E = edge(tree,X,Y)
E = edge(tree,X,Y,Name,Value)
returns
the classification edge for E
= edge(tree
,X
,Y
)tree
with data X
and
classification Y
.
computes
the edge with additional options specified by one or more E
= edge(tree
,X
,Y
,Name,Value
)Name,Value
pair
arguments.

A classification tree created by 

A matrix where each row represents an observation, and each
column represents a predictor. The number of columns in 

Class labels, with the same data type as exists in 
Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.

Observation weights, a numeric vector of length Default: 

The edge, a scalar representing the weighted average value of the margin. 
The classification margin is the difference
between the classification score for the true
class and maximal classification score for the false classes. Margin
is a column vector with the same number of rows as the matrix X
.
For trees, the score of a classification of a leaf node is the posterior probability of the classification at that node. The posterior probability of the classification at a node is the number of training sequences that lead to that node with the classification, divided by the number of training sequences that lead to that node.
For example, consider classifying a predictor X
as true
when X
< 0.15
or X
> 0.95
, and X
is
false otherwise.
Generate 100 random points and classify them:
rng(0,'twister') % for reproducibility X = rand(100,1); Y = (abs(X  .55) > .4); tree = fitctree(X,Y); view(tree,'Mode','Graph')
Prune the tree:
tree1 = prune(tree,'Level',1); view(tree1,'Mode','Graph')
The pruned tree correctly classifies observations that are less
than 0.15 as true
. It also correctly classifies
observations from .15 to .94 as false
. However,
it incorrectly classifies observations that are greater than .94 as false
.
Therefore, the score for observations that are greater than .15 should
be about .05/.85=.06 for true
, and about .8/.85=.94
for false
.
Compute the prediction scores for the first 10 rows of X
:
[~,score] = predict(tree1,X(1:10)); [score X(1:10,:)]
ans = 0.9059 0.0941 0.8147 0.9059 0.0941 0.9058 0 1.0000 0.1270 0.9059 0.0941 0.9134 0.9059 0.0941 0.6324 0 1.0000 0.0975 0.9059 0.0941 0.2785 0.9059 0.0941 0.5469 0.9059 0.0941 0.9575 0.9059 0.0941 0.9649
Indeed, every value of X
(the rightmost
column) that is less than 0.15 has associated scores (the left and
center columns) of 0
and 1
,
while the other values of X
have associated scores
of 0.91
and 0.09
. The difference
(score 0.09
instead of the expected .06
)
is due to a statistical fluctuation: there are 8
observations
in X
in the range (.95,1)
instead
of the expected 5
observations.
The edge is the weighted mean value of
the classification margin. The weights are the class probabilities
in tree
.Prior
. If you supply
weights in the weights
namevalue pair, those weights
are normalized to sum to the prior probabilities in the respective
classes, and are then used to compute the weighted average.
Compute the classification margin and edge for the Fisher iris data, trained on its first two columns of data, and view the last 10 entries:
load fisheriris
X = meas(:,1:2);
tree = fitctree(X,species);
E = edge(tree,X,species)
E =
0.6299
M = margin(tree,X,species);
M(end10:end)
ans = 0.1111 0.1111 0.1111 0.2857 0.6364 0.6364 0.1111 0.7500 1.0000 0.6364 0.2000
The classification tree trained on all the data is better.
tree = fitctree(meas,species); E = edge(tree,meas,species) E = 0.9384 M = margin(tree,meas,species); M(end10:end)
ans = 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565 0.9565