Applying Principal Component Analysis on joint kinematics data

[Farzaneh Yazdani]

Dear Biomch-L Members,
I decide to apply principal component analysis (PCA) on a series of joint kinematics data (Joint kinematics’ time series are filtered and 100% time normalized). Data are obtained from two different groups of participants and 5 successful trials for each subject are included. The question is: in the process of PCA, should I estimate the ensemble average of 5 trials for each subject as PCA input or I can use the trials directly without averaging?
If yes, How can I implement ensemble averaging in MatLab?

Any help would be greatly appreciated! And thank you for your time.

Yours sincerely,

Farzaneh Yazdani
PhD Candidate, SUMS School of Rehabilitation Sciences

[Allan Carman]

Re: Applying Principal Component Analysis on joint kinematics data

Farzaneh,

When using the PCA method you are attempting to correct segment axes mis-alignment by finding the axes directions that minimize calculated knee Abd/Add joint rotations. Axes misalignment of proximal and/or distal segments produce non-linear errors in the three calculated joint rotations (only an error in the distal segment’s axial rotation can be corrected linearly by adding a correction to the calculated internal/external rotation of the joint). Therefore correction of axes mis-alignment and non-linear errors should be carried out on each trial before ensemble averaging. However, as the 5 trials are within the same session with same marker placement, they should have a common static offset in proximal and distal segment axes alignment as calculated from the static calibration procedure and a similar dynamic offset during the movement trial due to skin movement artifact. Therefore you could get away with ensemble averaging the five trials first (if joint angles of the five trials have similar patterns) and then using the PCA method to attempt to correct the mean curve of the 5 trials. Something to consider, the PCA method removes nearly all knee abd/add rotations during gait (Jensen et al., 2016) and does not distinguish stance from swing phase, so if these are health individuals consider analyzing normal gait first and minimizing the difference to expected normal knee abd/add rotations in gait to confirm segment axes alignment before analyzing the movement of interest.

Cheers
Allan Carman

[Allison Clouthier]

Re: Applying Principal Component Analysis on joint kinematics data

Hi Farzaneh,

What are you trying to do with PCA? Are you trying to identify differences in the kinematic waveforms between groups, something similar to Deluzio & Astephen 2007?

If so, then I would say you should only be including one trial per participant. Either by choosing one representative trial for each person, or by ensemble averaging the 5 trials. You should be able to directly average the trials in matlab if you have already time normalized them to have the same number of points.

Allison Clouthier

[Ross Miller]

Re: Applying Principal Component Analysis on joint kinematics data

Piggybacking on Allison's reply:

If you are using PCA to identify "waveform features" that explain variance in your data, including individual trials in the PCA input seems like it merges two sources of variance, variance between trials and between subjects. I'm not sure if there is a way of reconciling this in the output, so your results would be difficult to interpret. I'm not terribly experienced with PCA so maybe there is a way of doing this, but I do not know of one. If you include only ensemble averages or representative trials in the input (i.e. one curve for each subject) then you would only have one source of variance (between subjects) so your results would be much easier to interpret.

I would be interested in if you get the same results doing it either way. Again maybe someone has already done that. The variance between subjects is presumably much larger than the variance between trials so I would expect similar results.

Similarly, if you include data for both groups in the input, then your PCA would be explaining two merged sources of variance (between subjects and between groups). With individual trials you would have three sources of variance. A way around this is to define the PCA model on just one group (usually the "Control" group) then run that same model again on the "Patient" group. This is what Deluzio et al. (1997) did:

http://www.sciencedirect.com/science/article/pii/S0167945796000516

Conceptually I think it's best to set up the PCA so that there is only one source of variance between the input samples.

Hope this helps,
Ross

[Farzaneh Yazdani]

Re: Applying Principal Component Analysis on joint kinematics data

Dear All,
Thank you I really appreciate your guidance.


Best Regards

Farzaneh Yazdani
PhD Candidate, SUMS school of Rehabilitation Sciences