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sift:tutorials:perform_principal_component_analysis [2024/07/17 15:44] – created sgrangersift:tutorials:perform_principal_component_analysis [2024/11/28 19:15] (current) – [Perform Principal Component Analysis] wikisysop
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 This tutorial will show you how to use Sift in order to perform [[Sift:Principal_Component_Analysis:Principal_Component_Analysis|Principal Component Analysis]] (PCA) using data from a [[Visual3D:Documentation:Definitions:CMO_Library_|CMO library]]. For a full treatment of waveform-based PCA to find differences in waveform data, see the explanation presented in [[https://us.humankinetics.com/products/research-methods-in-biomechanics-2nd-edition|the Research Methods in Biomechanics textbook]]. This tutorial will show you how to use Sift in order to perform [[Sift:Principal_Component_Analysis:Principal_Component_Analysis|Principal Component Analysis]] (PCA) using data from a [[Visual3D:Documentation:Definitions:CMO_Library_|CMO library]]. For a full treatment of waveform-based PCA to find differences in waveform data, see the explanation presented in [[https://us.humankinetics.com/products/research-methods-in-biomechanics-2nd-edition|the Research Methods in Biomechanics textbook]].
  
-For this tutorial, we will be comparing the the knee flexion angles between participants with osteoarthritis and the normal control group. Our problem is to provide an explanation for differences in knee flexion angles between osteoarthritic walking versus normal walking. We can accomplish this by defining two groups that meet these signal definitions, performing PCA, and interpreting the results.+For this tutorial, we will be comparing the knee flexion angles between participants with osteoarthritis and the normal control group. Our problem is to provide an explanation for differences in knee flexion angles between osteoarthritic walking versus normal walking. We can accomplish this by defining two groups that meet these signal definitions, performing PCA, and interpreting the results.
  
 +If you prefer, a video tutorial is available outlining the same process. It is available at this link: [[https://youtu.be/6lMsQpSx9BI?feature=shared|Sift Tutorial Video 3: Performing Principal Component Analysis (PCA)]]
 ==== Data ==== ==== Data ====
  
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 As with previous tutorials, we begin by loading the CMZ library and defining the queries relevant to our question. As with previous tutorials, we begin by loading the CMZ library and defining the queries relevant to our question.
  
-1. Click {{:sift_library_load.png}} **Load Library** in the [[Sift:Application:Toolbar|toolbar]] to open the Load Library dialog. +  - Click {{:sift_library_load.png?20}} **Load Library** in the [[Sift:Application:Toolbar|toolbar]] to open the Load Library dialog. 
- +  - Click {{:sift_browser.png?20}} **Browse** and select the folder where the data is stored. 
-2. Click {{:sift_browser.png}} **Browse** and select the folder where the data is stored. +  - Click {{:sift_apply.png?20}} **Load** button to import the data.
- +
-3. Click {{:sift_apply.png}} **Load** button to import the data.+
  
 ==== Define queries and calculate groups ==== ==== Define queries and calculate groups ====
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 For this tutorial we will manually create two groups based on tags, one for subjects with osteoarthritis and one for normal control subjects. We begin by defining a query for subjects with the OA tag (indicating osteoarthritis). For this tutorial we will manually create two groups based on tags, one for subjects with osteoarthritis and one for normal control subjects. We begin by defining a query for subjects with the OA tag (indicating osteoarthritis).
  
