As machine learning continues to evolve, feature engineering remains a crucial aspect of building effective models. One area that has fascinated me lately is the application of approximation theory in ML feature engineering, particularly the use of polynomial bases as features. In this post, I’ll share my learnings on orthogonal bases as informative feature generators, and how they can help align non-linear features with your data distribution.
The Problem with Non-Linear Features
Machine learning models rely heavily on the quality of the input features. However, when dealing with non-linear features, traditional methods often fall short. This is where orthogonal bases come in – a powerful tool for generating informative features that can capture complex relationships in the data.
What are Orthogonal Bases?
In essence, orthogonal bases are a set of functions that are perpendicular to each other. This property allows them to capture unique aspects of the data, making them ideal for feature generation. By using orthogonal bases, we can create a new set of features that are more informative and better aligned with the data distribution.
Benefits of Orthogonal Bases
- Improved model performance: By capturing non-linear relationships, orthogonal bases can lead to better model performance and accuracy.
- Reduced dimensionality: Orthogonal bases can help reduce the dimensionality of the feature space, making it easier to visualize and analyze.
- Enhanced interpretability: The orthogonal nature of these bases makes it easier to understand the relationships between the features and the target variable.
Real-World Applications
The applications of orthogonal bases are vast, from image compression to text analysis. By aligning non-linear features with the data distribution, we can unlock new insights and improve model performance in a wide range of domains.
Further Reading
If you’re interested in learning more about orthogonal bases and their application in machine learning, I’ve written a detailed blog post on the topic: https://alexshtf.github.io/2025/08/19/Orthogonality.html
I hope you find this topic as fascinating as I do, and I look forward to hearing your thoughts and feedback!