Automated decision tree classification of corneal shape

Abstract

Purpose: The volume and complexity of data produced during videokeratography examinations present a challenge of interpretation. As a consequence, results are often analyzed qualitatively by subjective pattern recognition or reduced to comparisons of summary indices. We describe the application of decision tree induction, an automated machine learning classification method, to discriminate between normal and keratoconic corneal shapes in an objective and quantitative way. We then compared this method with other known classification methods.

Methods: The corneal surface was modeled with a seventh-order Zernike polynomial for 132 normal eyes of 92 subjects and 112 eyes of 71 subjects diagnosed with keratoconus. A decision tree classifier was induced using the C4.5 algorithm, and its classification performance was compared with the modified Rabinowitz-McDonnell index, Schwiegerling's Z3 index (Z3), Keratoconus Prediction Index (KPI), KISA%, and Cone Location and Magnitude Index using recommended classification thresholds for each method. We also evaluated the area under the receiver operator characteristic (ROC) curve for each classification method.

Results: Our decision tree classifier performed equal to or better than the other classifiers tested: accuracy was 92% and the area under the ROC curve was 0.97. Our decision tree classifier reduced the information needed to distinguish between normal and keratoconus eyes using four of 36 Zernike polynomial coefficients. The four surface features selected as classification attributes by the decision tree method were inferior elevation, greater sagittal depth, oblique toricity, and trefoil.

Conclusion: Automated decision tree classification of corneal shape through Zernike polynomials is an accurate quantitative method of classification that is interpretable and can be generated from any instrument platform capable of raw elevation data output. This method of pattern classification is extendable to other classification problems.

Figure 1

Decision Tree Classification of Keratoconus. Decision Tree generated with C4.5, an automated induction algorithm. Classification attributes (circles) are labeled as double indexed Zernike polynomial coefficients using Optical Society of America conventions. The split criteria values label the branches of the decision tree in units of micrometers. Terminal nodes of the tree (boxes) are labeled with class assignments (Y = Keratoconus, N = Normal) and the number of records assigned to this class (correct / incorrect); total n = 244; Keratoconus n= 112; Normal = 132.

Figure 2

Individual geometric modes of a 4^th order Zernike polynomial expansion. Color is used to indicate modes selected as classification attributes by the automated decision tree. Polynomial coefficients are labeled using double index notation according to Optical Society of America standards; polynomial order (n) is indicated on the vertical axis, azimuthal component (± m) is indicated by the horizontal axis.

Figure 3

ROC Analysis. ROC curves and associated area under curve (see legend) for each of the 6 classification methods: C4.5 = Decision tree classifier; CLMI = Cone Location and Magnitude Index; RM = Modified Rabinowitz–McDonnell Index; KPI = Keratoconus Prediction Index; Z3 = 3^rd order Zernike Polynomial Index; KISA% = K-value, IS-value, and Astigmatism Index.

Figure 4

Decision Surface. Three-dimensional, right-eye representation of corneal surface features at the boundary between eyes with keratoconus and normal eyes. This surface was constructed from the Zernike polynomial coefficients (3.5 mm radius fit) and their associated values derived from the C4.5 decision tree; total n = 244; Keratoconus n = 112; Normal = 13