  It has been a long time, since data mining technologies have made their ways
to the field of data management. Classification is one of the most important
data mining tasks for label prediction, categorization of objects into groups,
advertisement and data management. In this paper, we focus on the standard
classification problem which is predicting unknown labels in Euclidean space.
Most efforts in Machine Learning communities are devoted to methods that use
probabilistic algorithms which are heavy on Calculus and Linear Algebra. Most
of these techniques have scalability issues for big data, and are hardly
parallelizable if they are to maintain their high accuracies in their standard
form. Sampling is a new direction for improving scalability, using many small
parallel classifiers. In this paper, rather than conventional sampling methods,
we focus on a discrete classification algorithm with O(n) expected running
time. Our approach performs a similar task as sampling methods. However, we use
column-wise sampling of data, rather than the row-wise sampling used in the
literature. In either case, our algorithm is completely deterministic. Our
algorithm, proposes a way of combining 2D convex hulls in order to achieve high
classification accuracy as well as scalability in the same time. First, we
thoroughly describe and prove our O(n) algorithm for finding the convex hull of
a point set in 2D. Then, we show with experiments our classifier model built
based on this idea is very competitive compared with existing sophisticated
classification algorithms included in commercial statistical applications such
as MATLAB.
