Introduction to Sparse Matrix in Python
The following article is an overview of the Python library’s Sparse Matrix package. If the majority of the values in a matrix are 0, we call that kind of matrix a sparse matrix. It has widespread use in the field of machine learning, particularly for the encoding of data, as well as in other areas, such as natural language processing. The ability to store more data and reduce the amount of time spent processing are two of the primary benefits of using a sparse matrix. Since the vast majority of the values are zero, it requires just a little amount of memory and can be quickly calculated by developing a data structure that searches exclusively for values that are not zero. The Syntax Behind a Sparse Matrix
A good illustration of a sparse matrix is the one that is shown below:
0 0 5 0 9 0 0 0 7 0 0 0 0 0 0 0 1 7 0 0
The degree to which a matrix is sparse may be determined by using the following formula: sparsity = (number of zeros) / size of the matrix
In the example that was just given, it has fifteen values of zero. As a result, the sparsity of the matrix is 0.75, which is equivalent to 75%. If there are just a few nonzero values in the matrix, then the sparse matrix is generally regarded to be the most effective data format for storing of the matrix.
There are seven distinct varieties of sparse matrices, which are as follows:
available.
 Block Sparse Matrix(bsr)
 Coordinate Format Matrix(coo)
 Compressed Space Column Matrix(csc)
 Compressed Space Row Matrix(csr)
 Sparse Matrix With Diagonal Storage(dia)
 Dictionary Of Keys Based Sparse Matrix(dok)
 Linked List Sparse Matrix(lil)
Choosing the Right Sparse Matrix Type
 It is very important to know when to use which type of sparse matrix. Choosing the right matrix only will make the operation more efficient.
 Whenever a new sparse matrix must be built from the bottom, then it is advisable to use either a Linked list sparse matrix or dictionary of keys matrix.
 These two matrices are, however, not efficient for doing arithmetic calculations.
 Whenever there is a need for multiplication or traverse compressed space column of a compressed space row would be the best option; while the former is efficient in slicing columns, the latter is used for efficiently slicing rows.
Drawbacks of Sparse Matrix
The following are the two most significant disadvantages of using a sparse matrix.
These are the complexities of time and place.
complexity.
1. Space Complexity
In instances taken from actual life, the vast majority of the matrices are sparse. A significant amount of memory is necessary in order to store a large matrix, particularly a link matrix, which displays connections between different websites. The comparison of the frequency with which a word appears in a book to the total number of words in a language is an example of a more specific kind of matrix. In both scenarios, the outcome of the matrix is likely to be somewhat close to zero, and memory will need to be reserved for it.
all.
2. Time Complexity
Even though the result of the vast majority of matrix operations is going to be zero, the operations performed on sparse matrices, such as the addition or multiplication of two sparse matrices, can take a significant amount of time. The magnitude of this issue is directly proportional to the size of the matrix. This is compounded by the fact that every approach to machine learning involves performing an operation on each row and column, which results in a longer time to complete the task. Examples of a sparse matrix taken from realworld situations:
 If a user has watched at least one movie from the movie catalog.
 If a user has purchased any product listed in the product catalog.
 The number of times a song is listened to in a song catalog.
 Natural language processing for manipulating text documents.
 Recommendations for products in a product catalog.
 When working with a large number of images which has lots of black pixels.
 Normalize scores of word frequency in a dictionary.
Examples of Sparse Matrix in Python
The examples of sparse matrices that can be found in are given below:
Python:
Example #1
Code:
print("demo of sparse matrix in python")
Output:
print("creating and printing csr matrix")
import numpy as num
from scipy.sparse import csr_matrix,csc_matrix
csrmatrixeg = csr_matrix((3, 2),dtype = num.int8).toarray()
print(csrmatrixeg)
print("next sparse matrix")
r= num.array([0, 1, 0, 2, 2, 0])
c = num.array([0, 0, 2, 0, 0, 2])
d = num.array([1, 2, 5, 7, 9, 3])
op= csr_matrix((d, (r, c)), shape = (3, 4)).toarray()
print(op)
print("demo of creating csc matrix in pyuthon")
egmat = csc_matrix((3, 5),dtype = num.int8).toarray()
print(egmat)
r1= num.array([0, 0, 0, 2, 2, 0])
c1 = num.array([0, 0, 1, 0, 0, 0])
d1 = num.array([1, 2, 0, 0, 9, 3])
op1= csc_matrix((d, (r, c)), shape = (4, 4)).toarray()
print(op1)
Example #2
Code:
print("demo of sparse matrix in python")
Output:
print("creating and printing c00 matrix")
import numpy as num
from scipy.sparse import coo_matrix
coomateg = coo_matrix((3, 2),dtype = num.int8).toarray()
print(coomateg)
print("ooo sparse matrix")
r= num.array([0, 1, 0, 2, 2, 0])
c = num.array([0, 0, 2, 0, 0, 2])
d = num.array([1, 2, 5, 7, 9, 3])
op= coo_matrix((d, (r, c)), shape = (3, 4)).toarray()
print(op)
When working with a sparse matrix, it is necessary to take into consideration an alternative data structure. For instance, only the values that are not zero should be taken into consideration, and the zeros should be disregarded.
There are a great number of data structures like this one.
follows:

Dictionary:
Here, a value is mapped by the intersection of a row and column. 
List of Lists:
Here, a list is used to store a matrix, and a sub list is used to store the value and column of the list. 
Coordinate List:
Matrix is stored as a list of tuples with the values of the tuple being row and column index along with the corresponding value.
In addition to compressed sparse rows and columns, compressed sparse rows and columns are two other data structures that are utilized frequently. However, because it allows for the multiplication of matrices, compressed space row is utilized more frequently in the field of machine learning.