Computational Resources
In the following discussion, let
| n = | number of observations in the training data set |
| v = | number of variables |
| c = | number of class levels |
| k = | number of canonical variables |
| l = | length of the CLASS variable |
Memory Requirements
The amount of temporary storage required depends on the discriminant
method used and the options specified. The least amount of temporary
storage in bytes needed to process the data is approximately
-
c(32v + 3l + 128) + 8v2 + 104v + 4l
A parametric method (METHOD=NORMAL) requires an
additional temporary memory of 12v2+100v bytes.
When you specify the CROSSVALIDATE option, this temporary
storage must be increased by 4v2+44v bytes.
When a nonparametric method (METHOD=NPAR) is used, an
additional temporary storage of 10v2+94v bytes is
needed if you specify METRIC=FULL to evaluate the distances.
With the MANOVA option, the temporary storage
must be increased by 8v2+96v bytes.
The CANONICAL option requires a temporary
storage of 2v2+94v+8k(v+c) bytes.
The POSTERR option requires a temporary
storage of 8c2+64c+96 bytes.
Additional temporary storage is also required for
classification summary and for each output data set.
For example, in the following statements,
proc discrim manova;
class gp;
var x1 x2 x3;
run;
if the CLASS variable gp has a length of eight and
the input data set contains two class levels, the
procedure requires a temporary storage of 1992 bytes.
This includes 1104 bytes for data processing,
480 bytes for using a parametric method, and
408 bytes for specifying the MANOVA option.
Time Requirements
The following factors determine the time
requirements of discriminant analysis.
- The time needed for reading the data and computing
covariance matrices is proportional to nv2.
PROC DISCRIM must also look up each class level in the list.
This is faster if the data are sorted by the CLASS variable.
The time for looking up class levels is proportional
to a value ranging from n to n ln(c).
- The time for inverting a covariance
matrix is proportional to v3.
- With a parametric method, the time required to classify
each observation is proportional to cv for a linear
discriminant function and is proportional to cv2
for a quadratic discriminant function.
When you specify the CROSSVALIDATE option,
the discriminant function is updated for
each observation in the classification.
A substantial amount of time is required.
- With a nonparametric method, the data are stored in a
tree structure (Friedman, Bentley, and Finkel 1977).
The time required to organize the observations into
the tree structure is proportional to nv ln(n).
The time for performing each tree
search is proportional to ln(n).
When you specify the normal KERNEL= option, all
observations in the training sample contribute to the
density estimation and more computer time is needed.
- The time required for the canonical
discriminant analysis is proportional to v3.
Each of the preceding factors has a different
machine-dependent constant of proportionality.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
