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scipy.spatial.

# KDTree

class scipy.spatial.KDTree(data, leafsize=10, compact_nodes=True, copy_data=False, balanced_tree=True, boxsize=None)

  kd-tree for quick nearest-neighbor lookup.

  This class provides an index into a set of k-dimensional points which can be used to rapidly look up the nearest neighbors of any point.

  Parameters:
    data array_like, shape (n,m)

      The n data points of dimension m to be indexed. This array is not copied unless this is necessary to produce a contiguous array of doubles, and so modifying this data will result in bogus results. The data are also copied if the kd-tree is built with copy_data=True.

    leafsize positive int, optional

      The number of points at which the algorithm switches over to brute-force. Default: 10.

    compact_nodes bool, optional

      If True, the kd-tree is built to shrink the hyperrectangles to the actual data range. This usually gives a more compact tree that is robust against degenerated input data and gives faster queries at the expense of longer build time. Default: True.

    copy_data bool, optional

      If True the data is always copied to protect the kd-tree against data corruption. Default: False.

    balanced_tree bool, optional

      If True, the median is used to split the hyperrectangles instead of the midpoint. This usually gives a more compact tree and faster queries at the expense of longer build time. Default: True.

    boxsize array_like or scalar, optional

      Apply an m-d toroidal topology to the KDTree. The topology is generated by \(x_i + n_i L_i\) where \(n_i\) are integers and \(L_i\) is the boxsize along i-th dimension. The input data shall be wrapped into \([0, L_i)\). A ValueError is raised if any of the data is outside of this bound.

  Attributes:
    data ndarray, shape (n,m)

      The n data points of dimension m to be indexed. This array is not copied unless this is necessary to produce a contiguous array of doubles. The data are also copied if the kd-tree is built with `copy_data=True`.

    leafsize positive int

      The number of points at which the algorithm switches over to brute-force.

    m int

      The dimension of a single data-point.

    n int

      The number of data points.

    maxes ndarray, shape (m,)

      The maximum value in each dimension of the n data points.

    mins ndarray, shape (m,)

      The minimum value in each dimension of the n data points.

    size int

      The number of nodes in the tree.

  Methods

  `count_neighbors`(other, r[, p, weights, ...]) | Count how many nearby pairs can be formed.
  `query`(x[, k, eps, p, distance_upper_bound, ...]) | Query the kd-tree for nearest neighbors.
  `query_ball_point`(x, r[, p, eps, workers, ...]) | Find all points within distance r of point(s) x.
  `query_ball_tree`(other, r[, p, eps]) | Find all pairs of points between self and other whose distance is at most r.
  `query_pairs`(r[, p, eps, output_type]) | Find all pairs of points in self whose distance is at most r.
  `sparse_distance_matrix`(other, max_distance) | Compute a sparse distance matrix.

  innernode |
  leafnode |
  node |

  Notes

  The algorithm used is described in [1]. The general idea is that the kd-tree is a binary tree, each of whose nodes represents an axis-aligned hyperrectangle. Each node specifies an axis and splits the set of points based on whether their coordinate along that axis is greater than or less than a particular value.

  During construction, the axis and splitting point are chosen by the “sliding midpoint” rule, which ensures that the cells do not all become long and thin.

  The tree can be queried for the r closest neighbors of any given point (optionally returning only those within some maximum distance of the point). It can also be queried, with a substantial gain in efficiency, for the r approximate closest neighbors.

  For large dimensions (20 is already large) do not expect this to run significantly faster than brute force. High-dimensional nearest-neighbor queries are a substantial open problem in computer science.

  References

  [1]

  S. Maneewongvatana and D.E. Mount, “Analysis of approximate nearest neighbor searching with clustered point sets,” Arxiv e-print, 1999, https://arxiv.org/pdf/cs.CG/9901013