Unit Variance Scaling

Autoscale a feature to zero mean and unit population variance.

Description

Unit-variance scaling centers a feature and divides by its population standard deviation.

Unit-variance scaling centers a feature and divides by its population standard deviation. The divisor is n rather than n−1.^[1]

Autoscale a feature to zero mean and unit population variance.

When to use Unit Variance Scaling

Use this tool to autoscale a feature to zero mean and unit population variance.

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 Unit Variance 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 using the field table and calculation rules, then run the tool.
Read zScores, 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

Enter at least two finite measurements with nonzero variation. Return standardized values in input order and original mean. A constant feature is an input error.

z_i=(x_i−mean)/sqrt(Σ(x−mean)²/n)

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

Output field	Meaning	Value type
zScores	Z scores	list of number
mean	Mean	number

json

{
  "input": {
    "values": [
      1,
      2,
      3
    ]
  },
  "output": {
    "zScores": [
      -1.224744871391589,
      0,
      1.224744871391589
    ],
    "mean": 2
  }
}

Limitations and assumptions

No missing-value handling or robust outlier treatment is provided. Scaling choices can affect downstream modeling and should be chosen before fitting.

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 Pareto Scaling: Apply mean-centered Pareto scaling by the square root of standard deviation. For a complementary task, use Log2 Skew Transform: Apply a pseudocount log2 transform and measure dynamic-range compression.

References

Unit Variance Scaling — tool.io

Similar or alternative tools

Pareto Scaling
Apply mean-centered Pareto scaling by the square root of standard deviation.
Log2 Skew Transform
Apply a pseudocount log2 transform and measure dynamic-range compression.