sparse_linear_binning: linear binning (optimized for sparsity)

Performs a linear binning technique described in Wand and Jones on a regularly-spaced grid in an arbitrary number of dimensions. The asymptotic behavior of this binning technique performs better than so-called simple binning (i.e. as in histograms). Each data point in d-dimensional space must have an associated weight (for equally weighted points just use a weight of 1.0 for each point).

For example, within a (segment of a) 2D grid with corners A, B, C, and D and a 2D data point P with weight wP:

A-----------------------------------B
|        |                          |
|                                   |
|        |                          |
|- - - - P- - - - - - - - - - - - - |
|        |                          |
D-----------------------------------C

• Assign a weight to corner A of the proportion of area between P and C (times wP)

• Assign a weight to corner B of the proportion of area between P and D (times wP)

• Assign a weight to corner C of the proportion of area between P and A (times wP)

• Assign a weight to corner D of the proportion of area between P and B (times wP)

Note that the under- and overflow bins need to be accounted for when specifying the numbers of grid points in each dimension (grid points act as bin centers). For instance, if you want grid points in steps of 0.1 in a range of [0,1] (i.e. (0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1)), specify the number of grid points to be 11. Internally, the grid points are stored in a high performance, C++-based hash table (sparsepp). This allows for finer binning in some circumstances because the hash table doesn’t allocates memory for grid points with near-zero weight. To accommodate arbitrary numbers of bins along each dimension, an arbitrary precision numeric library (boost multiprecision) may be used internally and will negatively impact performance. If this degradation in performance is unacceptable, consider reducing the number of grid points in such a way that the product of grid points in all dimensions is less than the numeric maximum of “unsigned long long” on your system. For instance, in 20 dimenisons with each dimension having 51 grid points gives a total of 14171098670753043575626125424226001 potential grid points at which point the arbitrary precision library must take care of all arithmetic related to determining grid points.

from sparse_linear_binning import sparse_linear_binning
import numpy as np

# generate one million random 2D points and weights
# (should take less than a second to bin)
n_samples=1000000
D=2

# coordinates, weights, and extents must be of type "double"
sample_coords = np.random.random(size=(n_samples, D))
sample_weights = np.random.random(size=n_samples)
extents = np.tile([0., 1.], D).reshape((D, 2))
n_bins = np.full(D, 51)

coords, weights = sparse_linear_binning(sample_coords, sample_weights,
                                        extents, n_bins)

# check that weights on grid match original weights
print(np.allclose(weights.sum(), sample_weights.sum()))