Matrices that have many values of zero are called **sparse**, and the matrices whose majority of values are non-zero are called **dense matrices**. The large Sparse Matrix is most common, especially when it comes to the applied machine learning techniques, like the data that contain counts, data encoding the map categories to counts, and the last but not the least, the subfield of the machine learning — natural language processing.

Sparse matrices are generally considered to be computationally a bit expensive to work with. However, they are dense, and much better performance can be achieved using representations that specifically handle the sparsity of the matrix. Throughout the blog, you will learn and discover what sparse matrices are, what are the issues between them, and how you could easily deal with them using Python.

## What is a Sparse Matrix?

A Sparse Matrix is a matrix that is generally comprised of the zero values, and are distinct from matrices that have non zero values, which are then called as a dense. The sparsity of the matrices can be quantified with the help of a score, which is again the numbers of zero values being divided by the total number of elements in the matrix.

## Problems with sparsity

The Sparse matrices can lead you to different kind of problems, especially in terms of space, time and complexity. Now let’s have a look at them in detail below.

### 1. The space complexity

It is believed that the larger matrices require a lot of memory, and some larger matrices that most wish to work with, are Sparse. One example of a smaller Sparse Matrix can be a word or team occurrence matrix for word in one book and against all the other words in English. In both these cases, the matrix contained here is Sparse containing many zero values than the data values. The problem that is further representing these sparses as the dense matrices, is a memory that is required and allocated for every 32 or 62-bit values in Matrix.

### 2. The time complexity

During the process of time complexity, it is generally assumed that a very large Sparse Matrix can fit into the memory, performing operations on the matrix. In case the matrix contains only zero values, then performing various actions across these operations can take a lot of time, and the bulk of computation performed will turn out to be adding or multiplying the zero values together.

## Sparse Matrices in Machine Learning

The Sparse Matrices tend to turn up a lot when it comes to applied machine learning. Through this section of the blog, we will now have a look at some of the best examples that would keep you aware of the issues related to sparse.

### Data

Sparse matrices generally come in the form of specific types of data, and most probably they are the observations that tend to record certain occurrences or count of a specific activity. One best example for this is whether the user had gone ahead and watched the movie in the movie catalog.

### The Data Preparation

Sparse matrices generally come up with the encoding schemes that are used in the preparation of a specific data. Say, for example, count coding that is used to represent the frequency of the words present in the vocabulary for a specific kind of a document.

### The Specific Areas of study

When it comes to the machine learning, it specializes some special kind of methods in order to address the sparsity directly as the data is almost or is always sparse. The best example for this could be the processing of natural language that is working with the documents of text.

## Sparse Matrices in Python

Scipy offers tools that help in creating tools for sparse matrices using multiple data structures, along with the tools that are used for converting a dense matrix or a sparse matrix. Most of the linear algebra Numpy and Scipy functions operate on Numpy and can also transparently operate on the Scipy sparse arrays. The machine learning libraries who use and operate Numpy can also operate on Scipy Sparse arrays like the scikit learning that is available for general machine learning and the key areas of deep learning.

We hope that throughout our blog post you understood what sparse matrix is, what are the issues that they represent and how do they directly need to work when it comes to the python software. Stay tuned to Magoosh data science blogs for more informative data science blogs!

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