In standard n-tuple
classifiers [2, 1]
the d-dimensional input space
is sampled by
m n-tuples. The range of each dimension in the general case is the
alphabet 
but most
n-tuple methods reported in the literature are defined over
a binary input space where 
and 
.
Each n-tuple defines a fixed set of locations in the input space. Let the set of locations defining the jth n-tuple be:
where each 
is chosen as a random integer in the specified range.
This mapping is normally the same
across all classes.
For a given d-dimensional input pattern 
an address 
may be calculated for each n-tuple mapping 
as shown in Equation 2.
These addresses are used to access memory elements, where there
is a memory 
for each class c in the set of all
classes C and n-tuple mapping . We denote the value
at location b in memory as 
.
The set of all memory values for all the n-tuple
mappings for a given class we denote 
, the model
for a given class.
The size of the address space of each memory is 
.
In standard n-tuple systems, each address location accesses
a single bit of information. The complete algorithm for training
a standard n-tuple classifier is given in Table 1,
and the recognition algorithm is given in Table 2.
X is the complete set of training
patterns while the subset of patterns of class c is
denoted as 
and 
is the
ith pattern in the cth class.
Training is performed by adjusting the values stored at each
address for each pattern in each
class, where all values are initially set to zero.
When an address is accessed by a pattern 
of class c under mapping
then 
is set to one.
For recognition the total output for each class is simply the sum of the outputs for each n-tuple in that class as shown in the fourth line of Step 2 in Table 2:
and the pattern is assigned to the class with the highest total output.
is a |C|-dimensional vector of real numbers 
