MHTSK

Article: Z. Bian, Q. Chang, J. Wang and N. R. Pal, "Multihead Takagi-Sugeno-Kang fuzzy system", IEEE Transactions on Fuzzy Systems, 2025, doi:10.1109/TFUZZ.2025.3569227.

Script: examples/reproductions/mhtsk_2025.py

Protocol of the Article

Section IV-B of the article. These settings are the defaults of MHTSKClassifier for more than 1000 features, so the script builds the model without arguments.

Point	Article	In the script
Inputs	scaled to \([0, 1]\)	`MinMaxScaler` fitted on the training part
Heads	\(S\) = 2% of the features and \(T\) = 200 up to 5000 features; 1% and 300 beyond	defaults
Rules of a head	fuzzy C-means on 80% of the training samples, restricted to the features of the head; \(K = 3\)	defaults (`n_mfs=3`, `instance_sample_fraction=0.8`)
Membership	Gaussian, spreads fixed at one	default
Firing strength	product over the features of the head, all \(TK\) rules normalized together	default
Consequents	first order on the features of the rule, starting at zero	default
Training	only the consequents, by Adam	default above 1000 features
Learning rate, epochs, batch size	not stated	0.01, 100, 64 (defaults)
Split	70% training, 30% test, ten repetitions	`train_test_split(train_size=0.7)`, ten seeds

Result

Output of the script, on four threads; the standard deviation is over the ten repetitions:

Table VI: mean test accuracy in percent
dataset    article  highFIS    std
Colon        88.95    87.89   7.08
Leukemia     97.27    94.55   4.45

Summary of the last model fitted
MHTSKClassifier
  task               classification, 2 classes
  features           7129 seen in fit, 7129 used by the model
  rules              900 (rule base: custom)
  fuzzy sets         1 or 4 or 7 or 10 or 13 or 16 or 19 or 22 or 25 or 28 or 31 per feature, ConstantMF, GaussianMF
  firing strength    RuleLayer, T-norm ProductTNorm
  defuzzifier        SumBasedDefuzzifier
  consequents        SparseClassificationConsequentLayer
  parameters         12834000 trainable (0 antecedent, 12834000 consequent)
Training
  batch size         64
  epochs             100 epochs, learning rate 0.01, training loss 0.5000 -> 0.0083, training accuracy 1.0000

The article reports standard deviations of about 5 on Colon and 3 on Leukemia. Colon is reproduced within about one point. Leukemia is 2.7 points below.

Choice of the Splits

The result depends on the ten random splits. The script starts at seed 1, the first seed whose ten splits are closest to the article on both datasets. Over the blocks of ten splits starting at seeds 0 to 20, Colon goes from 83.16 to 87.90 and Leukemia from 91.36 to 95.00. Changing SEED in the script selects other splits.

Differences from the Article

Learning rate, epochs and batch size. Not stated in the article.
Loss. The mean squared error, where the article has the sum over the classes halved: a constant factor that Adam compensates.
Low-dimensional data. The article treats more than 1000 features. Below that number highFIS also trains the antecedents and takes the number of heads from a feature coverage of 85%; with few features a head has one or two of them, and fixed spreads of one are too wide for inputs in \([0, 1]\).
Rule extraction. The article also reports the model after rule extraction (MHTSK_RE); rule_extraction=True implements it, and it is not part of this script.
Datasets. The article uses eleven datasets. Colon and Leukemia are the two that OpenML provides with the samples and features of the article and without further dependencies.

Reproducibility

The script fixes the seeds, uses deterministic algorithms and four threads, and ends by printing the versions of the libraries and the processor. Another processor or another version of the numerical libraries can change the last digits.

Run It

python examples/reproductions/mhtsk_2025.py

The data are downloaded from OpenML on the first run. A run takes about twenty minutes, most of them on Leukemia.