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Performance Benchmark Report for onorm

Generated: 2025-10-05 21:40:13 Random Seed: 2022

Executive Summary

This report benchmarks the computational performance of all normalizers in the onorm package to verify that:

  1. Performance does not degrade substantially as sample size increases
  2. All normalizers maintain O(1) or O(d²) per-observation complexity
  3. Pipelines have expected overhead from component normalizers

Sample Size Scaling (d=5, Normal)

Verifying that normalizers maintain constant per-observation complexity as sample size increases:

Normalizer n=100 (μs) n=250 (μs) n=500 (μs) n=1,000 (μs) n=2,500 (μs) n=5,000 (μs) n=10,000 (μs) Ratio (max/min) Constant?
MinMaxScaler 5.44 5.37 5.42 5.30 5.25 5.31 5.20 1.06 ✓ Yes
MultivariateNormalizer 24.05 22.54 22.04 21.81 21.75 21.62 21.65 1.11 ✓ Yes
StandardScaler 9.37 9.08 9.23 9.03 8.98 11.14 8.98 1.24 ✓ Yes
Standard»MinMax 24.48 23.89 24.14 23.99 23.78 23.72 24.02 1.03 ✓ Yes
Standard»Multivariate 55.15 54.02 54.38 54.17 53.86 53.53 53.93 1.04 ✓ Yes
Winsorizer(5-95%) 27.39 27.64 28.27 28.43 28.58 28.46 28.63 1.05 ✓ Yes

Sample Size Scaling

Dimensionality Scaling (n=500, Normal)

Performance across different dimensionalities:

Normalizer d=5 (μs) d=10 (μs) d=20 (μs) d=50 (μs)
MinMaxScaler 5.41 5.31 5.43 5.39
MultivariateNormalizer 22.00 23.97 30.33 72.64
StandardScaler 9.12 9.10 9.90 9.31
Standard»MinMax 24.05 24.09 24.19 25.30
Standard»Multivariate 54.72 75.49 68.41 151.93
Winsorizer(5-95%) 28.25 55.10 107.33 265.17

Dimensionality Scaling

Detailed Results

Correlated Distribution (d=5)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 6.35 0.27 6.28 6.35
MultivariateNormalizer 500 25.90 1.30 25.21 25.90
StandardScaler 500 11.01 0.41 11.10 11.01
Standard»MinMax 500 27.56 0.54 27.38 27.56
Standard»Multivariate 500 56.59 3.77 54.24 56.59
Winsorizer(5-95%) 500 32.45 0.49 32.33 32.45

Mixed(95N+5C) Distribution (d=5)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 5.30 0.14 5.20 5.30
MultivariateNormalizer 500 22.33 0.54 22.00 22.33
StandardScaler 500 9.10 0.15 9.10 9.10
Standard»MinMax 500 24.39 0.65 23.89 24.39
Standard»Multivariate 500 105.48 61.49 71.29 105.48
Winsorizer(5-95%) 500 28.38 0.33 28.27 28.38

