Benchmarks¶

TorchSOM’s computational performance and fidelity are evaluated against MiniSom, the most widely adopted and actively maintained SOM library. These benchmarks are from the paper (Section 4, Appendix D).

Methodology¶

Synthetic datasets are generated using scikit-learn’s make_blobs(), varying both sample size and feature dimensionality. Both implementations use identical hyperparameters:

Grid size: 25 x 15 (rectangular)
Initialization: PCA
Training iterations: 100 epochs
Neighborhood function: Gaussian
Distance function: Euclidean
Seed: Fixed for reproducibility

Hardware:

CPU: Intel Xeon Platinum 8370C (Ice Lake) @ 3.4 GHz, 8 cores, 16 GB RAM
GPU: NVIDIA Tesla T4, 2560 CUDA cores, 16 GB RAM

Each configuration is averaged over 10 independent runs.

Small Rectangular Map (25 x 15)¶

Samples	Features	QE (MiniSom)	TE% (MiniSom)	Time (MiniSom)	QE (CPU)	TE% (CPU)	Time (CPU)	QE (GPU)	TE% (GPU)	Time (GPU)
240	4	0.17	26	1.82 s	0.24	12	0.41 s	0.24	10	0.24 s
240	50	1.79	49	3.84 s	1.79	12	0.50 s	1.83	15	0.25 s
240	300	5.43	71	15.4 s	5.21	47	0.72 s	5.21	30	0.28 s
4,000	4	0.16	31	54.6 s	0.23	6	4.87 s	0.23	7	2.61 s
4,000	50	1.66	56	89.2 s	1.77	14	5.33 s	1.74	16	2.62 s
4,000	300	5.14	74	261 s	5.13	19	8.32 s	5.13	20	2.77 s
16,000	4	0.15	32	1,054 s	0.23	6	20.2 s	0.23	6	10.9 s
16,000	50	1.64	57	1,220 s	1.75	13	21.9 s	1.75	14	10.8 s
16,000	300	5.15	75	1,939 s	5.14	18	30.4 s	5.14	17	11.6 s

QE = Quantization Error (lower is better). TE% = Topographic Error as percentage (lower is better).

Key Findings¶

Training Speed¶

TorchSOM trains substantially faster than MiniSom:

CPU: 77–98% faster across all configurations
GPU: Up to 99% faster for large, high-dimensional datasets
The 16,000-sample / 300-feature case: MiniSom takes 32 minutes, torchsom (GPU) takes 12 seconds — a 167x speedup

These improvements hold even though torchsom computes both QE and TE at every epoch (an \(\mathcal{O}(2 \times \text{batch} \times \text{epochs})\) overhead that MiniSom does not incur).

Topographic Error¶

TorchSOM consistently produces maps with 34–81% lower Topographic Error, indicating significantly better topology preservation. This means the spatial relationships in the input data are more faithfully represented on the SOM grid.

Quantization Error¶

Both libraries achieve comparable Quantization Error across all configurations, confirming that torchsom’s batch learning approach maintains representation fidelity equivalent to MiniSom’s online learning.

Large Map Results (90 x 70)¶

For large maps, torchsom is the only viable option. MiniSom fails to complete within reasonable time for the largest configurations:

Samples	Features	QE (MiniSom)	Time (MiniSom)	QE (CPU)	Time (CPU)	QE (GPU)	Time (GPU)
240	300	5.45	364 s	5.17	7.07 s	5.18	0.40 s
4,000	300	5.0	6,149 s	5.11	77.8 s	5.10	4.57 s
16,000	300	N/A	N/A	5.11	321 s	5.12	19.5 s

MiniSom is unable to process the 16,000 x 300 configuration on a 90 x 70 grid within a reasonable time.

Interpretation¶

TorchSOM’s advantages stem from two design decisions:

Batch learning: Instead of updating weights sample-by-sample (online), torchsom processes entire batches, enabling vectorized operations and efficient GPU utilization.
PyTorch backend: Leverages optimized BLAS routines and CUDA kernels for distance computation, BMU search, and weight updates, all operating on contiguous tensor memory.

Together, these enable torchsom to scale to datasets and map sizes that are impractical with existing libraries, while maintaining or improving map quality.

Reproducibility¶

All benchmark scripts and configuration files live in the benchmark/ directory. The exact paper states are pinned by two Git tags — jmlr-submission-v1 (original submission) and jmlr-revision-v1 (this revision) — and the comparison uses MiniSom v2.3.5 (commit 65b6ba6).