F Approach Algorithm in Missing Landmark Problem

Abstract

Missing data may occur in every scientific studies. Statistical shape analysis involves methods that use geometric information obtained from objects. The most important input to the use of geometric information in statistical shape analysis is landmarks. Missing data in shape analysis occurs when there is a loss of information about landmark cartesian coordinates. The aim of the study is to propose F approach algorithm for estimating missing landmark coordinates and compare the performance of F approach with generally accepted missing data estimation methods, EM algorithm, PCA based methods such as Bayesian PCA, Nonlinear Estimation by Iterative Partial Least Squares PCA, Inverse non-linear PCA, Probabilistic PCA and regression imputation methods. Landmark counts were taken as 3, 6, 9 and sample sizes were taken as 5, 10, 30, 50, 100 in the simulation study. The data are generated based on multivariate normal distribution with positively defined variance-covariance matrices from isotropic models. In simulation study three different simulation scenarios and simulation based real data are considered with 1000 repetations. The best and the most different result in the performance evaluation according to all sample sizes is the Min (F) criteria of the F approach algorithm proposed in the study. In case of three landmarks which is only the proposed F approach and regression assignment method can be applied, Min (F) criteria give best results.