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. 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.
The 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."
Example This example shows the score for the data of the Hutter Prize, using the paq8f as a standard and 1 as the scaling constant. ApplicationCompression ratioCompression time [min]Weissman scorepaq8f5.4676003001.000000raq8g5.5149904200.952480paq8hkcc5.6825933001.039321paq8hp15.6925663001.041145paq8hp25.7502793001.051701paq8hp35.8000333001.060801paq8hp45.8688293001.073826paq8hp55.9177193001.082325paq8hp65.9766433001.093102paq8hp126.1042765401.012142decomp86.2615745401.038223decomp86.2762955401.040664
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).
#Standard compressorScored compressorWeissman scoreObservationsCompression ratioCompression timeLog (compression time)Compression ratioCompression timeLog (compression time)12.12 min0.301033.43 min0.4771211××=1.021506Change in unit or scale, changes the result.22.1120 sec2.0791813.4180 sec2.2552731××=1.49263232.21 min03.31.5 min0.1760911××=0If time is 1, its log is 0; then the score can be 0 or ±∞.42.20.667 min−0.1760913.31 min01××=−∞51.60.5 h−0.301032.91.1 h0.0413931××=−13.18138If time is less than 1, its log is negative; then the score can be negative.61.61.1 h0.0413931.60.9 h−0.0457571××=−0.904627
See also Benchmark Coding theory Information theory Phred quality score
References