Generic function that computes the sparseness of an object, as defined by Hoyer (2004). The sparseness quantifies how much energy of a vector is packed into only few components.
sparseness(x, ...)
usually a single numeric value -- in [0,1], or a numeric vector. See each method for more details.
In Hoyer (2004), the sparseness is defined for a real vector x as:
(srqt(n) - ||x||_1 / ||x||_2) / (sqrt(n) - 1)
, where n is the length of x.
The sparseness is a real number in [0,1].
It is equal to 1 if and only if x contains a single nonzero component,
and is equal to 0 if and only if all components of x are equal.
It interpolates smoothly between these two extreme values.
The closer to 1 is the sparseness the sparser is the vector.
The basic definition is for a numeric vector, and is extended for matrices as the
mean sparseness of its column vectors.
signature(x = "numeric"): Base method that computes the sparseness of a numeric vector.
It returns a single numeric value, computed following the definition given in section Description.
signature(x = "matrix"): Computes the sparseness of a matrix as the mean sparseness of its column vectors.
It returns a single numeric value.
signature(x = "NMF"): Compute the sparseness of an object of class NMF, as the sparseness of
the basis and coefficient matrices computed separately.
It returns the two values in a numeric vector with names ‘basis’ and ‘coef’.
Hoyer P (2004). "Non-negative matrix factorization with sparseness constraints." _The Journal of Machine Learning Research_,
*5*, pp. 1457-1469.