# Types of Weights

Author: Henrik Bengtsson
Created: 2005-02-01
Last updated: 2005-02-05
Phase: very alpha
Comments: Feedback is appreciated.

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## Introduction

For several normalization and calibration methods the estimation of the normalization (or calibration) function can be done with weights. Commonly, weights are proportional to a quality measure, that is, the less quality we assign to a signal, the less influence (weight) it should have on the estimation of calibration and normalization functions.

## General about weights

The definition of a weight is a single value in [0,1]. Weights outside this range and missing values (`NA`) are not allowed.

Below, we will define different entities such as signals, probes/spots, probesets, channels, arrays, and data-points. To any of these entities weights may be assigned.

## Signals and signal weights

A signal is a single value. A signal weight is a weight assigned to a signal. Thus, it is for entities within an array and never across/between arrays.

Example: In two-color microarray data, there are two signals for each spot, i.e. the red or the green signals, and each of them can be assigned a different signal weight. Typically, such signal weights are represented by an Nx2 `matrix`, where N is the number of probes/spots on the array.

Example: In Affymetrix microarray data, which is single-channel data, there is one signal per probe (in turn part of a probe set). Each such probe can be assigned a signal weight. Typically, such signal weights are represented by an Nx1 `matrix`, where N is the number of probes/spots on the array.

## Probes and probe weights

A probe is the smallest entity (not considering image pixels) on the array that measures the amount of hybridized samples in one or several channels.

Example: For two-color microarrays, a probe is a spot.

Example: For Affymetrix arrays, a probe can be either a perfect match probe (PM) or a mismatch probe (MM).

A probe weight is a weight assigned to a probe/spot (not a probe set).

Example: For two-color data, the signals in the two channels for a given spot share the same probe weight.

Example: For four-color data, the signals in the four channels for a given spot share the same probe weight.

Example: For single-channel data such as Affymetrix data, the probe weight is identical to a signal weight.

Typically, above signal weights are represented by an Nx1 `matrix`, where N is the number of probes/spots on the array.

The probe weight of probe i must be equal to the mean of its signal weights.

## Probesets and probeset weights

A probeset consists of a set of probes.

Example: For two-color microarrays, probesets are not defined.

Example: For Affymetrix arrays, a probeset is the set of perfect match (PM) and mismatch (MM) probes corresponding to the same gene.

A probeset weight is a weight assigned to a probeset.

Since Affymetrix is single-channel arrays, typically the above probeset weights are represented by an Nx1 `matrix`, where N is the number of probesets.

The probeset weight for probeset j must be equal to the mean of its probe weights (which in this case are identical the signal weights) by averaging the probe weights for each probeset.

## Data points and data-point weights

The definition of a data point depends on the context. It may be assigned to entities within an array, but also across/between arrays.

Example: (Paired data-point weight). In paired-channel normalization, such as curve-fit normalization (a.k.a. lowess intensity normalization), two and only two channels are normalized together at the same time, e.g. red and the green channels in two-color data, or two two single-channel data set obtained from two different Affymetrix arrays. Here a data point is constituted by two signals, e.g. X[i] = (G[i],R[i]). A data-point weight is assigned to the pair of signals corresponding to the same spot or gene, e.g. for lowess normalization a data-point weight is assigned to a log-ratio and a log-intensity.

Example: (Multi-channel data point weight). In multi-channel normalization, such as affine normalization or quantile normalization (within a singel array and/or across multiple arrays), each data point is consituted by multiple signals, e.g. for J two-color arrays it is X[i] = (R[i,1],G[i,1],...,R[i,J],G[i,J]). To this data point, a data-point weight can be assigned.

Typically, above signal weights are represented by an Nx1 `matrix`, where N is the number of data points.

Data-points weights can be generated from signal or probe weights, by averaging them for each data point.

If not stated elsewise, arguments named `weights` are assumed to take data-point weights.

## Arrays and array weights

An array weight is a weight assigned to an array, that is, to the complete set of signals in all channels constituting an array.

By definition, a channel weight can never apply across/between arrays.

Constraints: The array weight should be equal to the average of the channel (and signal/probe/probeset) weights. Hence, for single-channel arrays, the array weight should be identical to the channel weight.

## Channels and channel weights

A channel weight is a weight assigned to a channel, that is, to the set of signals constituting a channel.

By definition, a channel weight can never apply across/between arrays.

Example: In two-color data, two channel weights can exist.

Example: In Affymetrix (single-channel) data, only one channel weights can exists and is therefore identical to an array weight.

Constraints: The channel weight should be equal to the average of all signal/probe/probeset weights in the channel.

## Combining signal weights into spot weights

Spot weights can be generated from signal weights.

For a given spot, the spot weight is calculated as the arithmetical mean of the signal weights.

## Combining signal weights into data-point weights

Data-point weights can be generated from signal weights.

For a given data point, the data point weight is calculated as the arithmetical mean of the signal weights.

## Combining spot weights into data-point weights

Data-point weights can be generated from spot weights.

For a given data point, the data point weight is calculated as the arithmetical mean of the spot weights.

## Restrictions

Note, currently weights are only supported by the `RGData` class. [The plan is to make this class the "main" class.]

Currently, it is only methods that explicitly say they support weights which use weights. For all other methods, weights are ignored.

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