Comments on "An Algorithm for Finding Intrinsic Dimensionality of Data"

In the above paper,¹Fukunaga and Olsen present an alternative method of estimating the intrinsic dimensionality of data. Their proposed algorithm differs from others in that it relies heavily on operator interaction and provides a method of specifying variable local regions. The authors state: " This variability is critical as the practical problem of determining dimensionality depends on the size and number of samples in the local regions." This is illustrated in their summary Table II (B), in which, for local region sizes containing five and ten samples, the indicated dimensionalities are one and three, respectively, when using the 1 percent eigenvalue criterion; and one and two, respectively, when using the 10 percent criterion. While the authors may have a decision rule to select the correct answer from the summary table, I did not see it in their paper; and without such a rule, I do not believe the problem has been solved satisfactorily.