g

p

g

y search because the use of every partitioning rule divides a space

subspaces [Shapiro and Haralick, 1982]. This kind of learning

s still in use for biological/medical pattern analysis, such as the

A copy number data analysis [Ruan, et al., 2019].

e 3.37 shows the use of this binary search strategy. In Figure

ither the partitioning rule y = 2 or the partitioning rule y = 0 can

e whole space into two parts, i.e., two subspaces. After each

the data points of the whole space are sent to two subspaces. Some

ts distribute in the upper panel subspace and others distribute in the

nel subspace. The classification performance of these two partitions

on the outcome of how data points are distributed in two subspaces.

y, the upper panel in Figure 3.37(a) shows a great mixture of data

om two classes when using the partitioning rule y = 0. But the

ng rule y = 2 in Figure 3.37(a) generates two subspaces which are

an or pure to a single class, i.e., either subspace has a very limited

f data points from two classes.

ure 3.37(b), the partitioning rule y = 0 certainly does not help to

two classes of data points into two pure subspaces. Two more

ng rules x = 0 and x = 3 are therefore included into the decision-

ystem in addition to the partitioning rule y = 0 to make four

s for the classification of the data points. After this data space has

l-divided into four subspaces, data points can be well classified.

(a) (b)

Fig. 3.37. An illustration of the rule of divide and conquer.