Synthetic minority oversampling technique

In statistics, synthetic minority oversampling technique (SMOTE) is a method for oversampling samples when dealing with imbalanced classification categories within a dataset. The problem with doing statistical inference and modeling on imbalanced datasets is that the inferences and results from those analyses will be biased towards the majority class. Other solutions to addressing the problem of imbalanced data is to do undersampling of the majority class to be equivalently represented in the data with the minority class. Instead of undersampling the majority class, SMOTE oversamples the minority class. ^{[1] [2]}

Limitations

SMOTE does come with some limitations and challenges: ^[3]

• Overfitting during the training process
• Favorable outcomes in the machine learning process, but questionable translation to practical uses
• Synthetically created sample may belong to a different class
• Synthetic data may not match the original distribution of the minority class

Variations

Two variations to the SMOTE algorithm were proposed in the initial SMOTE paper: ^[2]

• SMOTE-NC: applies to datasets with a mix of nominal and continuous data
• SMOTE-N: accounts for nominal features, with the nearest neighbors algorithm being computed using the modified version of Value Difference Metric (VDM), which looks at the overlap of feature values over all feature vectors

Other variations include: ^[4]

• ADASYN: use a weighted distribution for different minority class examples according to their level of difficulty in learning ^{[5] [6]}
• Borderline-SMOTE: only the minority examples near the borderline are over-sampled ^{[5] [7]}
• SMOTE-Tomek: applying Tomek links to the oversampled training set as a data cleaning step to remove samples overlapping the category boundaries ^[8]
• SMOTE-ENN: uses the Edited Nearest Neighbor Rule, which removes any example whose class label differs from the class of at least two of its three nearest neighbors ^[8]

Algorithm

The SMOTE algorithm can be abstracted with the following pseudocode: ^[2]

if N < 100; then     Randomize the T minority class samples     T = (N/100) ∗ T     N = 100 endif N = (int)(N/100) k = Number of nearest neighbors numattrs = Number of attributes Sample[ ][ ]: array for original minority class samples newindex: keeps a count of number of synthetic samples generated, initialized to 0 Synthetic[ ][ ]: array for synthetic samples for i <- 1 to T     Compute k nearest neighbors for i, and save the indices in the nnarray     Populate(N , i, nnarray) endfor Populate(N, i, nnarray):     while N != 0         Choose a random number between 1 and k, call it nn         for attr <- 1 to numattrs             Compute: dif = Sample[nnarray[nn]][attr] − Sample[i][attr]             Compute: gap = random number between 0 and 1             Synthetic[newindex][attr] = Sample[i][attr] + gap ∗ dif         endfor         newindex++         N = N − 1     endwhile     return 

where

• N is the amount of SMOTE, where the amount of SMOTE is assumed to be a multiple of one hundred
• T is the number of minority class samples
• k is the number of nearest neighbors
• Populate() is the generating function for new synthetic minority samples

If N is less than 100%, the minority class samples will be randomized, as only a random subset of them will have SMOTE applied to them.

Implementations

Since the introduction of the SMOTE method, there have been a number of software implementations:

• imbalanced-learn (Python)
• smote_variants: implementation of 86 SMOTE variations (Python)
• ImbalancedLearningRegression (Python)

See also

• Stratified sampling
• Oversampling and undersampling in data analysis

References

1. Chawla, N. V.; Bowyer, K. W.; Hall, L. O.; Kegelmeyer, W. P. (2011-06-09), "SMOTE: Synthetic Minority Over-sampling Technique", Journal of Artificial Intelligence Research, 16: 321–357, arXiv: 1106.1813 , doi:10.1613/jair.953
2. Chawla, N. V.; Bowyer, K. W.; Hall, L. O.; Kegelmeyer, W. P. (2002-06-01). "SMOTE: Synthetic Minority Over-sampling Technique". Journal of Artificial Intelligence Research. 16: 321–357. arXiv: 1106.1813 . doi:10.1613/jair.953. ISSN   1076-9757.
3. Alkhawaldeh, Ibraheem M.; Albalkhi, Ibrahem; Naswhan, Abdulqadir Jeprel (2023-12-20). "Challenges and limitations of synthetic minority oversampling techniques in machine learning". World Journal of Methodology. 13 (5): 373–378. doi: 10.5662/wjm.v13.i5.373 . PMC   10789107 . PMID   38229946.
4. "Over-sampling methods — Version 0.13.0". imbalanced-learn.org. Retrieved 2025-07-16.
5. Elreedy, Dina; Atiya, Amir F. (2019-12-01). "A Comprehensive Analysis of Synthetic Minority Oversampling Technique (SMOTE) for handling class imbalance" . Information Sciences. 505: 32–64. doi:10.1016/j.ins.2019.07.070. ISSN   0020-0255.
6. He, Haibo; Bai, Yang; Garcia, Edwardo A.; Li, Shutao (2008-06-01). "ADASYN: Adaptive synthetic sampling approach for imbalanced learning". 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence). IEEE. pp. 1322–1328. doi:10.1109/ijcnn.2008.4633969. ISBN   978-1-4244-1820-6.
7. Han, Hui; Wang, Wen-Yuan; Mao, Bing-Huan (2005-08-23). "Borderline-SMOTE: A New Over-Sampling Method in Imbalanced Data Sets Learning". Advances in Intelligent Computing. ICIC'05. Vol. Part I. Berlin, Heidelberg: Springer-Verlag. pp. 878–887. doi:10.1007/11538059_91. ISBN   978-3-540-28226-6.{{cite book}}: |journal= ignored (help)
8. Batista, Gustavo E. A. P. A.; Prati, Ronaldo C.; Monard, Maria Carolina (2004-06-01). "A study of the behavior of several methods for balancing machine learning training data" . SIGKDD Explor. Newsl. 6 (1): 20–29. doi:10.1145/1007730.1007735. ISSN   1931-0145.