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| from dataclasses import dataclass | |
| def hyperbolic_smoother(x, n = 10.0): | |
| """n determines how strongly smaller values will be magnified""" | |
| return (n + 1) * x / (n * x + 1) | |
| @dataclass | |
| class Track: | |
| duration_seconds: int | |
| star_rating: int | |
| # if this is 4 valid ratings are: 0, 1, 2, 3, 4 | |
| MAX_RATING = 4 | |
| # for experiments | |
| WEIGHTED_INTERPOLATION_RATIO = 0.3 | |
| UNWEIGHTED_INTERPOLATION_RATIO = 1 - WEIGHTED_INTERPOLATION_RATIO | |
| # Limits a weight to this value * (1 / len(tracks)) | |
| MAX_WEIGHT_FACTOR = 1.2 | |
| MIN_WEIGHT_FACTOR = 1 / MAX_WEIGHT_FACTOR | |
| examples = [ | |
| [Track(10, 4), Track(100, 2), Track(1000, 1), Track(120, 1), Track(160, 3), | |
| Track(9000, 4), Track(200, 0)], | |
| [Track(120, 2), Track(240, 4), Track(600, 0)], | |
| [Track(120, 4), Track(140, 2), Track(210, 3), Track(200, 4), Track(180, 4), | |
| Track(35 * 60, 0)], | |
| [Track(120, 4), Track(240, 4), Track(1200, 0), Track(1600, 0)], | |
| [Track(299, 4), Track(265, 3), Track(391, 4), Track(250, 3), Track(325, 4), Track(195, 3), Track(346, 4), Track(347, 3), Track(317, 2), Track(407, 3), Track(346, 3), Track(239, 4)], | |
| ] | |
| print("The following (duration-based) weights represent the ratio / percentage" | |
| " a tracks'\nrating makes up of the album's average rating (which is in " | |
| "the TOTAL row).") | |
| print() | |
| for tracks in examples: | |
| total_duration = float(sum(i.duration_seconds for i in tracks)) | |
| mean_weight = 1 / len(tracks) | |
| mean_duration = total_duration / len(tracks) | |
| max_duration = mean_duration * MAX_WEIGHT_FACTOR | |
| smoothed_duration_weights = [] | |
| total_weight = 0 | |
| for t in tracks: | |
| dur = t.duration_seconds | |
| # experiment: directly limit the weight a single track can have | |
| # fail: often results in very flat weights (and feels wrong) | |
| #if dur > max_duration: | |
| # dur = max_duration | |
| duration_ratio = dur / total_duration | |
| weight = hyperbolic_smoother(duration_ratio) | |
| # experiment: interpolate between 1 / len(tracks) and duration / total | |
| # fail: when long track exists, the rest look very similar | |
| #weight = (UNWEIGHTED_INTERPOLATION_RATIO * mean_weight) + ( | |
| # WEIGHTED_INTERPOLATION_RATIO * duration_ratio) | |
| total_weight += weight | |
| smoothed_duration_weights.append(weight) | |
| print(" simple") | |
| print(" smoothed ratio") | |
| print(" partial simple partial") | |
| print(" smoothed weighted ratio weighted") | |
| print("rating minutes ➜ weight rating VERSUS weight rating") | |
| print('-' * 80) | |
| average_smoothed_rating = 0 | |
| average_simple_rating = 0 | |
| sum_of_ratings = 0 | |
| for track, weight in zip(tracks, smoothed_duration_weights): | |
| star_rating = track.star_rating | |
| dur = track.duration_seconds | |
| smoothed_ratio = weight / total_weight | |
| simple_ratio = dur / total_duration | |
| float_rating = star_rating / MAX_RATING | |
| sum_of_ratings += float_rating | |
| wr = smoothed_ratio * float_rating | |
| sr = simple_ratio * float_rating | |
| average_simple_rating += sr | |
| average_smoothed_rating += wr | |
| print(f"{star_rating}★ = {float_rating:1.2f} {dur / 60:>6.1f} " | |
| f"{smoothed_ratio:>6.1%} {wr:.4f} " | |
| f"{simple_ratio:>6.1%} {sr:.4f}") | |
| print('-' * 80) | |
| print(f"TOTAL: {total_duration / 60:>6.1f} " | |
| f"{average_smoothed_rating:.4f} " | |
| f"{average_simple_rating:.4f}") | |
| print() | |
| old_rating = sum_of_ratings / len(tracks) | |
| print(f"old (unweighted) average rating: {old_rating:.4f}") | |
| print(f"old (unweighted) weight (1/len): {mean_weight:6.1%}") | |
| print() |
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| The following (duration-based) weights represent the ratio / percentage a tracks' | |
