FRNN#

class frlearn.regressors.FRNN(k: int = <function at_most.<locals>._f>, dissimilarity: str = 'chebyshev', preprocessors=(<frlearn.statistics.feature_preprocessors.RangeNormaliser object>, ))#

Implementation of the Fuzzy Rough Nearest Neighbour (FRNN) regressor [1].

Predicts an output value of a test instance y on the basis of the output values of the k nearest neighbours of y, similar to KNN regression. The difference is that the output value is calculated as a weighted mean, with the weights corresponding to membership degrees in the upper and lower approximations of the tolerance sets of the output values of the neighbours.

Parameters:
k: int or (int -> float) = at_most(10)

Number of neighbours to consider. Should be either a positive integer, or a function that takes the training set size n and returns a float. All such values are rounded to the nearest integer in [1, n]. Due to the computational complexity of this algorithm, k should not be chosen too large.

dissimilarity: str or float or (np.array -> float) or ((np.array, np.array) -> float) = ‘chebyshev’

The dissimilarity measure to use. The similarity between two instances is calculated as 1 minus their dissimilarity.

A vector size measure np.array -> float induces a dissimilarity measure through application to y - x. A float is interpreted as Minkowski size with the corresponding value for p. For convenience, a number of popular measures can be referred to by name.

When a float or string is passed, the corresponding dissimilarity measure is automatically scaled to ensure that the dissimilarity of [1, 1, ..., 1] with [0, 0, ..., 0] is 1.

For the default Chebyshev norm, this is already the case, since it assigns the maximum of the per-attribute differences, but e.g. the Boscovich norm normally amounts to the sum of the per-attribute differences. In this case, the scaling step divides by the number of dimensions, and we obtain a dissimilarity that is the mean of the per-attribute differences.

This can be prevented by explicitly passing a dissimilarity measure without scaling.

preprocessorsiterable = (RangeNormaliser(), )

Preprocessors to apply. The default range normaliser ensures that all features have range 1.

Notes

Although proposed in the same paper [1], FRNN regression and FRNN classification are different algorithms.

[1] does not recommend any specific value for k, but seems to use k = 10 for its experiments.

References

class Model#