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Parameters

The parameters are represented by the pair (exponent, factor). The pair of values (0.00, 0.00) serves as a baseline, as this means that the indices in the color palettes are not taken into account to weigh color distances in the formula for palette distances.

Results

The results are shown as:

• statistics (min, median, mean, max) about the rank of the retrieved apps,
• a score which is the sum of these statistics. The lower the score, the better.

Benchmark

Top 2,000

This is a benchmark based on the top 2,000 popular apps, which leads to using 11 gift wrappings out of 17.

Using RGB

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00	1	142	411.82	1308	1862.82
0.18	0.98	1	132	428.00	1400	1961.00

Using raw HSV

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00	2	87	280.09	1063	1432.09
0.28	0.76	1	82	314.00	1175	1572.00
0.29	0.42	2	79	306.18	1145	1532.18

Using linearized HSV

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00	2	178	263.45	691	1134.45
0.01	0.03	2	178	263.36	690	1133.36
0.49	0.08	2	168	273.45	605	1048.45
0.90	0.04	2	169	273.73	604	1048.73

NB: I have run hundreds of trials with optuna for this benchmark, thanks to the short time required for each (~ 45 seconds).

Top 20,000

This is a benchmark based on the top 20,000 popular apps, which leads to using all of the 17 gift wrappings.

Using RGB

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00	6	1546	2527.35	12671	16750.35
0.09	0.49	7	1432	2574.18	13138	17151.18
0.46	0.11	8	1364	2628.47	13599	17599.47
0.97	0.33	14	1167	3079.82	15365	19625.82

Using raw HSV

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00

Using linearized HSV

Exponent	Factor	Min Rank	Median Rank	Mean Rank	Max Rank	Score (sum)
0.00	0.00	20	860	1804.35	7222	9906.35
0.57	0.05	17	1034	1839.00	6501	9391.00
0.23	0.32	16	1084	1875.59	6299	9274.59
0.32	0.21	15	1088	1881.29	6294	9278.29

NB: I have not run many trials with optuna for this benchmark, due to the long time required for each trial (~ 9 minutes).