Synthetic minority oversampling technique

In statistics, synthetic minority oversampling technique is a method for oversampling samples when dealing with imbalanced classification categories within a dataset. The problem with doing statistical inference and modelling on imbalanced datasets is that the inferences and results from those analyses will be biased towards the majority class. Other solutions undersample 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.

Limitations

SMOTE does come with some limitations and challenges:

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:

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, which looks at the overlap of feature values over all feature vectors

Other variations include:

ADASYN: use a weighted distribution for different minority class examples according to their level of difficulty in learning
Borderline-SMOTE: only the minority examples near the borderline are over-sampled
SMOTE-Tomek: applying Tomek links to the oversampled training set as a data cleaning step to remove samples overlapping the category boundaries
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

Algorithm

The SMOTE algorithm can be abstracted with the following pseudocode:

if N < 100; then
Randomize the T minority class samples
T = ∗ T
N = 100
endif
N =
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
endfor
Populate:
while N != 0
Choose a random number between 1 and k, call it nn
for attr <- 1 to numattrs
Compute: dif = Sample − Sample
Compute: gap = random number between 0 and 1
Synthetic = Sample + gap ∗ dif
endfor
newindex++
N = N − 1
endwhile
return

whereN is the amount of SMOTE, where the amount of SMOTE is assumed to be a multiple of one hundredT is the number of minority class samplesk is the number of nearest neighborsPopulate 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:

: implementation of 86 SMOTE variations