce the dimensionality of this text data, enabling faster processing and more efficient training of machine learning models.

Its ability to reduce dimensionality, clean data, and improve model efficiency makes it a powerful tool for various applications in machine learning.

Also Read: Learn Feature Engineering for Machine Learning

Next, let’s look at how upGrad can help you learn PCA in machine learning.

How Can upGrad Can Help You Learn PCA in Machine Learning?

Learning PCA in machine learning is crucial in today’s data-driven world, as it simplifies complex datasets and improves model efficiency in fields like machine learning, AI, and data science. PCA is highly relevant for roles such as data scientist or machine learning engineer, where handling high-dimensional data is key.

upGrad’s machine learning courses provide hands-on experience with PCA through expert-led sessions, real-world projects, and practical coding exercises. This approach ensures you gain a strong, actionable understanding of PCA, enhancing your career prospects.

In addition to the programs covered above, here are some additional courses that can complement your learning journey:

• Hypothesis Testing
• Unsupervised Learning: Clustering
• Logistic Regression for Beginners
• Linear Regression - Step by Step Guide
• Introduction to Natural Language Processing

If you're unsure where to begin or which area to focus on, upGrad’s expert career counselors can guide you based on your goals. You can also visit a nearby upGrad offline center to explore course options, get hands-on experience, and speak directly with mentors! 

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Reference:
https://www.baeldung.com/cs/pca