What is a subspace and what is a shared subspace? I'm totally new in machine learning. The first confusing concept is subspace. In multi label classification we have to share the subspace. What does one mean by that shared sub spaces?
I don't know what you mean by "In multi label classification we have to share the subspace.", but the concept of subspaces is fairly easy to explain.


  In mathematics, a space is a set (sometimes called a universe) with some added structure.


Source: Wikipedia

The most common spaces are $\mathbb{R}$ (the number line), $\mathbb{R}^2$ (the plane) and $\mathbb{R}^3$ (the space we often think in, with $x,y,z$ axes). Lets assume our main space is $\mathbb{R}^3$. Our data are datapoints in this space. However, we have to write a report. This report has to be printed on paper. Hence we project the data points from a 3-dimensional space to a two-dimensional subspace. So a subspace is just a part of the original space.