What is a Sparse Vector?

A sparse vector is a vector that contains mostly zeros, with only a few non-zero elements. It is a useful data structure for representing data that is mostly empty or has a lot of zeros. For example, if you have a vector of length 10,000 and only 10 elements are non-zero, then it is a sparse vector.

It is used in machine learning and data science when dealing with large datasets, as it can reduce the amount of memory needed to store the data. For example, if you have a dataset with millions of features where only a few features are important for each data point, you can represent it as a sparse vector, which will take up much less memory than a dense vector.

Sparse vectors can also be used in algorithms such as linear regression, where they can help reduce the computational complexity of the algorithm.