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Compute distances in numpy arrays with nans

Project description

Nandist: Calculating distances in arrays with missing values

The python library nandist enables (fast) computation of various distances in numpy arrays containing missing (NaN) values. These distances are implemented as a drop-in replacement for distance functions in the scipy.spatial.distance module.

The distance functions in nandist can be used as a drop-in replacement for the distance functions in scipy.spatial.distance. The library nandist offers replacements for all standalone distance functions in scipy and partial support for the fast pairwise distance calculating functions cdist and pdist.

Supported functions between two vectors

Supported "standalone" distance functions for calculating distances between two arrays (complete):

  • braycurtis
  • canberra
  • chebyshev
  • cityblock
  • cityblock
  • correlation
  • cosine
  • euclidean
  • jensenshannon
  • mahalanobis
  • minkowski
  • seuclidean
  • sqeuclidean

Supported functions between arrays of vectors

Supported functions for fast calculation of (pairwise) distances between multiple arrays (partial support for metrics):

  • cdist
  • pdist

Supported distance measures in cdist and pdist (passed as metric argument):

  • "chebyshev"
  • "cityblock"
  • "cosine"
  • "euclidean"
  • "minkowski"


Using pip:

pip install nandist


A simple example for calculating the cityblock distance between (0, 1) and (NaN, 0) is shown below.

>>> import nandist
>>> import scipy
>>> import numpy as np
>>> # City-block distance between  (0, 1) and (NaN, 0)
>>> u, v = np.array([0, 1]), np.array([np.nan, 0])
>>> scipy.spatial.distance.cityblock(u, v)
>>> nandist.cityblock(u, v)

You can replace the function cityblock by any of the supported distance functions.

You can get pairwise distances between arrays in two matrices using cdist. The NaNs do not need to be in the same component.

>>> import nandist
>>> import numpy as np

>>> # City-block distances between vectors A = [(0, 0), (1, NaN)] and vectors B=[(1, NaN) and (1, 1)]
>>> XA, XB = np.array([[0, 0], [1, np.nan]]), np.array([[1, np.nan], [1, 1]])
>>> Y = nandist.cdist(XA, XB, metric="cityblock")
array([[1., 2.],
       [0., 0.]])

Supported metrics

Supported distance metrics are:

  • Chebyshev: chebyshev, metric="chebyshev"
  • Cityblock: cityblock, metric="cityblock"
  • Cosine: cosine, metric="cosine"
  • Euclidean: euclidean, metric="euclidean"
  • Minkowski: minkowski, metric="minkowski"

If you require support for additional distance metrics, please submit an Issue or Merge Request.

How does it work

In nandist, the components where a vector is NaN will be ignored (interpreted as "any number") in the distance metric. This is achieved by replacing NaN values with zeros and correcting the resulting overestimated distance value. Under the hood, nandist calls functions from scipy.spatial.distance and then applies the corrections using numpy linear algebra. This ensures that the outcomes of nandist functions are equivalent to scipy.spatial.distance distance functions when arrays are passed without NaNs in them. In addition, all heavy computational lifting is done through scipy, requiring only the additional computational cost of applying the corrections.

Does it always work?

No. The package nandist performs a correction on an overestimation of the distances when missing values are imputed as zero. It is possible that this correction runs into the limits of floating point arithmetic. In that case, nandist will raise an appropriate error. However, you don't often run into these edge cases in typical usage.

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