# Normaliz

## Contents

### Purpose

Normalizes rows of matrix to unit vectors.

### Synopsis

[ndat,norms] = normaliz(dat)
[ndat,norms] = normaliz(dat,out,normtype,window)
[ndat,norms] = normaliz(dat,normtype,options);

### Description

NORMALIZ can be used for pattern normalization, which is useful for preprocessing in some pattern recognition applications and also for correction of pathlength effects for some quantification applications. The "norm type" defines the order of normalization (see algorithm below). Typical values cause each row to be normalized to:

1 = the absolute value of the area "under the curve" (sum of the absolute value of all values)
2 = the summed squared value of the values (the multivariate vector "length")
inf = the maximum value in of the row

#### Inputs

• dat = the data matrix

#### Optional Inputs

• out = flag to suppress warnings about the norm of a vector being zero. Supresses when set to 0 (zero) {default = 0}.
• normtype = used to specify the type of norm {default = 2}.
• window = indices for which columns of dat should be used to calculate the norm {default = [] which implies all values}

NOTE: If normtype is specified then out must be included, out can be empty [] giving the default value.

Alternatively, the out and window options can be passed in an options structure:

• options = An options structure can be passed as third input along with (dat) and (normtype). This input takes the place of the remaining inputs and should contain one or more of the following fields:
• display : [ 'off' |{'on'}] controls display (replacement for out input above)
• window : replacement for standard (window) input above (default = [])

#### Outputs

• ndat = matrix of normalized data where the rows have been normalized
• norms = vector of norms used in the normalization

### Algorithm

For a 1 by N vector x, the norm nx is given by ${\displaystyle n_{x}=\left(\sum \limits _{j=1}^{N}{\left|x_{i}^{p}\right|}\right)^{1/p}}$ where p is normtype. The normalized 1 by N vector xn is given by x/nx.

However, when p is inf (infinity) a simple location of the maximum value replaces the equation above.