| sparseness {NMF} | R Documentation |
Sparseness
Description
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.
Usage
sparseness(x, ...)
Arguments
x |
an object whose sparseness is computed. |
... |
extra arguments to allow extension |
Details
In Hoyer (2004), the sparseness is defined for a
real vector x as:
Sparseness(x) =
\frac{\sqrt{n} - \frac{\sum |x_i|}{\sqrt{\sum
x_i^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.
Value
usually a single numeric value – in [0,1], or a numeric vector. See each method for more details.
Methods
- sparseness
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.
- sparseness
signature(x = "matrix"): Computes the sparseness of a matrix as the mean sparseness of its column vectors. It returns a single numeric value.- sparseness
signature(x = "NMF"): Compute the sparseness of an object of classNMF, 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’.
References
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>.