Weissman score

The Weissman score is a performance metric for lossless compression applications. It was developed by Tsachy Weissman, a professor at Stanford University, and Vinith Misra, a graduate student, at the request of producers for HBO's television series Silicon Valley, a television show about a fictional tech start-up working on a data compression algorithm.^[1][2][3][4] It compares both required time and compression ratio of measured applications, with those of a de facto standard according to the data type.

The formula is the following; where r is the compression ratio, T is the time required to compress, the overlined ones are the same metrics for a standard compressor, and alpha is a scaling constant.^[1]

$${\displaystyle W=\alpha {r \over {\overline {r}}}{\log {\overline {T}} \over \log {T}}}$$

Weissman score has been used by Daniel Reiter Horn and Mehant Baid of Dropbox to explain real-world work on lossless compression. According to the authors it "favors compression speed over ratio in most cases."^[5]

Example

This example shows the score for the data of the Hutter Prize,^[6] using the paq8f as a standard and 1 as the scaling constant.

Limitations

Although the value is relative to the standards against which it is compared, the unit used to measure the times changes the score (see examples 1 and 2). This is a consequence of the requirement that the argument of the logarithmic function must be dimensionless. The multiplier also can't have a numeric value of 1 or less, because the logarithm of 1 is 0 (examples 3 and 4), and the logarithm of any value less than 1 is negative (examples 5 and 6); that would result in scores of value 0 (even with changes), undefined, or negative (even if better than positive).

See also

• Benchmark
• Coding theory
• Information theory
• Phred quality score

References