Data representation

Vector spaces are relevant in most Data Science problems where a dataset arranged in rows and columns (rows are data, columns are attributes). From this, we can picture that a dataset is an mxn matrix. To be short you can approximate any point in your data as a linear combination of some vectors, a base of a vector space. The choice of base depends on the problem you are trying to solve, different algorithms create different bases for example algorithms such as SVD/PCA, ICA, NMF and K-Means will create different bases.

So from the point of view of Data Science a vector space creates a representation of data from the point of view of a given base and thus it’s a very powerful and important concept.