How to calculate percentage of sparsity for a numpy array/matrix?
Solution 1
np.isnan(a).sum()
gives the number of nan
values, in this example 8.
np.prod(a.shape)
is the number of values, here 50. Their ratio should give the desired value.
In [1081]: np.isnan(a).sum()/np.prod(a.shape)
Out[1081]: 0.16
You might also find it useful to make a masked array from this
In [1085]: a_ma=np.ma.masked_invalid(a)
In [1086]: print(a_ma)
[[0.0 0.0 0.0 0.0 1.0]
[1.0 1.0 0.0 -- --]
[0.0 -- 1.0 -- --]
[1.0 1.0 1.0 1.0 0.0]
[0.0 0.0 0.0 1.0 0.0]
[0.0 0.0 0.0 0.0 --]
[-- -- 1.0 1.0 1.0]
[0.0 1.0 0.0 1.0 0.0]
[1.0 0.0 1.0 0.0 0.0]
[0.0 1.0 0.0 0.0 0.0]]
The number of valid values then is:
In [1089]: a_ma.compressed().shape
Out[1089]: (42,)
Solution 2
Definition:
Code for a general case:
from numpy import array
from numpy import count_nonzero
import numpy as np
# create dense matrix
A = array([[1, 1, 0, 1, 0, 0], [1, 0, 2, 0, 0, 1], [99, 0, 0, 2, 0, 0]])
#If you have Nan
A = np.nan_to_num(A,0)
print(A)
#[[ 1 1 0 1 0 0]
# [ 1 0 2 0 0 1]
# [99 0 0 2 0 0]]
# calculate sparsity
sparsity = 1.0 - ( count_nonzero(A) / float(A.size) )
print(sparsity)
Results:
0.555555555556
Solution 3
Measuring the percentage of missing values has already explained by 'hpaulj'.
I am taking the first part of your question, Assuming array has Zero's and Non-Zero's...
Sparsity refers to Zero values and density refers to Non-Zero values in array. Suppose your array is X, get count of non-zero values:
non_zero = np.count_nonzero(X)
total values in X:
total_val = np.product(X.shape)
Sparsity will be -
sparsity = (total_val - non_zero) / total_val
And Density will be -
density = non_zero / total_val
The sum of Sparsity and Density must equal to 100%...
ShanZhengYang
Updated on June 14, 2022Comments
-
ShanZhengYang almost 2 years
I have the following 10 by 5 numpy array/matrix, which has a number of
NaN
values:array([[ 0., 0., 0., 0., 1.], [ 1., 1., 0., nan, nan], [ 0., nan, 1., nan, nan], [ 1., 1., 1., 1., 0.], [ 0., 0., 0., 1., 0.], [ 0., 0., 0., 0., nan], [ nan, nan, 1., 1., 1.], [ 0., 1., 0., 1., 0.], [ 1., 0., 1., 0., 0.], [ 0., 1., 0., 0., 0.]])
How does one measure exactly how sparse this array is? Is there a simply function in numpy for measuring the percentage of missing values?
-
ShanZhengYang over 5 yearsThanks for this! This is helpful
-
Mohit Pandey over 4 yearsIf A_sparse is a sparse matrix, then correct expression is
sparsity = 1.0 - ( A_sparse.count_nonzero() / float(A_sparse.toarray().size) )
. Using float(A_sparse.size) would give incorrect sparsity of 0 for all sparse matrices. -
Mohit Pandey over 4 yearsActually float(A.toarray().size) and float(A.size) is not same if A is a sparse matrix. This is so because size for a sparse matrix gives the number of entries corresponding to non-zero elements. Also, np.prod(A_sparse.shape) is better than using A_sparse.toarray().size because the later one involves an computationally expensive step of converting a sparse matrix to dense martix.