A box plot is a statistical graph that visually represents the distribution of one or multiple sets of continuous quantitative data using five key values: the minimum observed value, the first quartile, the median, the third quartile, and the maximum observed value. It is named for its box-like shape.

Box plot components:

As the figure shows, most of the data is contained between the upper and lower limits, while a few data points lie outside these limits. These data points are uncommon and can be considered outliers.

Select a threshold-mode anomaly function:

TA[tu,td](x)=max(x-tu, td-x,0)/(tu-td)

The method to calculate tu and td using X[-k]_i is as follows:

tu=Q3+n*IQR
td=Q1-n*IQR

where Q1 is the first quartile, Q3 is the third quartile, n is a multiple of the interquartile range; adjusting n can adjust the size of tu and td .

The anomaly score is represented by od and can be calculated as follows:

od=max(x_i-tu, td-x_i,0)/( tu-td)

SPL routine:

import@i() returns a sequence when the data has only one column.

A.median(:k) divides the data into k equal segments and returns k-1 segment values. Adjusting n can adjust the values of tu and td . The value of n is typically between [1.5, 3].

Calculation result example:

The X-axis represents the sequence index, and the Y-axis represents the sequence value. In the legend, X denotes the data values, tu is the upper threshold, and td is the lower threshold (Note: While tu and td are numerical values, they are plotted as lines for better visualization). Because the final, bolded data point, x_i, falls between tu and td , its anomaly score is 0.