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.
an object whose sparseness is computed.
extra arguments to allow extension
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
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
usually a single numeric value – in [0,1], or a numeric vector. See each method for more details.
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
signature(x = "NMF"): Compute
the sparseness of an object of class
NMF, as the
sparseness of the basis and coefficient matrices computed
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. <URL: http://portal.acm.org/citation.cfm?id=1044709>.
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