On error bounds for linear feature extraction Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/w9505452g

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  • Linear transformation for dimension reduction is a well established problem in the field of machine learning. Due to the numerous observability of parameters and data, processing of the data in its raw form is computationally complex and difficult to visualize. Dimension reduction by means of feature extraction offers a strong preprocessing step to reduce the complexity of the data. In applications dealing with classification of high dimensional data, the goal of a feature extraction step is to achieve a classification accuracy close to that achieved by utilizing the complete high dimensional data. In search for better classification with reduced complexity, numerous dimension reduction methods have been proposed that directly or indirectly aim at minimizing the classification error. This thesis proposes a novel set of bounds on the probability of classification error for the dimension reduced data. A criteria called the Chernoff union bound is developed which acts as the upper bound on the bayes classification error in the transformed subspace. The bounds offer a closed-form solution to our problem under various data model assumptions. We demonstrate its applicability in feature extraction for parametric and non-parametric data model assumptions. A detailed numerical study has been presented comparing the performance with many state of- the-art methods demonstrating the competitiveness and validity of the proposed criteria.
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