Does 'sparse' mean different in sparse feature & sparse representation? In Google developers site, the meaning of the word sparse seems to contradict between the following two definitions:

*

*sparse feature:


Feature vector whose values are predominately zero or empty...



*sparse representation:


A representation of a tensor that only stores nonzero elements...


Can someone please help me make better sense out of this?

In a sparse array, the thing that is sparse is the storage: only nonzero elements are stored.
The two arrays in OP's question have the exact same number of 0s. The purpose of the image in the question is to illustrate that the dense array stores more than 900,000 entries, with nearly all of them 0, while the sparse array only stores the 3 non-zero entries. The absent entries are implicitly known to be 0 because their cells aren't stored in the sparse array.
A sparse array isn't much different than making a grocery list: you could either write down a sparse representation:

*

*butter

*eggs

*milk

or you could write down a dense representation:

*

*butter: 1

*cereal: 0

*eggs: 1

*lime: 0

*mango: 0

*soup: 0

*steak: 0

*...and so on, for every other item in the grocery store.

The "sparse grocery list" is going to be easier to read and understand. Likewise, a sparse array (tensor, matrix, vector) can be more economical to work with (less memory, some math operations are more efficient) than a dense array.
