Why the Curse of Dimensionality Matters in Machine Learning: A Simple, Practical Explanation

Key takeaways

• The curse of dimensionality describes the challenges created when increasing dimensionality expands the volume of the data space and makes the data appear sparse.

• High-dimensional data can increase the number of samples needed to fit a model and contribute to problems such as overfitting and slower model training.

• You can reduce the impact of high dimensionality with dimensionality reduction techniques such as principal component analysis (PCA).

Explore how the curse of dimensionality affects machine learning and how dimensionality reduction can make complex data more usable.

If you’re ready to get your start in machine learning right away, enroll in the Machine Learning Specialization from Stanford and DeepLearning.AI. Beginner-friendly, this program will give you the opportunity to develop practical knowledge and skills for machine learning, such as supervised and unsupervised learning, model evaluation, machine learning algorithms, and more.

What is the curse of dimensionality?

The curse of dimensionality describes what happens when working with high-dimensional data for tasks such as analysis, classification, or organization. This phenomenon makes it challenging to find structures within variables because, as dimensionality increases, so does the volume of space representing the data, making the data appear sparse as it struggles to fill the empty space. A matrix is an example of a high-dimensional data space.

Mathematician Richard Bellman, who was responsible for developing dynamic programming in the 1950s, is the person behind the phrase curse of dimensionality, as he discovered how increasing numbers of dimensions created rapid growth in the surrounding space, which presents increasingly difficult challenges when solving problems.

Why is high-dimensional data difficult to work with?

High-dimensional data is difficult to work with because, as dimensionality increases, so does the required number of samples needed in order to fit the data to the model. Sparse data can lead to problems with overfitting, where the model can make accurate predictions with training data but can’t perform at the same level when working with new data. This is because sparsity caused by high-dimensional data makes it challenging for the model to identify relationships within the data. Although you can address sparsity issues by obtaining more data, increasing the number of dimensions in a model will directly result in an exponential increase in the number of data points needed, ultimately resulting in the need for dimensionality reduction techniques to make the data more usable.

What problems does the curse of dimensionality cause?

Problems introduced by the curse of dimensionality include slower model training and difficulties in developing visualizations for data exceeding three dimensions, which may require alternative visualization techniques. Additionally, the potential for overfitting training data increases as an effort to compensate for sparsity created by high-dimensionality.

How does the curse of dimensionality affect machine learning models?

The curse of dimensionality affects machine learning models, as high-dimensional data is especially challenging for them to learn from, making it difficult to make accurate predictions. However, dimensionality reduction techniques give you the ability to bypass problems associated with the curse of dimensionality when working with machine learning models. As a result, you can experience faster model training times, prevent overfitting, and reduce excess noise in your data, making interpretation easier. Dimensionality reduction is valuable for several artificial intelligence (AI) applications, including natural language processing and computer vision.

What is a real-world example of the curse of dimensionality?

To better understand the impact of the curse of dimensionality, consider computer vision, where images contain several features, or dimensions. For example, an image can consist of complex features such as shapes and textures, as well as simpler features like edges, corners, and colors. In order for a model to effectively process image data and address the curse of dimensionality, it needs to first go through a feature extraction process, where algorithms transform images into pixel data to isolate the most meaningful characteristics of the data. The extracted attributes can then serve as inputs for computer vision tasks such as object detection and image segmentation.

Key dimensionality reduction techniques

Dimensionality reduction techniques, such as linear discriminant analysis (LDA) and principal component analysis (PCA), give you the ability to represent data in fewer dimensions to make interpreting data simpler. These techniques make it possible for you to take high-dimensional data and transform it to a lower-dimensional space without losing the key features of the data.

How to deal with the curse of dimensionality and reduce its impact

Managing problems associated with the curse of dimensionality is possible through dimensionality reduction, where you can take high-dimensional, complex data and extract key features, leaving you with approximate representations of the data, focusing only on the most important information. You can break dimensionality reduction techniques down into two main categories, feature extraction and feature selection:

• Feature extraction: By identifying the most meaningful characteristics within a data set, you can transform it into a numerical representation of the data while preserving important information. PCA is an example of feature extraction and is the most popular choice for dimensionality reduction tasks. PCA works by taking correlated variables and transforming them into a set of uncorrelated variables (principal components). This removes the least important variables while transforming the data into a lower-dimensional space.

• Feature selection: Rather than transforming your original data set into a new lower-dimensional space, feature selection filters your data and retains key features, while still maintaining the same properties of the original data set. This is a less computationally intensive process that simply leaves you with a refined version of the information you started with.

Read more: Data Preprocessing Steps: How to Prepare Data for Machine Learning and Analytics

Explore our free machine learning resources

Subscribe to our weekly LinkedIn newsletter, Career Chat, for updates on popular skills, tools, and certifications. Then, check out some of our other free resources to keep learning more about machine learning:

• Gain expert insights: 6 Questions With a Google AI Research Director

• Watch on YouTube: Decision Tree Machine Learning Explained Simply

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

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.