Nearest Neighbor Method
A slecture by Sang Ho Yoon
Partly based on the ECE662 Spring 2014 lecture material of Prof. Mireille Boutin.
Introduction
This slecture discusses how to whiten data that is normally distributed but keep in mind that although I have illustrated the whitening and coloring transforms with Gaussian data, these transforms can be used on data drawn from according to any probability law. Data whitening is required prior to many data processing techniques such as In this slecture, basic principles of implementing nearest neighbor rule will be covered. The error related to the nearest neighbor rule will be discussed in detail including convergence, error rate, and error bound. Since the nearest neighbor rule mostly relies on a metric function between patterns, the properties of metrics will be studied in detail. Several examples will be illustrated to help understanding throughout the lecture.
Nearest Neighbor Rule
Let's consider a testing sample x. Based on labeled training sample D$ ^n $ $ = x_{1},... ,x_{n}, $ the nearest neighbor technique will find the closest point x' to x. Then we assign the class of x' to x. This is how the classification based on the nearest neighbor rule is processed. Although this rule is very simple, it is also reasonable. The label $ \theta' $ used in the nearest neighbor is random variable which means $\theta' = w_{i}$ is same as a posterior probability $ P(w_{i}|x'). $ If sample sizes are big enough, it could be assumed that x' is sufficiently close to x that $ P(w_{i}|x') = P(w_{i}|x). $
References
Questions and comments
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