Oversampling and undersampling in data analysis

Random Oversampling involves supplementing the training data with multiple copies of some of the minority classes. Oversampling can be done more than once (2x, 3x, 5x, 10x, etc.) This is one of the earliest proposed methods, that is also proven to be robust. [3] Instead of duplicating every sample in the minority class, some of them may be randomly chosen with replacement.

There are a number of methods available to oversample a dataset used in a typical classification problem (using a classification algorithm to classify a set of images, given a labelled training set of images). The most common technique is known as SMOTE: Synthetic Minority Over-sampling Technique.[4] To illustrate how this technique works consider some training data which has s samples, and f features in the feature space of the data. Note that these features, for simplicity, are continuous. As an example, consider a dataset of birds for classification. The feature space for the minority class for which we want to oversample could be beak length, wingspan, and weight (all continuous). To then oversample, take a sample from the dataset, and consider its k nearest neighbors (in feature space). To create a synthetic data point, take the vector between one of those k neighbors, and the current data point. Multiply this vector by a random number x which lies between 0, and 1. Add this to the current data point to create the new, synthetic data point.

Many modifications and extensions have been made to the SMOTE method ever since its proposal. [5]

The adaptive synthetic sampling approach, or ADASYN algorithm,[6] builds on the methodology of SMOTE, by shifting the importance of the classification boundary to those minority classes which are difficult. ADASYN uses a weighted distribution for different minority class examples according to their level of difficulty in learning, where more synthetic data is generated for minority class examples that are harder to learn.

Randomly remove samples from the majority class, with or without replacement. This is one of the earliest techniques used to alleviate imbalance in the dataset, however, it may increase the variance of the classifier and may potentially discard useful or important samples. [5]

Cluster centroids is a method that replaces cluster of samples by the cluster centroid of a K-means algorithm, where the number of clusters is set by the level of undersampling.

Tomek links remove unwanted overlap between classes where majority class links are removed until all minimally distanced nearest neighbor pairs are of the same class. A Tomek link is defined as follows: given an instance pair ${\displaystyle (x_{i},x_{j})}$, where ${\displaystyle x_{i}\in S_{\min },x_{j}\in S_{\operatorname {max} }}$ and ${\displaystyle d(x_{i},x_{j})}$ is the distance between ${\displaystyle x_{i}}$ and ${\displaystyle x_{j}}$, then the pair ${\displaystyle (x_{i},x_{j})}$ is called a Tomek link if there's no instance ${\displaystyle x_{k}}$ such that ${\displaystyle d(x_{i},x_{k})<d(x_{i},x_{j})}$ or ${\displaystyle d(x_{j},x_{k})<d(x_{i},x_{j})}$. In this way, if two instances form a Tomek link then either one of these instances is noise or both are near a border. Thus, one can use Tomek links to clean up overlap between classes. By removing overlapping examples, one can establish well-defined clusters in the training set and lead to improved classification performance.

Undersampling with ensemble learning

A recent study shows that the combination of Undersampling with ensemble learning can achieve better results, see IFME: information filtering by multiple examples with under-sampling in a digital library environment.[7]