Mathematical Notations#
Notation |
Definition |
|---|---|
\(n\) or \(m\) |
The number of observations in a dataset. Typically \(n\) is used, but sometimes \(m\) is required to distinguish two datasets, e.g., the training set and the inference set. |
\(p\) or \(r\) |
The number of features in a dataset. Typically \(p\) is used, but sometimes \(r\) is required to distinguish two datasets. |
\(a \times b\) |
The dimensionality of a matrix (dataset) has \(a\) rows (observations) and \(b\) columns (features). |
\(|A|\) |
Depending on the context may be interpreted as follows:
|
\(\|x\|\) |
The \(L_2\)-norm of a vector \(x \in \mathbb{R}^d\),
\[\|x\| = \sqrt{ x_1^2 + x_2^2 + \dots + x_d^2 }.\]
|
\(\mathrm{sgn}(x)\) |
Sign function for \(x \in \mathbb{R}\),
\[\begin{split}\mathrm{sgn}(x)=\begin{cases}
-1, x < 0,\\
0, x = 0,\\
1, x > 0.
\end{cases}\end{split}\]
|
\(x_i\) |
In the description of an algorithm, this typically denotes the \(i\)-th feature vector in the training set. |
\(x'_i\) |
In the description of an algorithm, this typically denotes the \(i\)-th feature vector in the inference set. |
\(y_i\) |
In the description of an algorithm, this typically denotes the \(i\)-th response in the training set. |
\(y'_i\) |
In the description of an algorithm, this typically denotes the \(i\)-th response that needs to be predicted by the inference algorithm given the feature vector \(x'_i\) from the inference set. |