-1. Click on the {{:sift_query_builder.png}} **Query Builder** icon on the [[Sift:Application:Toolbar|toolbar]], or on the left panel of the [[Sift:Application:Explore_Page|Explore Page]], to open the Query Builder dialog. +  - Click on the {{:sift_query_builder.png?20}} **Query Builder** icon on the [[Sift:Application:Toolbar|toolbar]], or on the left panel of the [[Sift:Application:Explore_Page|Explore Page]], to open the Query Builder dialog. 
- +  - {{:sift_action_add.png?20}} Add a query, name it OA, and click **Save**. 
-2. {{:sift_action_add.png}} Add a query, name it OA, and click **Save**. +  - {{:sift_action_add.png?20}} Add a condition and name it OA. 
- +    - **Signals**: Set TYPE - DERIVED, FOLDER - PCA, NAME - RKNEE_ANGLE, COMPONENT - X. This is the only signal in the data set. 
-3. {{:sift_action_add.png}} Add a condition and name it OA. +    - **Events**: There are no events in this data set, so this tab can be skipped. 
- +    - **Refinements**: Check the **Refine using tag** checkbox and select the OA tag. 
-3.1. **Signals**: Set TYPE - DERIVED, FOLDER - PCA, NAME - RKNEE_ANGLE, COMPONENT - X. This is the only signal in the data set. +    - Click **Save**
- +
-3.2. **Events**: There are no events in this data set, so this tab can be skipped. +
- +
-3.3. **Refinements**: Check the **Refine using tag** checkbox and select the OA tag. +
- +
-3.4. Click **Save**+
  
 Next we will define a query for subjects with the NC tag (indicating Normal Control). In this case we can easily modify our previous query rather than starting from scratch. Next we will define a query for subjects with the NC tag (indicating Normal Control). In this case we can easily modify our previous query rather than starting from scratch.
  
-1. {{:sift_action_add.png}} Add a query, name it NC, and click **Save**. +  - {{:sift_action_add.png?20}} Add a query, name it NC, and click **Save**. 
- +  - {{:sift_action_add.png?20}} Add a condition and name it NC. 
-2. {{:sift_action_add.png}} Add a condition and name it NC. +  - In the **Refinements** tab, change the selected tag from OA to NC. 
- +  - Click **Save**.
-3. In the **Refinements** tab, change the selected tag from OA to NC. +
- +
-4. Click **Save**.+
  
 You can verify here that the new NC group has the same signal and event selections as the OA group. Click **Calculate All Queries** and then close the Query Builder dialog. You can verify here that the new NC group has the same signal and event selections as the OA group. Click **Calculate All Queries** and then close the Query Builder dialog.
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 There will now be two Groups in the [[Sift:Application:Explore_Page|Explore Page]] subwindow's **Groups** list. Selecting either of these will display the associated workspaces in the **Workspaces** list below. We can verify the queries that we produced in the first section by visualizing our traces. There will now be two Groups in the [[Sift:Application:Explore_Page|Explore Page]] subwindow's **Groups** list. Selecting either of these will display the associated workspaces in the **Workspaces** list below. We can verify the queries that we produced in the first section by visualizing our traces.
  
-1. Set the plot type to Signal-Time.+  - Set the plot type to Signal-Time. 
 +  - Select all groups and all workspaces. 
 +  - Check only the **Plot Workspace Mean** checkbox. 
 +  - Click **Refresh Plot**.
  
-2. Select all groups and all workspaces.+The plot that is produced will not be very informative if the traces are not coloured by group, which is the comparison we are interested in. If this is the case, open the {{:sift_data_options.png?20}} **Show Data Options** dialog from the application tool bar and in the top right of the dialog under **Display Styles from...** select "Group".
  
-3. Check only the **Plot Workspace Mean** checkbox. +{{:RunPCA1.png?800}}
- +
-4. Click **Refresh Plot**. +
- +
-The plot that is produced will not be very informative if the traces are not coloured by group, which is the comparison we are interested in. If this is the case, open the {{:sift_data_options.png}} **Show Data Options** dialog from the application tool bar and in the top right of the dialog under **Display Styles from...** select "Group". +
- +
-{{:RunPCA1.png}}+
  
 Once this is done, inspecting the plot shows that although participants from the two groups walk very differently, obvious when watching them in-person, their knee flexion angles are quite similar. Because the traces overlap significantly between the groups throughout the entire gait cycle, conventional statistics will likely not be useful for describing the differences between these two groups. Once this is done, inspecting the plot shows that although participants from the two groups walk very differently, obvious when watching them in-person, their knee flexion angles are quite similar. Because the traces overlap significantly between the groups throughout the entire gait cycle, conventional statistics will likely not be useful for describing the differences between these two groups.
  
