The ultimate guide to functional data analysis (FDA) for scientists and engineers
Data is often dynamic, varying over time or space, forming curves, trends or spectra with the potential to reveal important patterns and relationships. Functional data analysis (FDA), is a statistical approach designed to help you interpret and extract meaning from this type of data.
In this guide, I’ll explain what functional data analysis (FDA) is, when to use it, and how to apply it effectively. Along the way, you'll discover why FDA has become one of my favorite approaches for extracting meaning from data that change over time or space. Let’s start by answering a few basic questions:
What is functional data analysis?
Functional data analysis (FDA) is a modern branch of statistics for analyzing dynamic data that vary continuously. Instead of viewing data as isolated points, FDA models entire curves or functions to capture the underlying patterns. This approach is useful for such data as temperature profiles, growth and decay curves, and spectral measurements where the shape and structure of the data are key to understanding it.
From workarounds to real insight: Modeling the full shape of your data
Throughout my career, some of the most challenging and fascinating problems have involved data that change continuously: temperature profiles, absorbance spectra, stress-strain curves, and more. These types of data are prevalent across scientific and engineering disciplines, offering rich insights, but they can be tricky to analyze due to the highly correlated nature of the data.
Early on, I developed workarounds. I’d reduce the functional data into single summary points, like picking a specific wavelength from a spectrum or isolating the peak temperature from a thermal profile. But each time, I knew I was leaving useful information behind.
That’s why discovering functional data analysis was a turning point. FDA is designed specifically for this kind of continuous, highly correlated data. Instead of reducing the data, FDA helps you model the full shape capturing more detail, more signal, and ultimately, better insight.
Workarounds to try to make sense out of curves.
Why use functional data analysis?
As I mentioned above, functional data analysis is a powerful approach when the shape of your data – not just individual data points – holds valuable insights. Instead of reducing your data to a few summary measures, FDA lets you leverage the full richness of your data curves to gain deeper understanding and build stronger models. FDA does this by converting raw data into functions that capture the shape of the data. These shape functions can be utilized as inputs, responses, or both for your modeling purposes.
Use FDA when:
- You have dynamic data: The data is a series of continuously varying points.
- The overall shape of your data matters: Patterns, trends, and changes over time provide additional insights beyond the isolated points.
- You are using design of experiments (DOE): To achieve ideal curves, pinpointing the right factor settings is crucial.
- You'd like to reduce noise to understand trends: Smoothing noisy data into a continuous function can reveal underlying trends and reduce variability.
- You want to find anomalies: Analyze the full curve to identify unusual shapes or deviations from expected patterns.
Examples of curved data ideal for functional data analysis:
Sensor Data
Fermentation process
Spectral Data
NIR Spectroscopy
Time Series
Consumer Price Index
Key benefits of functional data analysis
Functional data analysis helps you uncover patterns, improve models, and better understand continuous, dynamic data.
Preserve the richness of your data
FDA lets you model the entire data shape using a function, preserving valuable detail and context that is lost with summarization.
Simplify high-dimensional data
FDA reduces dimensionality and preserves the structure, making complex data sets easier to explore and model.
Build stronger predictive models
Additional information gained from the shape of the functional data can be used to improve model accuracy, leading to better predictions and greater understanding.
Understand process dynamics
By allowing you to model data that changes continuously, FDA helps you detect trends, patterns, and anomalies for deeper insight into process behavior.
Reveal patterns and reduce noise
By smoothing data and using functional principal component analysis (FPCA) as a dimension-reduction technique, FDA highlights subtle trends, filters out noise, and makes important features easier to detect.
What are some examples of how functional data analysis is used?
Functional data analysis is useful across industries where it’s important to understand how the shape of dynamic data changes. From improving processes to spotting issues early, FDA helps uncover deeper insights. Here are a few examples:
Chemical
- Analyze reaction profiles (e.g., temperature or concentration over time) to optimize process conditions.
- Monitor batch-to-batch consistency using process curves such as pH, pressure, or flow rates.
- Compare sensor curves (e.g., spectroscopic data) for quality control and early fault detection.
Semiconductor wafer fabrication
- Study wafer thickness, etch depth, or temperature curves during fabrication to improve yield and reduce defects.
- Analyze tool performance over time from sensor data to schedule predictive maintenance.
- Use photolithography or plasma process curves to tune parameters and reduce variability.
Pharmaceuticals
- Monitor assay performance across batches or sites by analyzing potency and stability curves.
- Compare dissolution profiles of different drug formulations to ensure consistent drug release.
- Track patient biomarker trends over time to evaluate treatment effectiveness or drug safety.
Consumer goods
- Evaluate product stability (e.g., color, texture, pH) over shelf life by analyzing change curves.
- Study sensor or testing curves from packaging or material performance tests (e.g., compression, elasticity).
- Analyze consumer usage patterns from smart devices or testing panels over time.
Biotechnology
- Analyze growth curves of cell cultures or microbes for yield optimization.
- Study gene expression or protein concentration trends during fermentation or bioproduction.
- Use time-series biomarker data from experiments or clinical trials to understand biological responses.
Aerospace
- Analyze flight trajectories of aircraft to decrease fuel consumption and minimize noise pollution.
- Utilize aircraft engine sensor data to enhance prognostics and health management (PHM) capabilities.
- Improve detection and identification processes using radar, sonar, and lidar data.
- Reduce "tool wear" through study of part degradation curves.
Frequently asked questions about functional data analysis
How can I use functional data analysis to tackle specific scientific and engineering problems?
Functional data analysis offers flexible tools for tackling complex problems in science and engineering. Once your data is ready, you can use FDA to:
- Design experiments: Analyze how factors affect entire response curves or use functional inputs in your design.
- Build predictive models: Model relationships where inputs, outputs, or both are functions.
- Detect anomalies: Identify unusual or faulty curves by modeling normal behavior.