NND

class frlearn.data_descriptors.NND(dissimilarity: str or float or Callable[[np.array], float] or Callable[[np.array, np.array], float] = 'boscovich', k: int or Callable[[int], float] or None = 1, weights: Callable[[int], np.array] | None = None, proximity: Callable[[float], float] = <function shifted_reciprocal>, nn_search: NeighbourSearchMethod = <frlearn.neighbours.neighbour_search_methods.KDTree object>, preprocessors=(<frlearn.statistics.feature_preprocessors.IQRNormaliser object>,))

Implementation of the Nearest Neighbour Distance (NND) data descriptor, which goes back to at least [1]. It has also been used to calculate upper and lower approximations of fuzzy rough sets, where the addition of aggregation with OWA operators is due to [2].

Parameters

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

The dissimilarity measure to use.

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.

The default is the Boscovich norm (also known as cityblock, Manhattan or taxicab norm).

kint or (int -> float) or None = 1

Which nearest neighbour(s) to consider. Should be either a positive integer, or a function that takes the target 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]. If weights = None, only the kth neighbour is used, otherwise closer neighbours are also taken into account.

proximityfloat -> float = np_utils.shifted_reciprocal

The function used to convert distance values to proximity values. It should be be an order-reversing map from [0, ∞) to [0, 1].

weights(int -> np.array) or None = None

How to aggregate the proximity values from the k nearest neighbours. The default is to only consider the kth nearest neighbour distance.

preprocessorsiterable = (IQRNormaliser(), )

Preprocessors to apply. The default interquartile range normaliser rescales all features to ensure that they all have the same interquartile range.

Notes

k is the principal hyperparameter that can be tuned to increase performance. Its default value is based on the empirical evaluation in [3].

References

1

Knorr EM, Ng RT (1997). A Unified Notion of Outliers: Properties and Computation. KDD-97: Proceedings of the Third International Conference on Knowledge Discovery and Data Mining, pp 219–222. AAAI. doi: 10.5555/3001392.3001438

2

Cornelis C, Verbiest N, Jensen R (2010). Ordered weighted average based fuzzy rough sets. RSKT 2010: Proceedings of the 5th International Conference on Rough Set and Knowledge Technology, pp 78–85. Springer, Lecture Notes in Artificial Intelligence 6401. doi: 10.1007/978-3-642-16248-0_16

3

Lenz OU, Peralta D, Cornelis C (2021). Average Localised Proximity: A new data descriptor with good default one-class classification performance. Pattern Recognition, vol 118, no 107991. doi: 10.1016/j.patcog.2021.107991

class Model

Examples using frlearn.data_descriptors.NND

One class classification