Functional data geometric morphometrics with machine learning for craniodental shape classification in shrews

Abstract

This work proposes a functional data analysis approach for morphometrics in classifying three shrew species (S. murinus, C. monticola, and C. malayana) from Peninsular Malaysia. Functional data geometric morphometrics (FDGM) for 2D landmark data is introduced and its performance is compared with classical geometric morphometrics (GM). The FDGM approach converts 2D landmark data into continuous curves, which are then represented as linear combinations of basis functions. The landmark data was obtained from 89 crania of shrew specimens based on three craniodental views (dorsal, jaw, and lateral). Principal component analysis and linear discriminant analysis were applied to both GM and FDGM methods to classify the three shrew species. This study also compared four machine learning approaches (naïve Bayes, support vector machine, random forest, and generalised linear model) using predicted PC scores obtained from both methods (a combination of all three craniodental views and individual views). The analyses favoured FDGM and the dorsal view was the best view for distinguishing the three species.

Keywords: Functional data analysis; Geometric morphometrics; Landmarks; Linear discriminant analysis; Principal component analysis; Shrews.

Figure 1

Digital skull images of dorsal, jaw and ventral views of C. malayana, C. monticola, and S. murinus.

Figure 2

(a) 25 landmarks included for dorsal view of C. malayana. Landmarks and semilandmarks are represented by red and light blue dots, respectively (b) Dimension 1 of converted functional data of the landmark data for the dorsal view using the FDGM method (black lines represent specimens). (c) Dimension 2 of converted functional data of the landmark data for the dorsal view using the FDGM method (black lines represent specimens).

Figure 3

(a) 50 landmarks included for jaw view of C. malayana. Landmarks and semilandmarks are represented by red and light blue dots, respectively. (b) Dimension 1 of converted functional data of the landmark data for the jaw view using the FDGM method (black lines represent specimens) (c) Dimension 2 of converted functional data of the landmark data for the jaw view using the FDGM method (black lines represent specimens).

Figure 4

(a) 47 landmarks included for the lateral view of C. malayana. Landmarks and semilandmarks are represented by red and light blue dots, respectively. (b) 2D representation of the $x$ and $y-$ coordinates for the 47 landmarks of crania for the lateral view; (c) Dimension 1 of converted functional data of the landmark data for the lateral view using the FDGM method (black lines represent specimens). (d) Dimension 2 of converted functional data of the landmark data for the lateral view using the FDGM method (black lines represent specimens).

Figure 5

PCA plot using GM method and MFPCA plot using FDGM method for all combined craniodental views, dorsal view, jaw view, and lateral view.

Figure 6

LDA plot using GM method and FLDA plot using FDGM method for all combined craniodental views, dorsal view, jaw view, and lateral view.