Weissman score

Short description: Performance metric for lossless compression

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] W=αrr‾log⁡T‾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]

## Contents

* 1 Example
* 2 Limitations
* 2.1 Examples
* 3 See also
* 4 References

## 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.

Application  | Compression ratio  | Compression time [min]  | Weissman score

|
|
|

paq8f  | 5.467600  | 300  | 1.000000
raq8g  | 5.514990  | 420  | 0.720477
paq8hkcc  | 5.682593  | 300  | 1.039321
paq8hp1  | 5.692566  | 300  | 1.041145
paq8hp2  | 5.750279  | 300  | 1.051701
paq8hp3  | 5.800033  | 300  | 1.060801
paq8hp4  | 5.868829  | 300  | 1.073826
paq8hp5  | 5.917719  | 300  | 1.082325
paq8hp6  | 5.976643  | 300  | 1.093102
paq8hp12  | 6.104276  | 540  | 0.620247
decomp8  | 6.261574  | 540  | 0.63623
decomp8  | 6.276295  | 540  | 0.637726

## 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).

### Examples

# | Standard compressor | Scored compressor | Weissman score | Observations

|
|
|
|

Compression ratio | Compression time | Log (compression time) | Compression ratio | Compression time | Log (compression time)
1  | 2.1 | 2 min | 0.30103 | 3.4 | 3 min | 0.477121 | 1×(3.4/2.1)×(0.30103/0.477121)=1.021506 | Change in unit or scale, changes the result.
2  | 2.1 | 120 sec | 2.079181 | 3.4 | 180 sec | 2.255273 | 1×(3.4/2.1)×(2.079181/2.255273)=1.492632
3  | 2.2 | 1 min | 0 | 3.3 | 1.5 min | 0.176091 | 1×(3.3/2.2)×(0/0.176091)=0 | If time is 1, its log is 0; then the score can be 0 or infinity.
4  | 2.2 | 0.667 min | −0.176091 | 3.3 | 1 min | 0 | 1×(3.3/2.2)×(−0.176091/0)=infinity
5  | 1.6 | 0.5 h | −0.30103 | 2.9 | 1.1 h | 0.041393 | 1×(2.9/1.6)×(−0.30103/0.041393)=−13.18138 | If time is less than 1, its log is negative; then the score can be negative.
6  | 1.6 | 1.1 h | 0.041393 | 1.6 | 0.9 h | −0.045757 | 1×(1.6/1.6)×(0.041393/−0.045757)=−0.904627

## See also

* Benchmark
* Coding theory
* Information theory
* Phred quality score

## References

1. ↑ 1.0 1.1 Perry, Tekla (July 28, 2014). "A Fictional Compression Metric Moves Into the Real World". https://spectrum.ieee.org/view-from-the-valley/computing/software/a-madefortv-compression-metric-moves-to-the-real-world. Retrieved January 25, 2016.
2. ↑ Perry, Tekla (July 25, 2014). "A Made-For-TV Compression Algorithm". https://spectrum.ieee.org/view-from-the-valley/computing/software/a-madefortv-compression-algorithm. Retrieved January 25, 2016.
3. ↑ Sandberg, Elise (April 12, 2014). "HBO's 'Silicon Valley' Tech Advisor on Realism, Possible Elon Musk Cameo". The Hollywood Reporter. http://www.hollywoodreporter.com/live-feed/hbos-silicon-valley-tech-advisor-695513. Retrieved June 10, 2014.
4. ↑ Jurgensen, John; Rusli, Evelyn M. (April 3, 2014). "There's a New Geek in Town: HBO's 'Silicon Valley'". The Wall Street Journal. https://www.wsj.com/articles/SB10001424052702303987004579479244213599118. Retrieved June 10, 2014.
5. ↑ "Lossless compression with Brotli in Rust for a bit of Pied Piper on the backend" (in en). https://blogs.dropbox.com/tech/2016/06/lossless-compression-with-brotli/.
6. ↑ Hutter, Marcus (July 2016). "Contestants". http://prize.hutter1.net/#contestants. Retrieved January 25, 2016.

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