MA679 Physical Therapy Project

Audio Recording Apr 16, 2022 at 6:54:22 PM. MA679 Physical Therapy Project.

[Audio] This week we started off by fitting a univariate FPCA model with BSpline basis for all the variables of interest. We decided to fit a model that would explain atleast 90% of the variance in the data and we chose the number of components accordingly. Here, the first plot shows the mean of all observations of V_GRF, the second plot shows the functional principal components, the third plot shows a scatter plot matrix with distributions of the observations for the FPCs. The table on the right shows the total variance explained and the loading on the different components.

[Audio] For ML_GRF we needed 3 components to explain more than 90% variance. We see that the observations look like they are normally distributed (or slightly skewed in some cases) for different FPCs..

[Audio] For all the variables FPCA results show that there is a heavy loading on the first component.

[Audio] For some variables we needed 2 components while for some we needed 3..

[Audio] For some of the variables we were able to get very high(almost 100%) Variance explanation with just 2 components..

[Audio] Later on we tried Multivariate FPCA. Multivariate Functional Data consists of simultaneous variations of more than one random function. Since the 3 elements of GRF or 2 elements of COP in our data are just simultaneous variations along different axes of the same measure, we would be able to apply statistical techniques designed for MFD. MFPCA directly addresses any potential covariation between V, ML or AP elements in our data and thus is able to address any multicollinearity issues that might arise later in prediction modeling phase. While building an MFPCA model we can choose what %of variance we need the model to explain for each of the elements in the MFD and the model appropriately chooses the number of components required. When we specified that at least 95% of the variance needed to be explained for each element of MFD, the model outputted 11 components. The grap here show how the 11 components vary for each of the elements in GRF.

[Audio] THe above plot shows a scatterplot and distribution of observations for each of the PCs. We see that observations are normally distributed for most of the PCs..

[Audio] We then reconstructed our data using the MFPCs and we obtained plots very similar to our original plots..

[Audio] For COP, the model needed only 3 components to explain at least 95% of variance in both x and y elements..

[Audio] The distribution plots look slightly skewed..

[Audio] The reconstructed plots again resemble original plots..

[Audio] We want to understand MFPCA better and we are currently reading up on the behind it. We still need to figure a way to calculate total variance explained and component loading and then refine our models. Our ambitious target is to use AutoEncoders for dimension reduction and we will get started on this in the coming week!.