In the ever-evolving field of biomechanics, researchers are continually exploring innovative methodologies to analyze and interpret data more effectively. Principal Component Analysis (PCA) stands out as a promising technique for its potential to identify variations within data, guiding researchers to new conclusions. However, the challenge lies in accurately describing what these variations signify, a crucial step in leveraging PCA to its fullest potential.
Principal Component Analysis
PCA is a method of waveform analysis that reduces raw data into principal components. PCA extracts these components based on their ability to explain variation within the data. Principal components (PCs) are abstract mathematical constructions, and are a bit difficult to interpret biomechanically. PCA extracts independent variables as “features” from the underlying data, sorting them into a new arrangement of independent variables based on how important they are to retaining information about the dataset. This means that the first feature in the new arrangement will retain the most information of all of the features, and will have the most variation. We can use this new arrangement to reduce the data because we only really need to look at a few features to retain almost all of the information about the variability in the dataset.
For example, this image shows that only 4 PCs explain 99% of the variation in a sample dataset. And we can see, as mentioned above, the first feature (or PC) explains the highest percentage of the variation. But what does a PC really mean? What do these features represent and how else can we interpret them? This isn’t as straightforward as comparing explicit metrics like peak joint angles, since the interpretation is more obvious when “Group A has a greater peak joint angle than Group B”.
PCA in Biomechanics
PCA was first used in biomechanics by Dr. Kevin Deluzio in 1995. Since then he has used PCA to analyze kinetic and kinematic gait waveform measures, and distinguish gait patterns in patients with knee osteoarthritis. (You can find more work by Dr. Kevin Deluzio here). You can perform PCA analysis using Sift and we have a tutorial walking through PCA comparing joint angles of participants with and without osteoarthritis. These examples show how PCA can separate and distinguish groups very quickly and effectively, but there is a trade-off between the challenge of actually interpreting the PCs and the power to separate groups.
This example demonstrates how PCA categorizes patient gait patterns by comparing two groups, but it is just one way to utilize waveform variability. PCA quantifies the variability between groups while considering the entire waveform of the underlying data, rather than comparing individual metrics that summarize the wave (such as the mean or peak).
This example is a straightforward application of PCA in biomechanics research, but how to interpret the results may not be as intuitive. We recognize that this example found variation between patients with osteoarthritis and control patients, but what does each component truly represent from the underlying data, and how do we know exactly where the differences lie in their gait? In the video example, we walked through the various ways to visualize and interpret the PCs using Sift (such as comparing mean PC scores, group scores, and loading vectors), however, the ability to interpret the PC variability may be different using other datasets.
Outro
Reducing high-dimensional signals into single components that explain variation in the data set is exciting. However, translating PC scores into biomechanically meaningful results can be tricky. We provide researchers the tools to explore various comparisons and visualizations of PCA results in Sift, but we wonder if this powerful tool will be used to its full potential if interpretation isn’t clear. We are looking forward to seeing how this tool is used by the community, and if you have used PCA we would love to hear about it.
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