Regarding your main question: "When a point of the dataset is selected to train an isolation tree, can it be used to train another tree?", the short answer is yes, that point (or observation) can be used to train a different tree. The sampling process for each tree begins with the full set of data points/observations.
This can be seen on the doc page: https://www.mathworks.com/help/stats/anomaly-detection-with-isolation-forest.html
- NumObservationsPerLearner (number of observations for each isolation tree) — Each isolation tree corresponds to a subset of training observations. For each tree, iforest samples min(N,256) number of observations from the training data without replacement, where N is the number of training observations. The isolation forest algorithm performs well with a small sample size because it helps to detect dense anomalies and anomalies close to normal points. However, you need to experiment with the sample size if N is small. For an example, see Examine NumObservationsPerLearner for Small Data."
So, given that each tree begins with the full dataset, it is no problem to train an isolation forest of 100 trees with NumObservationPerLearner of 149 using a data set of only 150 observations. See the doc section Examine NumObservationsPerLearner for Small Data for more info.
load fisheriris
size(meas)
[forest,tf,scores]=iforest(meas,NumObservationsPerLearner=149);
forest
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