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Explain the concept of Sparse Vector

A sparse vector is represented by two parallel arrays: indices and values. Zero entries are not stored. A dense vector is backed by a double array representing its entries. For example, a vector [1., 0., 0., 0., 0., 0., 0., 3.] can be represented in the sparse format as (7, [0, 6], [1., 3.]), where 7 is the size of the vector, as illustrated below:

 it is best to represent the vector (a one-dimensional array of numbers) as a sparse vector to maximise storage and computing efficiency.They are a crucial concept in many fields, allowing efficient handling of data with a significant number of zero elements.

Take the Python API as an example. MLlib recognizes the following types as dense vectors:

• NumPy’s array,
• Python’s list, e.g., [1, 2, 3].

and the following as sparse vectors:

• MLlib’s SparseVector,
• SciPy’s csc_matrix with a single column.

We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented in Vectors to create sparse vectors.

Below is example of sparse vector :

import scipy.sparse as sp

# Create a sparse vector using CSR format
sparse_vector = sp.csr_matrix((data, indices, indptr), shape=(1, n))

Conclusion :

In conclusion, sparse vectors are a mathematical representation that optimises memory use by only storing non-zero elements, making them suitable for dealing with high-dimensional data and enhancing computing performance in particular processes..A sparse vector is a mathematical and computational concept used to represent a vector (a one-dimensional array of numbers) in a way that optimizes storage and computational efficiency.