sparseness | R Documentation |

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, ...)

`x` |
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
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.

usually a single numeric value – in [0,1], or a numeric vector. See each method for more details.

- 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 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. <URL: http://portal.acm.org/citation.cfm?id=1044709>.

Other assess: `entropy`

, `purity`

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