| rating makes up of the album's average rating (which is in the TOTAL row). | |
| simple | |
| smoothed ratio | |
| partial simple partial | |
| smoothed weighted ratio weighted | |
| rating minutes ➜ weight rating VERSUS weight rating | |
| -------------------------------------------------------------------------------- | |
| 4★ = 1.00 0.2 0.5% 0.0050 0.1% 0.0009 | |
| 2★ = 0.50 1.7 4.6% 0.0231 0.9% 0.0047 | |
| 1★ = 0.25 16.7 26.0% 0.0650 9.4% 0.0236 | |
| 1★ = 0.25 2.0 5.4% 0.0136 1.1% 0.0028 | |
| 3★ = 0.75 2.7 7.0% 0.0527 1.5% 0.0113 | |
| 4★ = 1.00 150.0 47.9% 0.4790 85.0% 0.8499 | |
| 0★ = 0.00 3.3 8.5% 0.0000 1.9% 0.0000 | |
| -------------------------------------------------------------------------------- | |
| TOTAL: 176.5 0.6384 0.8933 | |
| old (unweighted) average rating: 0.5357 | |
| old (unweighted) weight (1/len): 14.3% | |
| simple | |
| smoothed ratio | |
| partial simple partial | |
| smoothed weighted ratio weighted | |
| rating minutes ➜ weight rating VERSUS weight rating | |
| -------------------------------------------------------------------------------- | |
| 2★ = 0.50 2.0 26.1% 0.1303 12.5% 0.0625 | |
| 4★ = 1.00 4.0 33.5% 0.3350 25.0% 0.2500 | |
| 0★ = 0.00 10.0 40.4% 0.0000 62.5% 0.0000 | |
| -------------------------------------------------------------------------------- | |
| TOTAL: 16.0 0.4653 0.3125 | |
| old (unweighted) average rating: 0.5000 | |
| old (unweighted) weight (1/len): 33.3% | |
| simple | |
| smoothed ratio | |
| partial simple partial | |
| smoothed weighted ratio weighted | |
| rating minutes ➜ weight rating VERSUS weight rating | |
| -------------------------------------------------------------------------------- | |
| 4★ = 1.00 2.0 10.8% 0.1076 4.1% 0.0407 | |
| 2★ = 0.50 2.3 12.0% 0.0599 4.7% 0.0237 | |
| 3★ = 0.75 3.5 15.5% 0.1161 7.1% 0.0534 | |
| 4★ = 1.00 3.3 15.0% 0.1504 6.8% 0.0678 | |
| 4★ = 1.00 3.0 14.1% 0.1410 6.1% 0.0610 | |
| 0★ = 0.00 35.0 32.6% 0.0000 71.2% 0.0000 | |
| -------------------------------------------------------------------------------- | |
| TOTAL: 49.2 0.5750 0.2466 | |
| old (unweighted) average rating: 0.7083 | |
| old (unweighted) weight (1/len): 16.7% | |
| simple | |
| smoothed ratio | |
| partial simple partial | |
| smoothed weighted ratio weighted | |
| rating minutes ➜ weight rating VERSUS weight rating | |
| -------------------------------------------------------------------------------- | |
| 4★ = 1.00 2.0 11.8% 0.1179 3.8% 0.0380 | |
| 4★ = 1.00 4.0 18.5% 0.1850 7.6% 0.0759 | |
| 0★ = 0.00 20.0 33.9% 0.0000 38.0% 0.0000 | |
| 0★ = 0.00 26.7 35.8% 0.0000 50.6% 0.0000 | |
| -------------------------------------------------------------------------------- | |
| TOTAL: 52.7 0.3029 0.1139 | |
| old (unweighted) average rating: 0.5000 | |
| old (unweighted) weight (1/len): 25.0% | |
| simple | |
| smoothed ratio | |
| partial simple partial | |
| smoothed weighted ratio weighted | |
| rating minutes ➜ weight rating VERSUS weight rating | |
| -------------------------------------------------------------------------------- | |
| 4★ = 1.00 5.0 8.2% 0.0824 8.0% 0.0802 | |
| 3★ = 0.75 4.4 7.7% 0.0577 7.1% 0.0533 | |
| 4★ = 1.00 6.5 9.5% 0.0948 10.5% 0.1049 | |
| 3★ = 0.75 4.2 7.4% 0.0558 6.7% 0.0503 | |
| 4★ = 1.00 5.4 8.6% 0.0862 8.7% 0.0872 | |
| 3★ = 0.75 3.2 6.4% 0.0477 5.2% 0.0392 | |
| 4★ = 1.00 5.8 8.9% 0.0891 9.3% 0.0928 | |
| 3★ = 0.75 5.8 8.9% 0.0670 9.3% 0.0698 | |
| 2★ = 0.50 5.3 8.5% 0.0426 8.5% 0.0425 | |
| 3★ = 0.75 6.8 9.7% 0.0725 10.9% 0.0819 | |
| 3★ = 0.75 5.8 8.9% 0.0669 9.3% 0.0696 | |
| 4★ = 1.00 4.0 7.2% 0.0723 6.4% 0.0641 | |
| -------------------------------------------------------------------------------- | |
| TOTAL: 62.1 0.8350 0.8361 | |
| old (unweighted) average rating: 0.8333 | |
| old (unweighted) weight (1/len): 8.3% |
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