====== Using Principal Component Analysis in Biomechanics ======

{{:SIFT_PCA_Example.png}}

Sift provides a number of ways to visualize and interact with the results of PCA. An overview of all PCA visualizations can be found in [[Sift:Application:Analyse_Page#Principal_Component_Analysis|Sift - Analyse Page]]. More detail on the mathematics behind PCA can be found on our page: [[Sift:Principal_Component_Analysis:The_Math_of_Principal_Component_Analysis_(PCA)|The Math of Principal Component Analysis (PCA)]].

This page includes:

  * Visualizing the [[Sift:Application:Analyse_Page#Variance_Explained|variance explained by each PC individually]];
  * Visualizing the [[Sift:Application:Analyse_Page#Loading_Vector|variance explained by each PC at each point in the signal's cycle]];
  * [[Sift:Application:Analyse_Page#Workspace_Scores|Scatter-plotting workspace scores]] in PC-space;
  * Showing the [[Sift:Application:Analyse_Page#Group_Scores|distribution of scores by group]] for each PC;
  * Visualizing the [[Sift:Application:Analyse_Page#Extreme_Plot|mean and extreme values]] that result from reconstructing the underlying data with each PC; and
  * Visualizing how the signals can be [[Sift:Application:Analyse_Page#PC_Reconstruction|reconstructed from the computed PCs]].

==== Further Analysis ====

Sift has several built in modules to take you further with you PCA Analysis, including:

  * [[Sift:Principal_Component_Analysis:T-Squared_and_Q-Test_Dialog|T-Squared Tests:]] Finding outliers using a Multi Variate T-Squared Distribution.
  * [[Sift:Principal_Component_Analysis:T-Squared_and_Q-Test_Dialog|Q-Tests:]] Finding Outliers on small datasets using a Q-Test.
  * [[Sift:Principal_Component_Analysis:Mahalanobis_Distance_and_SPE_Dialog|Mahalanobis Distances:]] Finding outliers through their Mahalanobis Distances.
  * [[Sift:Principal_Component_Analysis:Local_Outlier_Factor_Dialog|Local Outlier Factors:]] Finding outliers through the Local Outlier Factor.
  * [[Sift:Principal_Component_Analysis:K-Means_Dialog|K-Means Analysis:]] Clustering PCA results through K-Means clustering.

==== Tutorials ====

For a step-by-step example of how to use Sift to perform PCA on your data, see the [[Sift:Tutorials:Perform_Principal_Component_Analysis|PCA Tutorial]].

For a step-by-step example of how to use Sift to perform further statistical testing on PCA results, see the [[Sift:Tutorials:Run_K-Means|Tutorial: Run K-Means]].

For a step-by-step example of processing and analyzing large data sets in Sift and using PCA to distinguish between groups, see the [[Sift:Tutorials:Treadmill_Walking_in_Healthy_Individuals|Tutorial: Treadmill Walking In Healthy Individuals]] and the [[Sift:Tutorials:OpenBiomechanics_Project:Analysis_of_Baseball_Hitters_at_Different_Levels_of_Competition|Tutorial: Analysis of Baseball Hitters]].