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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.

For this benchmark with optuna, each trial requires 2 to 3 seconds.

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
0.29	0.42	2	79	306.18	1145	1532.18
0.28	0.76	1	82	314.00	1175	1572.00

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
0.90	0.04	2	169	273.73	604	1048.73
0.74	0.05	2	169	273.64	604	1048.64
0.49	0.08	2	168	273.45	605	1048.45

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.

For this benchmark with optuna, each trial requires 3 to 5 seconds.

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
0.46	0.11	8	1364	2628.47	13599	17599.47
0.97	0.33	14	1167	3079.82	15365	19625.82
0.09	0.49	7	1432	2574.18	13138	17151.18

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
0.50	0.09	18	1063	1864.53	6272	9217.53
0.45	0.10	18	1061	1862.35	6273	9214.35

Top 100,000 (no constraint)

This is a benchmark based on the ~ 100,000 apps, i.e. without any constraint, which leads to using 17 gift wrappings out of 17.

For this benchmark with optuna, each trial requires 12 to 15 seconds.

Using linearized HSV

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