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I have read this paper https://arxiv.org/pdf/1803.03674v1.pdf for outlier detection problem with real data (online training)

In this paper, the authors used Incremental Decision Tree to build subspaces (nodes in tree) by 2-mean method. The problem is in the algorithm 2 (build tree in paper), the condition (line 22): if t = beta power k. with t is the round observations (maybe each round we observe one sample) the splitting is performed.

The question is: What is beta and k? I spent a lot of time thinking about this. In the experiment you can see the authors plot chart describe splitting space process. At round 5, 11, 40? These are t (in my understanding) 5 can't be a result of any number power any number.

Thanks you.

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It appears that $\beta$ is a constant, and $k$ ranges over the integers. See paragraph 3 of Section IV.B.

Line 1 of Algorithm 2 tells you that $\beta$ is a parameter: it says "Select parameters $\beta$ and ..." Based on the body text in Section IV.B, presumably "if $t= \beta^k$" means "if there exists $k \in \mathbb{N}$ such that $t=\beta^k$".

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