Pareto Scaling

Apply mean-centered Pareto scaling by the square root of standard deviation.

Description

Pareto scaling centers a feature but divides by the square root of a supplied standard deviation.

Pareto scaling centers a feature but divides by the square root of a supplied standard deviation. Its scaling is weaker than unit-variance normalization.^[1]

Apply mean-centered Pareto scaling by the square root of standard deviation.

When to use Pareto Scaling

Use this tool to apply mean-centered Pareto scaling by the square root of standard deviation.

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.

How to use Pareto Scaling and understand its results

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.
Enter values, standardDeviation using the field table and calculation rules, then run the tool.
Read paretoScaled, mean. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
values	Values	list of number	Required
standardDeviation	Standard deviation	number	Required

Enter a nonempty finite feature list and positive standard deviation. Calculate the list mean and return scaled entries in original order. Constant lists produce zeros.

scaled_i=(x_i−mean(x))/sqrt(suppliedSD)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
paretoScaled	Pareto scaled	list of number
mean	Mean	number

json

{
  "input": {
    "values": [
      1,
      2,
      3
    ],
    "standardDeviation": 4
  },
  "output": {
    "paretoScaled": [
      -0.5,
      0,
      0.5
    ],
    "mean": 2
  }
}

Limitations and assumptions

The supplied deviation is not estimated or checked against the feature. It means standard deviation rather than variance.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Unit Variance Scaling: Autoscale a feature to zero mean and unit population variance. For a complementary task, use Log2 Skew Transform: Apply a pseudocount log2 transform and measure dynamic-range compression.

References

Pareto Scaling — tool.io

Similar or alternative tools

Unit Variance Scaling
Autoscale a feature to zero mean and unit population variance.
Log2 Skew Transform
Apply a pseudocount log2 transform and measure dynamic-range compression.