1 files changed, 109 insertions, 0 deletions
diff --git a/src/python/gudhi/point_cloud/dtm.py b/src/python/gudhi/point_cloud/dtm.py
index 13e16d24..55ac58e6 100644
--- a/src/python/gudhi/point_cloud/dtm.py
+++ b/src/python/gudhi/point_cloud/dtm.py
@@ -8,6 +8,7 @@
 #   - YYYY/MM Author: Description of the modification
 
 from .knn import KNearestNeighbors
+import numpy as np
 
 __author__ = "Marc Glisse"
 __copyright__ = "Copyright (C) 2020 Inria"
@@ -68,3 +69,111 @@ class DistanceToMeasure:
         # 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 only renormalizes when asked, and the renormalization
+    only works for a Euclidean metric, so in other cases the total measure may not be 1.
+
+    .. note:: When the dimension is high, using it as an exponent can quickly lead to under- or overflows.
+        We recommend using a small fixed value instead in those cases, even if it won't have the same nice
+        theoretical properties as the dimension.
+    """
+
+    def __init__(self, k=None, weights=None, q=None, dim=None, normalize=False, n_samples=None, **kwargs):
+        """
+        Args:
+            k (int): number of neighbors (possibly including the point itself). Optional if it can be guessed
+                from weights or metric="neighbors".
+            weights (numpy.array): weights of each of the k neighbors, optional. They are supposed to sum to 1.
+            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 is "neighbors" or "precomputed").
+            normalize (bool): normalize the density so it corresponds to a probability measure on ℝᵈ.
+                Only available for the Euclidean metric, defaults to False.
+            n_samples (int): number of sample points used for fitting. Only needed if `normalize` is True and
+                metric is "neighbors".
+            kwargs: same parameters as :class:`~gudhi.point_cloud.knn.KNearestNeighbors`, except that
+                metric="neighbors" means that :func:`transform` expects an array with the distances to
+                the k nearest neighbors.
+        """
+        if weights is None:
+            self.k = k
+            if k is None:
+                assert kwargs.get("metric") == "neighbors", 'Must specify k or weights, unless metric is "neighbors"'
+                self.weights = None
+            else:
+                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
+        self.normalize = normalize
+        self.n_samples = n_samples
+
+    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 = KNearestNeighbors(
+                self.k, return_index=False, return_distance=True, sort_results=False, **self.params
+            )
+            self.knn.fit(X)
+            if self.params["metric"] != "precomputed":
+                self.n_samples = len(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
+        k = self.k
+        weights = self.weights
+        if self.params["metric"] == "neighbors":
+            distances = np.asarray(X)
+            if weights is None:
+                k = distances.shape[1]
+                weights = np.full(k, 1.0 / k)
+            else:
+                distances = distances[:, :k]
+        else:
+            distances = self.knn.transform(X)
+        distances = distances ** q
+        dtm = (distances * weights).sum(-1)
+        if self.normalize:
+            dtm /= (np.arange(1, k + 1) ** (q / dim) * weights).sum()
+        density = dtm ** (-dim / q)
+        if self.normalize:
+            import math
+
+            if self.params["metric"] == "precomputed":
+                self.n_samples = len(X[0])
+            # Volume of d-ball
+            Vd = math.pi ** (dim / 2) / math.gamma(dim / 2 + 1)
+            density /= self.n_samples * Vd
+        return density
+        # 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?