# Representing data using graphs: A sparse signal approximation view

** Published:**

## Why do we need to represent data using graphs?

Graph driven machine learning has seen a surge of interest in the past few years with several applications in social sciences, biology, and network analysis, to name a few.

However, in some scenarios, no graph is given a priori and one has to *infer and construct* a graph to fit the data given. These graphs are useful for a few reasons:

- Unlike machine learning methods that learn a function to each point, one can leverage explicitly the information across points to obtain
*better*functions over regions of space. - Allows one to characterize data under minimal assumptions for use in semi-supervised and unsupervised learning scenarios

In a typical graph learning problem, we are given *N* data points and the goal is to learn an *efficient* graph representation of the data. The keyword here is efficient: An efficient graph can be defined as one with number of edges of the same order as the number of nodes (*N*). Efficient graphs lead to faster downstream processing making them