Sampling is a method used to reduce the sample size of a data set prior calculating a statistics of interest. Different sampling methods are available in FCS Express and can be used in conjunction with several Transformation tools.

 

Available sampling methods are:

 

•None. Sampling is not performed. All events selected in the Gate drop-down menu of the Transformation dialog are used.

 

•Interval. A defined number of cells (i.e. the Sample Size) is sampled from the main population (i.e. the one selected in the Gate drop-down menu of the Transformation dialog) according to a fixed periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired Sample Size. For example, if the main population counts 1000 events and the Sample Size is 100, every 10th event will be selected (e.g. 1st, 11th, 21st, 31st...). If the specified Sample Size is higher than the number of available events, all available events will be considered.

 

Target Density and Weighted Density are examples of Density Based sampling. This means the probability that an event will be sampled (i.e. included in the dataset for analysis) is based on the local density around that event.  The local density of an event x is defined as the number of other events within a certain radius around event x. The radius used is arbitrary, and properties to control it are defined below.  

Density based sampling involves two stages. The first stage is to calculate the local density around each cell. The second stage is to decide whether or not to sample the cell based on the local density.

 

Local Density Calculation

The local density is calculated identically for both the Target Density and Weighted Density options. In order to calculate the local density, a radius must be determined. In order to determine the radius, 2000 events are randomly selected and the distance matrix of these events are calculated. The median distance is then multiplied by the Alpha value that can be entered in the properties to determine the radius for the local density.

Once the radius is determined as described above, the number of events within the radius is calculated based on the Local Density Method whose options are:

•Exact - the exact number of events within the radius is determined

•Kernel - an approximation of the number of events within the radius is determined. Generally, the kernel method is much faster than the exact method and provides comparable results.

 

Sampling Calculation

After the local density has been calculated, the cells are sampled based on the density using two different approaches which the user can select: Target Density and Weighted Density.