Overview
Feature dimensions refers to the number of degrees of freedom that a sample datapoint has. In the standard case, a data point is represented by a vector
{% \vec{v} \in \mathbb{R}^n %}
That is, the vector would look like a
column vector
{%
\begin{bmatrix}
a \\
c \\
e \\
\end{bmatrix}
%}
Projection
An example of a dataset that spans 3 dimensions.The dataset can be reduced to two dimensions by just ignoring one dimension. The following shows the same dataset but graphed in only 2 dimensions
The result is effectively to remove one feature, or alternatively, setting it to zero. In this case, this is just projecting each point down to its shadow on the x-y plane. This type of transformation is often called a projection.
{% f(\begin{bmatrix}
x \\
y \\
z \\
\end{bmatrix}) \rightarrow \begin{bmatrix}
x \\
y \\
0 \\
\end{bmatrix} %}