LOESS Intensity Normalization

Apply tricube local intensity-bias smoothing to log-ratio signals.

Description

Intensity-dependent log-ratio bias can be estimated by nearby observations.

Intensity-dependent log-ratio bias can be estimated by nearby observations. This implementation uses a tricube-weighted local mean rather than fitting a local polynomial regression.^[1]

Apply tricube local intensity-bias smoothing to log-ratio signals.

When to use LOESS Intensity Normalization

Use this tool to apply tricube local intensity-bias smoothing to log-ratio signals.

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 LOESS Intensity 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 intensities, logRatios, bandwidth using the field table and calculation rules, then run the tool.
Read correctedLogRatios, estimatedBias. 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
intensities	Intensities	list of number	Required
logRatios	Log ratios	list of number	Required
bandwidth	Bandwidth	number	Required

Enter aligned nonempty finite intensity/log-ratio lists and positive bandwidth in intensity units. Compute weights at each input point, including the point itself, estimate local mean bias and subtract it. Points exactly one bandwidth away have zero weight.

w_ij=(1−(|x_i−x_j|/bandwidth)³)³ for distance<bandwidth, else 0; bias_i=Σw_ij ratio_j/Σw_ij

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

Output field	Meaning	Value type
correctedLogRatios	Corrected log ratios	list of number
estimatedBias	Estimated bias	list of number

json

{
  "input": {
    "intensities": [
      1,
      2,
      3
    ],
    "logRatios": [
      2,
      0,
      2
    ],
    "bandwidth": 1
  },
  "output": {
    "correctedLogRatios": [
      0,
      0,
      0
    ],
    "estimatedBias": [
      2,
      0,
      2
    ]
  }
}

Limitations and assumptions

This is quadratic in observation count and has no robust fitting iterations, adaptive neighbor span or local-linear correction. With only self neighbors, each corrected ratio becomes zero.

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 Two Color Log Ratio: Compute log2 Cy5/Cy3 spot ratios with an optional pseudocount. For a complementary task, use Quantile Normalization: Quantile-normalize multiple arrays, averaging tied-rank assignments.

References

LOESS Intensity Normalization — tool.io

Similar or alternative tools

Two Color Log Ratio
Compute log2 Cy5/Cy3 spot ratios with an optional pseudocount.
Quantile Normalization
Quantile-normalize multiple arrays, averaging tied-rank assignments.