Understanding NormalizeData() function

In this short article, using a tiny, 5x5 matrix example dataset, I will explain the NormalizeData() function and the three Normalization.method() choices.

The cell expression data is often contained in the form of a $\mathbf{\text{Genes x Sample}}$ matrix.

• Rows: Genes
• Columns: Cells/Samples/Replicates
• Entries: Number of RNA transcripts detected

$\text{Example dataset:}$

The expression data is contained

As columns in count matrix represent UMI counts for each cells, the sums of UMI counts in a column represent total cellular expression.

As mentioned above, there are three Normalization.method() choices under NormalizeData() function in Seurat.

$\text{Method 1: LogNormalize}$

$\mathbf{\text{Step1: Scaling}}$

By default, the NormalizeData() function of Seurat pipeline uses 10,000 as a scale.factor. The UMI counts for each cell is multiplied by the scale.factor and divided by the total UMI counts for the cell.

$\mathbf{\text{Step2: Log-Normalization}}$

In this step, the scaled UMI counts are natural log transformed using log1p, i.e. ln(x + 1).

Why +1?

If any empty cell is detected, i.e. zero UMI count, the log-normalization, ln(0), will result in a ‘mathematical error’. In contrast, ln(0 + 1) will give a value of 0.

In short,

• ln(0) = Numerical error
• ln(0 + 1) = 0

$\text{Result}$

$\text{Method 2: Centered Log Ratio (CLR)}$

(This section is under development)

$\text{Method 3: Relative counts}$

In contrast to $\text{Method 1:}$ Log-Normalize, the relative count normalization is a one-step method, only involves the scaling.

$\mathbf{\text{Scaling}}$

By default, the NormalizeData() function of Seurat pipeline uses 10,000 as a scale.factor. The UMI counts for each cell is multiplied by the scale.factor and divided by the total UMI counts for the cell.

$\text{Result:}$