Mathematical Notations of Machine Learning

notations가 헷갈려서 정리.. 생각날때마다 업뎃. 단순한 notations간 category 분류만을 위한 포스트이다.

Most of the notations based on the book title "Pattern Recognition and Machine Learning"

vector	(column vector, basic vector form)	행벡터, 벡터의 기본 형태.
	(row vector)	열벡터  row vector with M elements If we have N  values  of a D-dimensional vector  we can combine the observations into a data matrix X in which the row of X corresponds to the row vector  Thus the n, i  element of X(matrix) corresponds to the element of the observation  For the case of one-dimensional variables we shall denote such a matrix by x, which is a column vector whose element is  Note that X (a matrix which has dimensionality N) uses a different typeface to distinguish it from x (a vector which has dimensionality D)
interval		the closed interval from a to b, this is the interval including the values a and b themselves.
		denotes an interval that includes a but excludes b
identity  matrix		M by M identity Matrix (also known as the unit matrix) which will be abbreviated to I  where there is no ambiguity about it dimensionality.
functional		A functional's notation. where y(x) is some function.  functional은 function을 return하는 것을 말한다.
		denotes that  is bounded as   for instance if , then
expectation		The expectation of a function  with respect to a random variable  is denoted by   In situations where there is no ambiguity as to which variable is being averaged over, this will be simplified by omitting the suffix, for instance
		If the distribution of x is conditioned on another variable z, then the corresponding conditional expectation will be written
variance		Similarly, the variance is denoted
covariance		for vector variables the covariance   : shorthand notation of

(Delta)	Dirac delta  (디랙 델타)    continuous한 x일 경우	x가 0일때 무한대로 가며, x가 0이 아닐때 0을 반환한다.	디랙 델타
	Kronecker Delta  (크로네커 델타) discrete한 i,j일때 쓰임	i = j 일때 1, i가 j와 같지 않을 때 0이 된다. (주로 identity matrix 를 나타낼때 많이 쓰이는 듯 하다. 기타 identity matrix의 notation으로는 , 가 있다.)	크로네커 델타
	Linear Transformation	Linear Transformation :  L(v)라는 function이 있는데, vector input을 linear transform을 한 vector output을 낸다.
	Loss Function	말 그대로 Loss를 측정하는 function