## Introduction

Neighbors-based classification is a type of instance-based learning or non-generalizing learning: it does not attempt to construct a general internal model, but simply stores instances of the training data. Classification is computed from a simple majority vote of the nearest neighbors of each point: a query point is assigned the data class which has the most representatives within the nearest neighbors of the point.

## Implementation

scikit-learn implements two different nearest neighbors classifiers: *KNeighborsClassifier* implements learning based on the *k* nearest neighbors of each query point, where *k* is an integer value specified by the user. *RadiusNeighborsClassifier* implements learning based on the number of neighbors within a fixed radius *r* of each training point, where *r* is a floating-point value specified by the user.

import numpy as np import matplotlib.pyplot as plt from matplotlib.colors import ListedColormap from sklearn import neighbors, datasets n_neighbors = 15 # import some data to play with iris = datasets.load_iris() X = iris.data[:, :2] # we only take the first two features. y = iris.target h = .02 # step size in the mesh # Create color maps cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF']) cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF']) # we create an instance of Neighbours Classifier and fit the data. clf = neighbors.KNeighborsClassifier(n_neighbors) clf.fit(X, y) # Plot the decision boundary. For that, we will assign a color to each # point in the mesh [x_min, m_max]x[y_min, y_max]. x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1 y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]) # Put the result into a color plot Z = Z.reshape(xx.shape) plt.figure() plt.pcolormesh(xx, yy, Z, cmap=cmap_light) # Plot also the training points plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold) plt.xlim(xx.min(), xx.max()) plt.ylim(yy.min(), yy.max()) plt.show()

Now let's see how *RadiusNeighborsClassifier* works. After playing a bit with hyperparameters, we'll achieve the following plot:

... clf = neighbors.RadiusNeighborsClassifier(3.0, weights='distance') ...

## Conclusion

Despite its simplicity, nearest neighbors has been successful in a large number of classification and regression problems, including handwritten digits or satellite image scenes. Being a non-parametric method, it is often successful in classification situations where the decision boundary is very irregular.