Weissman score

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

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 was used in Dropbox Tech Blog to explain real-world work on lossless compression.

Example

This example shows the score for the data of Hutter Prize,^[5] 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). And the times 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).

Examples

See also

• Benchmark
• Coding theory
• Information theory

References