Principal Component Analysis (PCA) is a powerful dimensionality reduction technique commonly used in biomechanics research to identify patterns and sources of variation across large, high-dimensional datasets. Commonly time-series joint angle or force data collected across many subjects or trials.

Sift provides a number of ways to visualize and interact with the results of PCA. An overview of all PCA visualizations is available on the Sift - Analyse Page, and the underlying mathematics are described in detail on: The Math of Principal Component Analysis (PCA).

• Visualizing the variance explained by each PC individually;
• Visualizing the variance explained by each PC at each point in the signal's cycle;
• Scatter-plotting workspace scores in PC-space;
• Showing the distribution of scores by group for each PC;
• Visualizing the mean and extreme values that result from reconstructing the underlying data with each PC; and
• Visualizing how the signals can be reconstructed from the computed PCs.

Once PCA has been run in SIFT, several built-in modules support deeper investigation of results:

• Outlier Detection for PCA: An overview of the PCA outlier detection methods built into Sift.
• Mahalanobis Distances: Finding outliers through their Mahalanobis Distances.
• Squared Prediction Error: Finding outliers through their SPE.
• Local Outlier Factors: Finding outliers through the Local Outlier Factor.
• K-Means Analysis: Clustering PCA results through K-Means clustering.

Step-by-step tutorials are available for common PCA workflows in Sift:

• PCA Tutorial: Introduction to running PCA on biomechanical data
• Run K-Means: Clustering PCA results using K-Means
• PCA Outlier Analysis: Detecting and reviewing outliers in PCA results
• Treadmill Walking in Healthy Individuals: A full example processing a large dataset and using PCA to distinguish between groups
• Analysis of Baseball Hitters**: Applying PCA to compare athletes across different levels of competition