Neural networks and isomaps: a comparison of dimensionality reduction frameworks. (Senior Division).
Isomap is an unsupervised learning algorithm that extracts
low-dimensional embeddings from high-dimensional data. A neural network is a supervised algorithm that can be trained to perform the same
function. These two methods perform a very similar function, but by very
different methods. A comparative analysis of these two algorithms
reveals underlying differences between them. Isomap consistently
recognizes known underlying embeddings with approximately 89% accuracy.
The neural network, exposed to a sample of half of the known data
points, generates a model for the remaining data points with 97%
accuracy. However, training the neural network with smaller data sets
predictably results in poorer generalization; the neural network matches
Isomap's accuracy with training samples consisting of 17-18 % of
the sample size (chosen randomly). A hybrid approach, utilizing Isomap
as a preprocessor for the neural network, yields 92% accuracy with a
half data sample (a level between the pure Isomap and pure neural
network), with a similar (though not as pronounced) degradation in
accuracy because of a reduced training sample size. The hybrid also has
the same accuracy as Isomap at 17% data exposure. Thus, all three
approaches analyzed can complete the same task, although with varying
levels of efficiency and accuracy.
Kevin Christopher, Cherry Creek High School.