message: Add density estimator
diff: # - YYYY/MM Author: Description of the modification
  from .knn import KNN
  +import numpy as np
  class DTM:
  @@ -54,3 +55,68 @@ class DTM:
  # We compute too many powers, 1/p in knn then q in dtm, 1/q in dtm then q or some log in the caller.
  # Add option to skip the final root?
  return dtm
  +
  +
  +class DTMDensity:
  + """
  + Density estimator based on the distance to the empirical measure defined by a point set, as defined in :cite:`dtmdensity`. Note that this implementation does not renormalize so the total measure is not 1, see the reference for suitable normalization factors in the Euclidean case.
  + """
  +
  + def __init__(self, k=None, weights=None, q=None, dim=None, **kwargs):
  + """
  + Args:
  + k (int): number of neighbors (possibly including the point itself).
  + weights (numpy.array): weights of each of the k neighbors, optional.
  + q (float): order used to compute the distance to measure. Defaults to dim.
  + dim (float): final exponent representing the dimension. Defaults to the dimension, and must be specified when the dimension cannot be read from the input (metric="neighbors" or metric="precomputed").
  + kwargs: same parameters as :class:`~gudhi.point_cloud.knn.KNN`, except that metric="neighbors" means that :func:`transform` expects an array with the distances to the k nearest neighbors.
  + """
  + if weights is None:
  + assert k is not None, "Must specify k or weights"
  + self.k = k
  + self.weights = np.full(k, 1.0 / k)
  + else:
  + self.weights = weights
  + self.k = len(weights)
  + assert k is None or k == self.k, "k differs from the length of weights"
  + self.q = q
  + self.dim = dim
  + self.params = kwargs
  +
  + def fit_transform(self, X, y=None):
  + return self.fit(X).transform(X)
  +
  + def fit(self, X, y=None):
  + """
  + Args:
  + X (numpy.array): coordinates for mass points.
  + """
  + if self.params.setdefault("metric", "euclidean") != "neighbors":
  + self.knn = KNN(self.k, return_index=False, return_distance=True, sort_results=False, **self.params)
  + self.knn.fit(X)
  + return self
  +
  + def transform(self, X):
  + """
  + Args:
  + X (numpy.array): coordinates for query points, or distance matrix if metric is "precomputed", or distances to the k nearest neighbors if metric is "neighbors" (if the array has more than k columns, the remaining ones are ignored).
  + """
  + q = self.q
  + dim = self.dim
  + if dim is None:
  + assert self.params["metric"] not in {
  + "neighbors",
  + "precomputed",
  + }, "dim not specified and cannot guess the dimension"
  + dim = len(X[0])
  + if q is None:
  + q = dim
  + if self.params["metric"] == "neighbors":
  + distances = X[:, : self.k]
  + else:
  + distances = self.knn.transform(X)
  + distances = distances ** q
  + dtm = (distances * weights).sum(-1)
  + return dtm ** (-dim / q)
  + # We compute too many powers, 1/p in knn then q in dtm, d/q in dtm then whatever in the caller.
  + # Add option to skip the final root?
  