Normal Distribution (d=5)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 100 5.44 0.18 5.40 5.44
MinMaxScaler 250 5.37 0.24 5.27 5.37
MinMaxScaler 500 5.31 0.24 5.21 5.31
MinMaxScaler 500 5.50 0.41 5.20 5.50
MinMaxScaler 500 5.42 0.12 5.44 5.42
MinMaxScaler 1,000 5.30 0.21 5.21 5.30
MinMaxScaler 2,500 5.25 0.06 5.22 5.25
MinMaxScaler 5,000 5.31 0.28 5.18 5.31
MinMaxScaler 10,000 5.20 0.07 5.18 5.20
MultivariateNormalizer 100 24.05 3.27 22.70 24.05
MultivariateNormalizer 250 22.54 0.87 22.20 22.54
MultivariateNormalizer 500 21.86 0.25 21.80 21.86
MultivariateNormalizer 500 22.09 0.41 22.22 22.09
MultivariateNormalizer 500 22.04 0.32 22.16 22.04
MultivariateNormalizer 1,000 21.81 0.24 21.74 21.81
MultivariateNormalizer 2,500 21.75 0.18 21.70 21.75
MultivariateNormalizer 5,000 21.62 0.17 21.60 21.62
MultivariateNormalizer 10,000 21.65 0.20 21.54 21.65
StandardScaler 100 9.37 0.45 9.23 9.37
StandardScaler 250 9.08 0.27 8.94 9.08
StandardScaler 500 9.04 0.16 8.96 9.04
StandardScaler 500 9.09 0.16 9.10 9.09
StandardScaler 500 9.23 0.20 9.18 9.23
StandardScaler 1,000 9.03 0.10 9.01 9.03
StandardScaler 2,500 8.98 0.06 8.97 8.98
StandardScaler 5,000 11.14 4.57 9.03 11.14
StandardScaler 10,000 8.98 0.08 8.97 8.98
Standard»MinMax 100 24.48 1.04 24.01 24.48
Standard»MinMax 250 23.89 0.49 23.75 23.89
Standard»MinMax 500 23.83 0.39 23.71 23.83
Standard»MinMax 500 24.18 0.39 23.94 24.18
Standard»MinMax 500 24.14 0.44 23.84 24.14
Standard»MinMax 1,000 23.99 0.24 23.90 23.99
Standard»MinMax 2,500 23.78 0.15 23.72 23.78
Standard»MinMax 5,000 23.72 0.20 23.65 23.72
Standard»MinMax 10,000 24.02 0.16 24.01 24.02
Standard»Multivariate 100 55.15 1.76 54.29 55.15
Standard»Multivariate 250 54.02 0.75 53.70 54.02
Standard»Multivariate 500 54.20 0.59 54.03 54.20
Standard»Multivariate 500 55.57 1.39 54.88 55.57
Standard»Multivariate 500 54.38 0.86 54.09 54.38
Standard»Multivariate 1,000 54.17 0.37 54.07 54.17
Standard»Multivariate 2,500 53.86 0.29 53.78 53.86
Standard»Multivariate 5,000 53.53 0.19 53.51 53.53
Standard»Multivariate 10,000 53.93 0.21 53.97 53.93
Winsorizer(5-95%) 100 27.39 1.50 26.96 27.39
Winsorizer(5-95%) 250 27.64 0.55 27.52 27.64
Winsorizer(5-95%) 500 28.12 0.25 28.12 28.12
Winsorizer(5-95%) 500 28.37 0.45 28.21 28.37
Winsorizer(5-95%) 500 28.27 0.37 28.15 28.27
Winsorizer(5-95%) 1,000 28.43 0.66 28.21 28.43
Winsorizer(5-95%) 2,500 28.58 0.13 28.55 28.58
Winsorizer(5-95%) 5,000 28.46 0.06 28.46 28.46
Winsorizer(5-95%) 10,000 28.63 0.06 28.62 28.63

Normal Distribution (d=10)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 5.31 0.18 5.19 5.31
MultivariateNormalizer 500 23.97 0.49 23.66 23.97
StandardScaler 500 9.10 0.15 9.09 9.10
Standard»MinMax 500 24.09 0.38 23.96 24.09
Standard»Multivariate 500 75.49 18.58 64.86 75.49
Winsorizer(5-95%) 500 55.10 0.38 55.08 55.10

Normal Distribution (d=20)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 5.43 0.25 5.31 5.43
MultivariateNormalizer 500 30.33 0.93 30.13 30.33
StandardScaler 500 9.90 0.50 9.77 9.90
Standard»MinMax 500 24.19 0.38 24.00 24.19
Standard»Multivariate 500 68.41 0.62 68.21 68.41
Winsorizer(5-95%) 500 107.33 0.74 107.05 107.33

Normal Distribution (d=50)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 5.39 0.15 5.35 5.39
MultivariateNormalizer 500 72.64 1.31 72.00 72.64
StandardScaler 500 9.31 0.20 9.21 9.31
Standard»MinMax 500 25.30 0.48 25.16 25.30
Standard»Multivariate 500 151.93 0.41 152.00 151.93
Winsorizer(5-95%) 500 265.17 1.14 265.31 265.17

Uniform Distribution (d=5)

Normalizer n Mean (μs/obs) Std (μs) Median (μs/obs) Time/1000 obs (ms)
MinMaxScaler 500 5.27 0.12 5.21 5.27
MultivariateNormalizer 500 22.18 0.41 22.04 22.18
StandardScaler 500 9.12 0.18 9.07 9.12
Standard»MinMax 500 24.05 0.53 23.73 24.05
Standard»Multivariate 500 54.09 0.62 53.82 54.09
Winsorizer(5-95%) 500 28.22 0.35 28.22 28.22

Methodology

  • Timing: time.perf_counter() for high-resolution measurements
  • Replications: 5 runs with fresh data to reduce Monte Carlo error
  • Metrics: Time per observation (microseconds), extrapolated time per 1000 observations
  • Constant Time Criterion: Time ratio (max/min) < 1.5 across sample sizes

Conclusions

✓ All 6 normalizers passed the constant-time scaling test.

All normalizers demonstrate efficient online performance suitable for streaming data applications.