-{{:RunPCA2.png}}+{{:RunPCA2.png?800}}
  
 This is one of the motivations behind PCA: by transforming our original data into a coordinate system based on principal components we will end up with a few dimensions that explain most of the variance in the data set. This, in turn, will help us to explain and detect the differences between the groups. This is one of the motivations behind PCA: by transforming our original data into a coordinate system based on principal components we will end up with a few dimensions that explain most of the variance in the data set. This, in turn, will help us to explain and detect the differences between the groups.
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 ==== Running Principal Component Analysis ==== ==== Running Principal Component Analysis ====
  
-1. Ensure that all groups and workspaces are selected in the **Groups** and **Workspaces** lists. +  - Ensure that all groups and workspaces are selected in the **Groups** and **Workspaces** lists. 
- +  - Select the {{:sift_run_pca.png?20}} icon on the [[Sift:Application:Toolbar|toolbar]]. This will bring you to the analysis page and prompt the PCA settings dialog. 
-2. Select the {{:sift_run_pca.png}} icon on the [[Sift:Application:Toolbar|toolbar]]. This will bring you to the analysis page and prompt the PCA settings dialog. +  - Set the name for this PCA. 
- +  - Set **Number PCs** to 4. 
-3. Set the name for this PCA. +  - Ensure that **Use Workspace Mean** is checked. 
- +  - Click **Run PCA**. 
-4. Set **Number PCs** to 4. +  - The results of these calculations will automatically populate the PCA graphs on the [[Sift:Application:Analyse_Page|Analyse Page]]
- +
-5. Ensure that **Use Workspace Mean** is checked. +
- +
-6. Click **Run PCA**. +
- +
-7. The results of these calculations will automatically populate the PCA graphs on the [[Sift:Application:Analyse_Page|Analyse Page]]+
  
  
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 === Variance Explained === === Variance Explained ===
  
-The Variance Explained window, which displays the variance explained by each principal component as well as the cumulative variance for each principal components. It is important to verify that the calculated principal components do explain a significant amount of the data set's variability. A good heuristic to use is that you want enough principal components to explain 95% of the data set's variety, otherwise there will be at least a moderate amount of variation that your analysis has not captured. In this example, our 4 principal components explain 96% of the data set's variability, which is sufficient and we can continue the exploration. If there less than 95% of the data set's variance was explained then we should re-run the analysis with more principal components.+The Variance Explained window, which displays the variance explained by each principal component as well as the cumulative variance for each principal components. It is important to verify that the calculated principal components do explain a significant amount of the data set's variability. A good heuristic to use is that you want enough principal components to explain 95% of the data set's variety, otherwise there will be at least a moderate amount of variation that your analysis has not captured. In this example, our 4 principal components explain 96% of the data set's variability, which is sufficient and we can continue the exploration. If less than 95% of the data set's variance was explained then we should re-run the analysis with more principal components.
  
-{{:Sift_pca_tut_Results1.png}}+{{:Sift_pca_tut_Results1.png?800}}
  
 Clicking on a bar will display the exact variance explained by that principal component. In this example, the second principal component explains 17.6% of the variation in the original data set. Clicking on a bar will display the exact variance explained by that principal component. In this example, the second principal component explains 17.6% of the variation in the original data set.
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 Next, the Group Scores window helps us to determine if there is a significant differences between the groups for any individual principal component. This is established by looking at each principal component's mean score and their standard errors, where if the mean scores for a principal component +/- their standard errors do not cross the x-axis then there are significant differences in the scores for this principal component. In this tutorial principal components 1 and 2 show significant differences for the groups and will therefore be the focus of the remaining investigation. Next, the Group Scores window helps us to determine if there is a significant differences between the groups for any individual principal component. This is established by looking at each principal component's mean score and their standard errors, where if the mean scores for a principal component +/- their standard errors do not cross the x-axis then there are significant differences in the scores for this principal component. In this tutorial principal components 1 and 2 show significant differences for the groups and will therefore be the focus of the remaining investigation.
  
