A sparse principal component analysis of Class III malocclusions

To identify the most characteristic variables out of a large number of anatomic landmark variables on three-dimensional computed tomography (CT) images. A modified principal component analysis (PCA) was used to identify which anatomic structures would demonstrate the major variabilities that would most characterize the patient.

Data were collected from 217 patients with severe skeletal Class III malocclusions who had undergone orthognathic surgery. The input variables were composed of a total of 740 variables consisting of three-dimensional Cartesian coordinates and their Euclidean distances of 104 soft tissue and 81 hard tissue landmarks identified on the CT images. A statistical method, a modified PCA based on the penalized matrix decomposition, was performed to extract the principal components.

The first 10 (8 soft tissue, 2 hard tissue) principal components from the 740 input variables explained 63% of the total variance. The most conspicuous principal components indicated that groups of soft tissue variables on the nose, lips, and eyes explained more variability than skeletal variables did. In other words, these soft tissue components were most representative of the differences among the Class III patients.

On three-dimensional images, soft tissues had more variability than the skeletal anatomic structures. In the assessment of three-dimensional facial variability, a limited number of anatomic landmarks being used today did not seem sufficient. Nevertheless, this modified PCA may be used to analyze orthodontic three-dimensional images in the future, but it may not fully express the variability of the patients.