Principal Component Analysis (PCA): Definition, How It Works, and Why It Matters

Key takeaways

• Principal component analysis (PCA) is a method for reducing the complexity of data while maintaining key features, for easier processing and analysis.

• Principal component analysis, explained simply, involves preparing data for machine learning by reducing dimensionality to remove unnecessary or redundant features, making the data set easier to process.

• To interpret PCA results, review the plot’s arrow lengths and assess the extent of variation within your data set; good results balance the need to keep valuable features and the right amount to remove to reduce dimensionality.

If you’re ready to start developing machine learning skills, enroll in the Machine Learning Specialization from Stanford and DeepLearning.AI. This beginner-level program can help you gain valuable experience building machine learning models using unsupervised learning techniques and training a neural network.

When you should apply PCA may depend on your application, which could include transforming data for visualization or enhancing natural language processing.

What is principal component analysis?

Principal component analysis (PCA) is a dimensionality reduction technique that helps make the data set more user-friendly for further processing and analysis, while retaining key information.

Dimensionality reduction involves reducing and removing features (dimensions) from a complex data set. At the same time, the process preserves the most important characteristics of the data, such as structure and patterns. These features are important input variables that help predict the output in machine learning.

However, when the data set contains significantly more data points than features, it can compromise output accuracy and increase computational power and storage needs. PCA is among the oldest and most widely used methods for dimensionality reduction and is simpler than other techniques.

What is the difference between PCA and ANOVA?

PCA and analysis of variance (ANOVA) serve different purposes: PCA extracts the critical features from a data set to reduce dimensionality, while ANOVA refers to a statistical method you can use to analyze the variances of two or more data groups or classes to assess whether their means are the same. Put simply, PCA prepares datasets for analysis, while ANOVA is an actual analysis technique.

Why use PCA?

PCA is useful because it reduces unnecessary complexity within an otherwise large data set. Particlarly in these cases:

• Machine learning - this preprocessing step leads to high-performing models by effectively mitigating problems such as overfitting, in which the model performs well on the training data but struggles with new data it hasn’t seen before.

• Speeds up computation - PCA largely reduces the computational resource requirements during analysis, particularly from a time perspective, since data processing can occur much faster.

• Improves model visualization - an important consideration for real-time data applications, such as fraud detection in financial institutions, dynamic pricing for online retailers, and recommendation systems. Lowers storage requirements

When you should apply PCA may depend on your application, which could include transforming data for visualization or enhancing natural language processing.

How does principal component analysis work?

Principal component analysis works by transforming data into a coordinate system. The most significant variance in the data set corresponds to the first principal component, which is the first coordinate. This pattern repeats: the second coordinate represents the second-largest variance, followed by the next-largest, and so on. It results in linear representations of the original data, with eigenvectors and eigenvalues determining the significance and direction of the data.

This process generates new data consisting of valuable variables while removing less important ones. Ultimately, PCA creates an accurate representation of the original data set, but in a low-dimensional space.

How do you interpret PCA results?

To interpret the results of a PCA, take a look at both the direction and length of the plot arrows. The significant variables will have large loadings ( close to 1 or -1), indicating a strong correlation, either positive or negative, with the principal component. You can determine the amount of variation your original data set contains based on the number of principal components you have left following your PCA. Therefore, you can also use the information to assess the extent to which you were able to reduce the dimensions of your data set.

What is a good PCA result?

A good PCA yields an optimal balance between retaining valuable features in a data set and removing features to reduce dimensionality. Often, finding this balance takes trial and error as you assess model performance.

Another technique for identifying the right number of features to retain is a scree plot, which shows principal components and their corresponding eigenvalues and helps you spot where the slope changes and determine how many principal components to retain.

What are real-world applications of PCA?

The real-world applications of PCA span a wide range of industries and use cases in artificial intelligence and machine learning applications. Explore the following examples:

• Natural language processing: PCA is an effective method for reducing word dimensionality, helping models understand relationships within text. This is beneficial for tasks such as document classification, developing recommendation systems, and sentiment analysis. Law firms, for example, can implement natural language processing to sort through large amounts of documents and classify them by their type, whether that’s case filings, court rulings, contracts, or other forms of unstructured documents, making them more accessible.

• Data visualization: You can transform complex, high-dimensional data using PCA to produce 2D and 3D visualizations, enabling exploratory analysis and the extraction of meaningful insights. This makes PCA a valuable tool in chemometrics, where scientists can explore the chemical makeup of products, such as during the development of new engineering materials or when analyzing the toxicity of certain foods within the agricultural industry.

• Computer vision: PCA compresses complex images into versions that take up a lower-dimensional space, for easier computation and storage. Image compression is vital for the health care industry, for example, given medical imaging’s significant storage demands for uses such as MRIs and CT scans, as well as the need for high-quality transmission so doctors can accurately diagnose patients when analyzing images.

Read more: 10 Machine Learning Applications

Explore our free machine learning resources

Subscribe to our weekly LinkedIn newsletter, Career Chat, for updates on popular tools and certifications, and skill-building resources. Then check out some of our other free resources to keep learning.

• Take the quiz: Which Machine Learning Course Should You Take? Find Out in 1 Minute

• Watch on YouTube: Your Machine Learning Roadmap: What to Learn and When

• Gain expert insights: 6 Questions with an IBM Data Scientist and AI Engineer

Whether you want to develop a new skill, get comfortable with an in-demand technology, or advance your abilities, keep growing with a Coursera Plus subscription. You’ll get access to over 10,000 flexible courses.