Edited Nearest Neighbors

ENN operates by iterating through every instance in the dataset. For each data point, it finds its k nearest neighbors (typically k=3). If the instance's actual class label does not match the majority vote of its neighbors, it is considered noisy or ambiguous and is removed. This process exclusively targets majority class examples for deletion, leaving minority class instances untouched to preserve rare event information.

The primary goal of ENN is to smooth the decision boundary. By removing majority class points that intrude deeply into minority class space, ENN eliminates overlapping regions. This is distinct from simple random under-sampling:

• Noise Removal: Deletes mislabeled or ambiguous majority instances.
• Boundary Cleaning: Removes majority points surrounded by minority neighbors, making the class separation more distinct for algorithms like k-NN or SVM.

ENN is rarely used in isolation. It is a critical component of combined resampling strategies designed to address severe class imbalance:

• SMOTEENN: Applies SMOTE to oversample the minority class, then immediately uses ENN to clean the resulting dataset of any noisy synthetic or original majority points.
• Neighborhood Cleaning Rule (NCR): Uses ENN as a first pass to clean the majority class, followed by a second pass that removes minority class examples misclassified by its three nearest neighbors.

The ENN algorithm requires calculating the k-nearest neighbors for every single instance in the dataset. This results in a computational complexity of O(n²) for a brute-force search, making it slow on large-scale financial transaction datasets. In practice, optimized spatial indexing structures like k-d trees or ball trees are used to accelerate the neighbor search, but the method remains more computationally intensive than simple random under-sampling.

By removing ambiguous majority class examples, ENN typically increases the true positive rate (recall) for the minority class. The classifier is no longer confused by overlapping instances, allowing it to draw a more aggressive boundary. However, aggressive cleaning can also increase the false positive rate if the boundary becomes too tightly wrapped around the minority class. The choice of k is critical: a smaller k removes more instances, while a larger k is more conservative.

Both are data cleaning methods, but they operate on different principles:

• ENN: Removes a majority instance if its class differs from the plurality of its k neighbors. It can remove multiple majority points in a dense overlapping region.
• Tomek Links: Identifies pairs of minimally distanced opposite-class instances and removes only the majority class instance in the pair. It is a more conservative, pair-wise cleaning strategy that focuses strictly on the borderline.