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CMU CS 10701 - NONPARAMETRIC CLASSIFICATION AND ERROR ESTIMATION (10 pages)

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NONPARAMETRIC CLASSIFICATION AND ERROR ESTIMATION



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NONPARAMETRIC CLASSIFICATION AND ERROR ESTIMATION

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10
School:
Carnegie Mellon University
Course:
Cs 10701 - Introduction to Machine Learning
Introduction to Machine Learning Documents

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Chapter 7 NONPARAMETRIC CLASSIFICATION AND ERROR ESTIMATION After studying the nonparametric density estimates in Chapter 6 we are now ready to discuss the problem of how to design nonparumetric clussifiers and estimate their classification errors A nonparametric classifier does not rely on any assumption concerning the structure of the underlying density function Therefore the classifier becomes the Bayes classifier if the density estimates converge to the true densities when an infinite number of samples are used The resulting error is the Bayes error the smallest achievable error given the underlying distributions As was pointed out in Chapter 1 the Bayes error is a very important parameter in pattern recognition assessing the classifiability of the data and measuring the discrimination capabilities of the features even before considering what type of classifier should be designed The selection of features always results in a loss of classifiability The amount of this loss may be measured by comparing the Bayes error in the feature space with the Bayes error in the original data space The same is true for a classifier The performance of the classifier may be compared with the Bayes error in the original data space However in practice we never have an infinite number of samples and due to the finite sample size the density estimates and subsequently the estimate of the Bayes error have large biases and variances particularly in a high dimensional space 300 7 Nonparametric Classification and Error Estimation 301 A similar trend was observed in the parametric cases of Chapter 5 but the trend is more severe with a nonparametric approach These problems are addressed extensively in this chapter Both Parzen and kNN approaches will be discussed These two approaches offer similar algorithms for classification and error estimation and give similar results Also the voting kNN procedure is included in this chapter because the procedure is very popular although this approach


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