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By computing one linear score per class and normalizing them with Softmax, we obtain multiclass probabilities without changing the core logic.

The loss, the gradients, and the optimization remain the same.
Only the number of parallel scores increases.

Implemented in Excel, the model becomes transparent: you can see the scores, the probabilities, and how the coefficients evolve over time.

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Using the tiny dataset 1, 2, 3, 9, we can see the logic clearly. We build several random trees, measure how many splits each point needs, average the depths, and convert them into anomaly scores. Short depths become scores close to 1, long depths close to 0.

The Excel implementation is painful, but the algorithm itself is elegant. It scales to many features, makes no assumptions about distributions, and even works with categorical data. Above all, Isolation Forest asks a different question: not “What is normal?”, but “How fast can I isolate this point?”

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