  Classification is the task of assigning a new instance to one of a set of
predefined categories based on the attributes of the instance. A classification
tree is one of the most commonly used techniques in the area of classification.
In this paper, we introduce a novel classification tree algorithm which we call
Direct Nonparametric Predictive Inference (D-NPI) classification algorithm. The
D-NPI algorithm is completely based on the Nonparametric Predictive Inference
(NPI) approach, and it does not use any other assumption or information. The
NPI is a statistical methodology which learns from data in the absence of prior
knowledge and uses only few modelling assumptions, enabled by the use of lower
and upper probabilities to quantify uncertainty. Due to the predictive nature
of NPI, it is well suited for classification, as the nature of classification
is explicitly predictive as well. The D-NPI algorithm uses a new split
criterion called Correct Indication (CI). The CI is about the informativity
that the attribute variables will indicate, hence, if the attribute is very
informative, it gives high lower and upper probabilities for CI. The CI reports
the strength of the evidence that the attribute variables will indicate, based
on the data. The CI is completely based on the NPI, and it does not use any
additional concepts such as entropy. The performance of the D-NPI
classification algorithm is tested against several classification algorithms
using classification accuracy, in-sample accuracy and tree size on different
datasets from the UCI machine learning repository. The experimental results
indicate that the D-NPI classification algorithm performs well in terms of
classification accuracy and in-sample accuracy.