-{{:Sift_pca_tut_GS.png}}+{{:Sift_pca_tut_GS.png?800}}
  
 As with the Variance Explained window, hovering over a point will display a tooltip with precise values for that group score. As with the Variance Explained window, hovering over a point will display a tooltip with precise values for that group score.
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 Having identified our principal components of interest, switch to the Workspace Scores window and plot the chosen principal components against one another (i.e., for this tutorial, plot PC1 versus PC2). We are looking to be able to distinguish our groups and in this case there is a pretty clear separation between the groups in this 2D space. Although PC1 may describe more of the data set's variability than PC2, PC2 can discriminate between the groups better (this isn't mathematically shown here, but can be seen if the visual inspection is followed by a cluster analysis). Of course, PC1 and PC2 can discriminate between the groups even better if they are used together instead of separately. Having identified our principal components of interest, switch to the Workspace Scores window and plot the chosen principal components against one another (i.e., for this tutorial, plot PC1 versus PC2). We are looking to be able to distinguish our groups and in this case there is a pretty clear separation between the groups in this 2D space. Although PC1 may describe more of the data set's variability than PC2, PC2 can discriminate between the groups better (this isn't mathematically shown here, but can be seen if the visual inspection is followed by a cluster analysis). Of course, PC1 and PC2 can discriminate between the groups even better if they are used together instead of separately.
  
-{{:Sift_pca_tut_WS.png}}+{{:Sift_pca_tut_WS.png?800}}
  
 If you want to investigate the original data for a particular workspace, click on the workspace's scatter point and the corresponding data will be highlighted in the original Queried Data plot on the [[Sift:Application:Explore_Page|Explore Page]]. Similarly, if you click on a trace in the original Queried Data plot then the corresponding workspace is highlighted in the Workspace Score widget. This can be useful to identify outliers. If you want to investigate the original data for a particular workspace, click on the workspace's scatter point and the corresponding data will be highlighted in the original Queried Data plot on the [[Sift:Application:Explore_Page|Explore Page]]. Similarly, if you click on a trace in the original Queried Data plot then the corresponding workspace is highlighted in the Workspace Score widget. This can be useful to identify outliers.
  
-{{:Sift_pca_tut_WS2.png}} {{:Sift_pca_tut_WS3.png}}+{{:Sift_pca_tut_WS3.png?700 }} {{ :Sift_pca_tut_WS2.png?700}}
  
  
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 For the **Plot Type** drop-down menu, select the Mean and Slider option. Leave the **PC Number** set to 1 and then click **Play**. The mean reconstruction (gray in the figure below) will remain static while the other reconstruction (blue in the figure below) will vary in the range Mean +/- 2 Standard Deviations. Watching this animation demonstrates that PC1 is capturing variability as an offset in the signal. Vertical offsets in gait data can occur for a variety of reasons, including differences in standing calibration posture. Therefore, PC1 may explain a significant amount of variability that is not very helpful for answering our question. For the **Plot Type** drop-down menu, select the Mean and Slider option. Leave the **PC Number** set to 1 and then click **Play**. The mean reconstruction (gray in the figure below) will remain static while the other reconstruction (blue in the figure below) will vary in the range Mean +/- 2 Standard Deviations. Watching this animation demonstrates that PC1 is capturing variability as an offset in the signal. Vertical offsets in gait data can occur for a variety of reasons, including differences in standing calibration posture. Therefore, PC1 may explain a significant amount of variability that is not very helpful for answering our question.
  
-{{:Sift_pca_tut_Slider.png}}+{{:Sift_pca_tut_Slider.png?800}}
  
 Now select **PC Number** 2 and click **Play** again. This PC shows a different story, with the largest differences in this animation occurring during late stance and mid-swing. Now select **PC Number** 2 and click **Play** again. This PC shows a different story, with the largest differences in this animation occurring during late stance and mid-swing.
sift/tutorials/perform_principal_component_analysis.1721231097.txt.gz · Last modified: 2024/07/17 15:44 by sgranger