Source code for geomstats.learning.kernel_density_estimation_classifier

"""The kernel density estimation classifier on manifolds.

Lead author: Yann Cabanes.

import math

from sklearn.neighbors import RadiusNeighborsClassifier

import geomstats.backend as gs

[docs] def wrap(function): """Wrap a function to first convert args to arrays.""" def wrapped_function(*args, **kwargs): new_args = map(gs.from_numpy, args) return function(*new_args, **kwargs) return wrapped_function
[docs] class KernelDensityEstimationClassifier(RadiusNeighborsClassifier): """Classifier implementing the kernel density estimation on manifolds. The kernel density estimation classifier classifies the data according to a kernel density estimation of each dataset on the manifold. The density estimation is performed using radial kernel functions: the distance is the only geometrical tool used to estimate the density on the manifold. This classifier inherits from the radius neighbors classifier of the scikit-learn library, we expect the classifier presented here to be easier to use on manifolds. Compared with the radius neighbors classifier, we force the parameter 'algorithm' to be equal to 'brute' in order to be compatible with any metric. We also changed some default values of the scikit-learn algorithm in order to take into account every point of the dataset during the kernel density estimation, i.e. the default value of the parameter 'radius' is set to infinity instead of 1 and the default value of the parameter 'weight' is set to 'distance' instead of 'uniform'. Our main contribution is a greater choice of kernel functions, see the file in the learning directory. The radial kernel functions are now easier to define by a user: the input data should be an array of distances instead of an array of arrays. Moreover the new parameter 'bandwidth' of our classifier can be used to adapt the kernel function to the size of the dataset. The scikit-learn library also provides a kernel density estimation tool (see sklearn.neighbors.KernelDensity), however this algorithm is not built as a classifier and is not available with all metrics. Parameters ---------- space : Manifold Equipped manifold. radius : float, optional (default = inf) Range of parameter space to use by default. kernel : string or callable, optional (default = 'distance') Kernel function used in prediction. Possible values: - 'distance' : weight points by the inverse of their distance. In this case, closer neighbors of a query point will have a greater influence than neighbors which are further away. - 'uniform' : uniform weights. All points in each neighborhood are weighted equally. - [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights. bandwidth : float, optional (default = 1.0) Bandwidth parameter used for the kernel. The kernel parameter is used if and only if the kernel is a callable function. outlier_label : {manual label, 'most_frequent'}, optional (default = None) Label for outlier samples (samples with no neighbors in given radius). - manual label: str or int label (should be the same type as y) or list of manual labels if multi-output is used. - 'most_frequent' : assign the most frequent label of y to outliers. - None : when any outlier is detected, ValueError will be raised. n_jobs : int or None, optional (default = None) The number of parallel jobs to run for neighbors search. ``None`` means 1; ``-1`` means using all processors. Attributes ---------- classes_ : array-like, shape=[n_classes,] Class labels known to the classifier. effective_metric_ : string or callable The distance metric used. It will be same as the `distance` parameter or a synonym of it, e.g. 'euclidean' if the `distance` parameter set to 'minkowski' and `p` parameter set to 2. effective_metric_params_ : dict Additional keyword arguments for the distance function. For most distances will be same with `distance_params` parameter, but may also contain the `p` parameter value if the `effective_metric_` attribute is set to 'minkowski'. outputs_2d_ : bool False when `y`'s shape is [...,] or [..., 1] during fit, otherwise True. References ---------- This algorithm uses the scikit-learn library: sklearn.neighbors.RadiusNeighborsClassifier.html """ def __init__( self, space, radius=math.inf, kernel="distance", bandwidth=1.0, leaf_size=30, outlier_label=None, n_jobs=None, ): = space self.bandwidth = bandwidth if isinstance(kernel, str): weights = kernel else: def weights(distance_matrix): weights_matrix = gs.array( [ kernel(distance=dist, bandwidth=self.bandwidth) for dist in distance_matrix ] ) return weights_matrix self.kernel = kernel distance = wrap(space.metric.dist) super().__init__( radius=radius, weights=weights, algorithm="brute", leaf_size=leaf_size, metric=distance, outlier_label=outlier_label, n_jobs=n_jobs, )