Alladi Ramakrishnan Hall

On New Algorithms for AI and Neural Network Research

Kumar Eswaran

Department of Computer Science, Sreenidhi Institute of Science and Technology, Yamnampet, Ghatkesar, Hyderabad

In every classification problem it is necessary to separate clusters of
points, in feature space (of say d-dimensions) belonging to a particular
class, from other clusters which belong to other classes by hyper planes.
This has been the aim of neural network researchers and deep learning
researchers. Statisticians, traditionally use probabilistic techniques
(multivariate methods) assuming clusters to be be ellipsoids and perform
principle component analysis. However, the task of separating one cluster
of points (belonging to one class) from another cluster of points belonging
to another class, has not been easy because clusters are ill defined
objects in n-dimension space and can have any odd shape, even snake-like
and dragon like configurations. Since a point is a well define geometrical
object it serves well to begin tackling the problem at the point level.

We thus describe an alternative approach: We first separate all points
from one another i.e. we separate EACH POINT from one another by hyper
planes. We have discovered a non-iterative algorithm which does this in O(N
logN) time,**, N being the number of points. The number of planes, q,
required is around O(logN), for large d-dimension space. After this, we
apply a new "Cluster Discovery" algorithm, which uses the information
already available (the coefficients of the hyper planes). The aim of this
second algorithm is to examine all the "training data" and place those
points which belong to the same class in "bubbles" ie. small spherical
clusters, which can always be done. We discover small spherical clusters
by this algorithm. It so turns out that most of the existing planes already
separate most of these clusters from one another, to separate the few that
are not separated we add a few more planes. Now since the clusters are
known and are separated by hyper planes whose coefficients are known, the
neural network architecture is completely known (with its weights). This
method being non iterative gives a Neural architecture very quickly (there
is no need to use back-propagation to train the neural network). It is
therefore expected that these methods will be widely used in the areas of
classification and AI research.

The lecture, gives the theory behind the algorithms and outlines their
proof and presents a few actual examples.
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** (footnote) The algorithm is fast: we have separated 50,000 random points
in a 25 dimension unit cube by 27 planes, (N=50,000, d=25, q=27) and the
time taken to calculate all the coefficients of the hyper planes is around
6 min. on a desk top.