FRNN

class frlearn.classifiers.FRNN(*, upper_weights: ~typing.Callable[[int], ~numpy.array] = LinearWeights(), upper_k: int = <function at_most.<locals>._f>, lower_weights: ~typing.Callable[[int], ~numpy.array] = LinearWeights(), lower_k: int = <function at_most.<locals>._f>, dissimilarity: str = 'boscovich', nn_search: ~frlearn.neighbours.neighbour_search_methods.NeighbourSearchMethod = <frlearn.neighbours.neighbour_search_methods.KDTree object>, preprocessors=(<frlearn.statistics.feature_preprocessors.RangeNormaliser object>,))

Implementation of Fuzzy Rough Nearest Neighbour (FRNN) classification.

Parameters:

upper_weights(int -> np.array) or None = LinearWeights()

OWA weights to use in calculation of upper approximation of decision classes. If None, only the upper_kth neighbour is used.

upper_k: int or (int -> float) or None = at_most(20)

Effective length of upper weights vector (number of nearest neighbours to consider). Should be either a positive integer, or a function that takes the class size n and returns a float, or None, which is resolved as n. All such values are rounded to the nearest integer in [1, n]. Alternatively, if this is 0, only the lower approximation is used.

lower_weights(int -> np.array) or None = LinearWeights()

OWA weights to use in calculation of lower approximation of decision classes. If None, only the lower_kth neighbour is used.

lower_k: int or (int -> float) or None = at_most(20)

Effective length of lower weights vector (number of nearest neighbours to consider). Should be either a positive integer, or a function that takes the size n of the complement of the class and returns a float, or None, which is resolved as n. All such values are rounded to the nearest integer in [1, n]. Alternatively, if this is 0, only the upper approximation is used.

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

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 instance, the default Boscovich norm (also known as cityblock, Manhattan or taxicab norm) normally assigns a dissimilarity that is 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.

nn_searchNeighbourSearchMethod = KDTree()

Nearest neighbour search algorithm to use.

preprocessorsiterable = (RangeNormaliser(), )

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

Notes

If upper_weights = lower_weights = None and upper_k = lower_k = 1, this is the original strict FRNN classification as presented in [1]. The use of OWA operators for the calculation of fuzzy rough sets was proposed in [2], and OWA operators were first explicitly combined with FRNN in [3].

References

[1]

Jensen R, Cornelis C (2008). A New Approach to Fuzzy-Rough Nearest Neighbour Classification. In: Chan CC, Grzymala-Busse JW, Ziarko WP (eds). Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science, vol 5306. Springer, Berlin, Heidelberg. doi: 10.1007/978-3-540-88425-5_32

[2]

Cornelis C, Verbiest N, Jensen R (2010). Ordered Weighted Average Based Fuzzy Rough Sets. In: Yu J, Greco S, Lingras P, Wang G, Skowron A (eds). Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science, vol 6401. Springer, Berlin, Heidelberg. doi: 10.1007/978-3-642-16248-0_16

[3]

Ramentol E, Vluymans S, Verbiest N, Caballero Y, Bello R, Cornelis C, Herrera F (2015). IFROWANN: Imbalanced Fuzzy-Rough Ordered Weighted Average Nearest Neighbor Classification. IEEE Transactions on Fuzzy Systems, vol 23, no 5, pp 1622–1637. doi: 10.1109/TFUZZ.2014.2371472

class Model

Examples using frlearn.classifiers.FRNN

Multiclass classification with FRNN

Multiclass classification with FRNN

Feature selection with FRFS

Feature selection with FRFS

Instance selection with FRPS

Instance selection with FRPS