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×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: If A is a set, this denotes its cardinality, i.e., the number of elements in the set A. If A is a real number, this denotes an absolute value of A.
‖x‖	The L2-norm of a vector x∈Rd, ‖x‖=√x21+x22+⋯+x2d.
sgn(x)	Sign function for x∈R, sgn(x)={−1,x<0,0,x=0,1,x>0.
xi	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.
yi	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.