Hyperlog—A flexible log‐like transform for negative, zero, and positive valued data

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Abstract
Background: The remarkable success of cytometry over the past 30 years is largely due to its uncanny ability to display populations that vastly differ in numbers and fluorescence intensities on one scale. The log transform implemented in hardware as a log amplifier or in software normalizes signals or channels so that these populations appear as clearly discernible peaks. With the advent of multiple fluorescence cytometry, spectral crossover compensation of these signals has been necessary to properly interpret the data. Unfortunately, because compensation is a subtractive process, it can produce negative and zero valued data. The log transform is undefined for these values and, as a result, forces computer algorithms to truncate these values, creating a few problems for cytometrists. Data truncation biases displays making properly compensated data appear undercompensated; thus, enticing many operators to overcompensate their data. Also, events truncated into the first histogram channel are not normally visible with typical two‐dimensional graphic displays, thus hiding a large number of events and obscuring the true proportionality of negative distributions. In addition, the log transform creates unequal binning that can dramatically distort negative population distributions.Methods and Results: The HyperLog transform is a log‐like transform that admits negative, zero, and positive values. The transform is a hybrid type of transform specifically designed for compensated data. One of its parameters allows it to smoothly transition from a logarithmic to linear type of transform that is ideal for compensated data.Conclusions: The HyperLog transform is easily implemented in computer systems and results in display systems that present compensated data in an unbiased manner.

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