Quantile Normalization

Quantile-normalize multiple arrays, averaging tied-rank assignments.

Description

Quantile normalization shares a rank-based reference distribution across arrays.

Quantile normalization shares a rank-based reference distribution across arrays. Equal raw values receive the average normalized value across their tied ranks.^[1]

Quantile-normalize multiple arrays, averaging tied-rank assignments.

When to use Quantile Normalization

Use this tool to quantile-normalize multiple arrays, averaging tied-rank assignments.

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.

How to use Quantile Normalization and understand its results

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.
Enter arrays using the field table and calculation rules, then run the tool.
Read normalizedArrays, rankMeans. 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
arrays	Arrays	list of list of number	Required

Enter at least two equal-length nonempty arrays, each as a matrix row. Sort each row while preserving original indices, average every rank across rows and restore values to original feature positions. Average rank means over tied blocks and return normalized rows plus rank means.

rankMean_r=mean across arrays of sorted value at rank r; tied value=mean of its rankMeans

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

Output field	Meaning	Value type
normalizedArrays	Normalized arrays	list of list of number
rankMeans	Rank means	list of number

json

{
  "input": {
    "arrays": [
      [
        1,
        3,
        5
      ],
      [
        2,
        4,
        6
      ]
    ]
  },
  "output": {
    "normalizedArrays": [
      [
        1.5,
        3.5,
        5.5
      ],
      [
        1.5,
        3.5,
        5.5
      ]
    ],
    "rankMeans": [
      1.5,
      3.5,
      5.5
    ]
  }
}

Limitations and assumptions

Finite signed values are accepted. Assuming comparable distributions is a scientific choice, and ties can prevent exactly identical final distributions. No feature mapping or background correction is performed.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Microarray Background Correction: Subtract local microarray background for each probe spot. For a complementary task, use LOESS Intensity Normalization: Apply tricube local intensity-bias smoothing to log-ratio signals.

References

Quantile Normalization — tool.io

Similar or alternative tools

Microarray Background Correction
Subtract local microarray background for each probe spot.
LOESS Intensity Normalization
Apply tricube local intensity-bias smoothing to log-ratio signals.