Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes
In this article, multilevel principal components analysis (mPCA) is used to treat dynamical changes in shape. Results of standard (single-level) PCA are also presented here as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contain...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Journal of Imaging |
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| Online Access: | https://www.mdpi.com/2313-433X/9/4/86 |
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| author | Damian J. J. Farnell Peter Claes |
| author_facet | Damian J. J. Farnell Peter Claes |
| author_sort | Damian J. J. Farnell |
| collection | DOAJ |
| description | In this article, multilevel principal components analysis (mPCA) is used to treat dynamical changes in shape. Results of standard (single-level) PCA are also presented here as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contain two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that (broadly) represent an eye; these data also have two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed by an application of mPCA and single-level PCA to “real” data consisting of twelve 3D landmarks outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the “blinking” and “surprised” trajectories for the MC “eye” data. Results for the “smile” data show that the smile trajectory is modelled correctly; that is, the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mPCA model shows only subtle and minor changes in mouth shape due to sex; whereas the first mode of variation at level 2 of the mPCA model governs whether the mouth is upturned or downturned. These results are all an excellent test of mPCA, showing that mPCA presents a viable method of modeling dynamical changes in shape. |
| first_indexed | 2024-03-11T04:53:29Z |
| format | Article |
| id | doaj.art-ee4e808039b348d6a9fa85c9b4fa6bc8 |
| institution | Directory Open Access Journal |
| issn | 2313-433X |
| language | English |
| last_indexed | 2024-03-11T04:53:29Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Imaging |
| spelling | doaj.art-ee4e808039b348d6a9fa85c9b4fa6bc82023-11-17T19:53:48ZengMDPI AGJournal of Imaging2313-433X2023-04-01948610.3390/jimaging9040086Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape ChangesDamian J. J. Farnell0Peter Claes1School of Dentistry, Cardiff University, Cardiff CF14 4XZ, UKMedical Imaging Research Center, UZ Leuven, 3000 Leuven, BelgiumIn this article, multilevel principal components analysis (mPCA) is used to treat dynamical changes in shape. Results of standard (single-level) PCA are also presented here as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contain two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that (broadly) represent an eye; these data also have two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed by an application of mPCA and single-level PCA to “real” data consisting of twelve 3D landmarks outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the “blinking” and “surprised” trajectories for the MC “eye” data. Results for the “smile” data show that the smile trajectory is modelled correctly; that is, the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mPCA model shows only subtle and minor changes in mouth shape due to sex; whereas the first mode of variation at level 2 of the mPCA model governs whether the mouth is upturned or downturned. These results are all an excellent test of mPCA, showing that mPCA presents a viable method of modeling dynamical changes in shape.https://www.mdpi.com/2313-433X/9/4/86multilevel principal components analysis (mPCA)dynamical shape changes |
| spellingShingle | Damian J. J. Farnell Peter Claes Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes Journal of Imaging multilevel principal components analysis (mPCA) dynamical shape changes |
| title | Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes |
| title_full | Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes |
| title_fullStr | Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes |
| title_full_unstemmed | Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes |
| title_short | Initial Steps towards a Multilevel Functional Principal Components Analysis Model of Dynamical Shape Changes |
| title_sort | initial steps towards a multilevel functional principal components analysis model of dynamical shape changes |
| topic | multilevel principal components analysis (mPCA) dynamical shape changes |
| url | https://www.mdpi.com/2313-433X/9/4/86 |
| work_keys_str_mv | AT damianjjfarnell initialstepstowardsamultilevelfunctionalprincipalcomponentsanalysismodelofdynamicalshapechanges AT peterclaes initialstepstowardsamultilevelfunctionalprincipalcomponentsanalysismodelofdynamicalshapechanges |