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, ...)


an object whose sparseness is computed.
extra arguments to allow extension


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.


  1. sparsenesssignature(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.

  2. sparsenesssignature(x = "matrix"): Computes the sparseness of a matrix as the mean sparseness of its column vectors. It returns a single numeric value.

  3. sparsenesssignature(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. .

See also

Other assess: entropy, purity