The ellipse is shaped by the covariance matrix and is independent from the balance scheme. The ellipse encloses only 15% of land points and completely miss the top island (Rocher-aux-oiseaux). Again, increasing the number of dimensions only makes the prediction worse.
Using machine learning
Machine learning is a concept comprising hundreds of computing techniques that aim to detect patterns in data sets. Because, with the island example, we aim at predicting territory categories (just like we would have done with yield categories), we are looking for a supervised classification algorithm.
The k-nearest neighbors (KNN) algorithm looks for the k nearest training samples surrounding an observation whose outcome is to be predicted, then outputs the most likely outcome according to the ones of these k nearest training samples. These values can be categories (most common category of the k nearest points) or continuous values (the mean of the outcome of the k nearest points). A KNN model based on an Euclidean distance matrix is appropriate for isometric log-ratios, which are orthonormal. However, other machine learning algorithms could be used \cite{tolosana-delgadoMachineLearningAlgorithms2019}.
With KNNs, I coarsely fitted a model predicting land/water loci according to Longitude and Latitude coordinates and their associated categories (land or water), with 3 neighbors. The probability of land closely overlaps the land perimeter in figure \ref{771661}.