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FRM Part I · FRM Exam Part I · Machine-Learning Methods

An analyst has a feature with values 2, 4, 6, 8 and 20 in a training sample. The analyst applies min-max scaling to the range [0, 1] using the sample minimum and maximum. What is the scaled value of the observation equal to 8, and what is the main drawback illustrated by the data?

The scaled value is 0.333, from (8 - 2) / (20 - 2). The example shows min-max scaling is sensitive to outliers: the extreme value of 20 stretches the range and squeezes the remaining observations into the lower third of the interval, reducing their distinguishing power.

  1. A0.333; the outlier of 20 compresses the other values into a narrow part of the rangeCorrect
  2. B0.667; the outlier of 20 compresses the other values into a narrow part of the range
  3. C0.333; min-max scaling forces the mean of the scaled data to be zero
  4. D0.400; min-max scaling removes the outlier completely

Explanation

Min = 2 and max = 20, so the scaled value is (8 - 2) / (20 - 2) = 6/18 = 0.333. The values 2, 4, 6 and 8 map to 0, 0.111, 0.222 and 0.333, so the outlier compresses them into the lower third of the range. The 0.667 option uses (8 - 2)/9, wrong denominator. Min-max scaling does not center the mean at zero or remove outliers.

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