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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.
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Author:Christopher, Kevin
Publication:Journal of the Colorado-Wyoming Academy of Science
Article Type:Brief Article
Geographic Code:1USA
Date:Apr 1, 2002
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