What is "one-hot" encoding called in scientific literature? What is the name of the operator that takes a categorical vector and transforms it to the binary representation using one-hot encoding?
I am wondering since I am writing a scientific paper and need a proper name for that.
 A: It depends on your target audience.
As Tim said, statisticians call it dummy coding, and that's what I would expect to see when describing something like a regression model. "Dummy coded variables were included to adjust for the store's location." I think calling it a one-hot encoding would seem slightly strange here.
However, as another Tim also said, one-hot encoding is fairly common in the machine learning literature. It faintly implies the existence of nodes (as in a neural network), physical wires (in a device), or something like that, at least to me. 
Formally, I guess you are applying a set of indicator functions $\mathbb{I}_X$, but that's probably way too formal outside of a proof. 
A: The term comes from electronics engineering. Just think who would call 1 "hot"? Only those who work with electricity, where "hot" or "live" means there's electrical potential on the wire. "One hot" refers to the circuit design where discrete electrical signal level on one wire would be decoded into hot/cold on a set of wires. I suppose some machine learning folks with EE background found the analogy compelling.
In econometrics and statistics you may encounter dummy or indicator variables, which are quite similar because these are used to represent distinct categories with their distinct indicators. There's a subtle difference though. For instance, you make K-1 dummies for K categories, because the base category corresponds to all dummies set to 0. In contrast, I think that in one hot encoding you have K wires, where the base category will have its own wire (variable). 
A: I'm statistically trained, and have recently heard of "one-hot encoding" in machine learning/comp sci lit.  I've usually just referred to the one-hotted matrix as a design matrix/data matrix/design frame.
A: In physical sciences and engineering, it's called the (generalized) Kronecker delta.
In simplest form, the Kroneker delta's defined as $$
\begin{align*}
{\delta}_{i,j} {\equiv} 
\begin{cases}
1 &\text{if} & i=j \\
0 &\text{else}
\end{cases}
\end{align*},
$$though this trivially generalized to$$
\begin{align*}
{\delta}_{\left[\text{condition}\right]} {\equiv} 
\begin{cases}
1 &\text{if} & \left[\text{condition}\right] \\
0 &\text{else}
\end{cases}
\end{align*}.
$$
So, "${\delta}_{i{\in}\text{category}}$" will tend to be read as$$
\begin{align*}
{\delta}_{i{\in}\text{category}} {\equiv} 
\begin{cases}
1 &\text{if} & i{\in}\text{category} \\
0 &\text{else}
\end{cases}
\end{align*},
$$
which most authors would tend to truncate to "${\delta}_{i}$", if the category is obvious from context.
The Kronecker delta is really useful in Sigma/Pi/Einstein/etc. notations since it allows for terms to be specified conditionally.
Just to relate this to common programming structures, the Kronecker delta's condition?1:0, where ?: is the conditional operator.

As a tangential note, I'd encourage authors to abandon the old-fashion ${\delta}_{i,j}$ in favor of the generalized equivalent, ${\delta}_{i=j}$.  There's no advantage to the old-fashion notation, while the generalized notation's more explicit and extensible.
A: Pattern Recognition and Machine Learning by Christopher Bishop uses the term $1$-of-$K$ scheme. 
Here is a quote from the book,

Binary variables can be used to describe quantities that can take one of two possible values. Often, however, we encounter discrete variables that can take on one of $K$ possible mutually exclusive states. Although there are various alternative ways to express such variables, we shall see shortly that a particularly convenient representation is the $1$-of-$K$ scheme in which the variable is represented by a $K$-dimensional vector $\textbf{x}$ in which one of the elements $x_k$ equals $1$, and all remaining elements equal $0$. So, for instance if we have a variable that can take $K = 6$ states and a particular observation of the variable happens to correspond to the state where $x_3 = 1$, then $\textbf{x}$
  will be represented by,
$\textbf{x} = (0, 0, 1, 0, 0, 0)^{T}$

A: Statisticians call one-hot encoding as dummy coding. As others suggested (including Scortchi in the comments), this is not exact synonym, but this is the term that would be usually used for the 0-1 encoded categorical variables.
See also: "Dummy variable" versus "indicator variable" for nominal/categorical data 
