If most of the elements of the matrix have 0 value, then it is called a sparse matrix. The two major benefits of using sparse matrix instead of a simple matrix are:
- Storage: There are lesser non-zero elements than zeros and thus lesser memory can be used to store only those elements.
- Computing time: Computing time can be saved by logically designing a data structure traversing only non-zero elements.
Sparse matrices are generallyutilized in applied machine learning such as in data containing data-encodings that map categories to count and also in entire subfields of machine learning such as natural language processing [NLP].
Example:
0 0 3 0 4 0 0 5 7 0 0 0 0 0 0 0 2 6 0 0
Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases. So, instead of storing zeroes with non-zero elements, we only store non-zero elements. This means storing non-zero elements with triples- [Row, Column, value].
Create a Sparse Matrix in Python
Python’s SciPygives tools for creating sparse matrices using multiple data structures, as well as tools for converting a dense matrix to a sparse matrix. The function csr_matrix[] is used to create a sparse matrix of compressed sparse row format whereas csc_matrix[] is used to create a sparse matrix of compressed sparse column format.
# Usingcsr_matrix[]
Syntax:
scipy.sparse.csr_matrix[shape=None, dtype=None]
Parameters:
shape: Get shape of a matrix
dtype: Data type of the matrix
Example 1:
Python
import
numpy as np
from
scipy.sparse
import
csr_matrix
sparseMatrix
=
csr_matrix[[
3
,
4
],
dtype
=
np.int8].toarray[]
print
[sparseMatrix]
Output:
[[0 0 0 0] [0 0 0 0] [0 0 0 0]]
Example 2:
Python
import
numpy as np
from
scipy.sparse
import
csr_matrix
row
=
np.array[[
0
,
0
,
1
,
1
,
2
,
1
]]
col
=
np.array[[
0
,
1
,
2
,
0
,
2
,
2
]]
data
=
np.array[[
1
,
4
,
5
,
8
,
9
,
6
]]
sparseMatrix
=
csr_matrix[[data, [row, col]],
shape
=
[
3
,
3
]].toarray[]
print
[sparseMatrix]
Output:
[[ 1 4 0] [ 8 0 11] [ 0 0 9]]
# Usingcsc_matrix[]
Syntax:
scipy.sparse.csc_matrix[shape=None, dtype=None]
Parameters:
shape: Get shape of a matrix
dtype: Data type of the matrix
Example 1:
Python
import
numpy as np
from
scipy.sparse
import
csc_matrix
sparseMatrix
=
csc_matrix[[
3
,
4
],
dtype
=
np.int8].toarray[]
print
[sparseMatrix]
Output:
[[0 0 0 0] [0 0 0 0] [0 0 0 0]]
Example 2:
Python
import
numpy as np
from
scipy.sparse
import
csc_matrix
row
=
np.array[[
0
,
0
,
1
,
1
,
2
,
1
]]
col
=
np.array[[
0
,
1
,
2
,
0
,
2
,
2
]]
data
=
np.array[[
1
,
4
,
5
,
8
,
9
,
6
]]
sparseMatrix
=
csc_matrix[[data, [row, col]],
shape
=
[
3
,
3
]].toarray[]
print
[sparseMatrix]
Output:
[[ 1 4 0] [ 8 0 11] [ 0 0 9]]