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Regularization Techniques for Machine Learning on Graphs and Networks with Biological Applications

Commun. Math. Anal.
Volume 8, Number 3 (2010), 136 - 145

Regularization Techniques for Machine Learning on Graphs and Networks with Biological Applications 

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Abstract

The representation of a high dimensional machine learning (ML) feature space $F$ as a function space for the purpose of denoising data is introduced. We illustrate an application of such a representation of feature vectors by applying a local averaging denoising method for functions on Euclidean and metric spaces (together with its graph generalization) to the regularization of feature vectors in ML. We first discuss this technique for noisy functions on $\mathbb{R}$, and then extend it to functions defined on graphs and networks. This method exhibits a paradoxical property of the bias-variance problem in machine learning, namely, that as the scale over which averages are taken decreases, the error rate for classification first decreases and then increases. This approach is tested on two benchmark DNA microarray data sets used for classification of breast tumors based on predicted metastasis.