RenDim {IDmining} | R Documentation |
Renyi's Generalized Dimensions
Description
Estimates Rényi's generalized dimensions (or Rényi's dimensions of order). It is
mainly for
that the result is used as an estimate of the intrinsic dimension of data.
Usage
RenDim(X, scaleQ=1:5, qMin=2, qMax=2)
Arguments
X |
A |
scaleQ |
A vector (at least two values). It contains the values of |
qMin |
The minimum value of |
qMax |
The maximum value of |
Details
-
is the edge length of the grid cells (or quadrats). Since the variables (and consenquently the grid) are rescaled to the
interval,
is equal to
for a grid consisting of only one cell.
-
is the number of grid cells (or quadrats) along each axis of the Euclidean space in which the data points are embedded.
-
is equal to
where
is the number of grid cells and
is the number of variables (or features).
-
is directly related to
(see References).
-
is the diagonal length of the grid cells.
Value
A list of two elements:
a
data.frame
containing the value of Rényi's information oforder (computed using the natural logarithm) for each value of
and
. The values of
are provided with regard to the
interval.
a
data.frame
containing the value offor each value of
.
Author(s)
Jean Golay jeangolay@gmail.com
References
C. Traina Jr., A. J. M. Traina, L. Wu and C. Faloutsos (2000). Fast feature selection using fractal dimension. Proceedings of the 15th Brazilian Symposium on Databases (SBBD 2000), João Pessoa (Brazil).
E. P. M. De Sousa, C. Traina Jr., A. J. M. Traina, L. Wu and C. Faloutsos (2007). A fast and effective method to find correlations among attributes in databases, Data Mining and Knowledge Discovery 14(3):367-407.
J. Golay and M. Kanevski (2015). A new estimator of intrinsic dimension based on the multipoint Morisita index, Pattern Recognition 48 (12):4070–4081.
H. Hentschel and I. Procaccia (1983). The infinite number of generalized dimensions of fractals and strange attractors, Physica D 8(3):435-444.
Examples
sim_dat <- SwissRoll(1000)
scaleQ <- 1:15 # It starts with a grid of 1^E cell (or quadrat).
# It ends with a grid of 15^E cells (or quadrats).
qRI_ID <- RenDim(sim_dat[,c(1,2)], scaleQ[5:15])
print(paste("The ID estimate is equal to",round(qRI_ID[[1]][1,2],2)))