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 xRd,

x=x12+x22++xd2.

sgn(x)

Sign function for xR,

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.

xi

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.

yi

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 xi from the inference set.