Related Experiment Video
Updated: May 29, 2026
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
The nearest neighbor and the bayes error rates
1Department of Computer Science, Birkbeck College, University of London, Malet Street, London WC1E 7HX, England.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
The (k, l) nearest neighbor method offers comparable error rates to the Bayes method in pattern classification. When acceptance rates match, their asymptotic error rates are closely related, with a defined function
Area of Science:
- Pattern classification
- Statistical learning theory
- Machine learning algorithms
Background:
- The (k, l) nearest neighbor method is a versatile pattern classification technique.
- Bayes method provides a probabilistic framework for classification tasks.
- Comparing different classification algorithms is crucial for optimizing performance.
Purpose of the Study:
- To compare the asymptotic error rates of the (k, l) nearest neighbor method and the Bayes method.
- To establish inequalities relating the error rates of both methods under specific conditions.
- To derive an optimal expression for a function relating these error rates.
Main Methods:
- Asymptotic error rate analysis
- Comparative study of pattern classification algorithms
- Mathematical derivation of error rate inequalities
Main Results:
- Established inequalities for asymptotic error rates: Ek,l + 1 ≤ E*(¿) ≤ Ek,l + dE*(¿).
- Defined 'd' as a function of k, l, and the number of pattern classes.
- Provided an explicit, optimal expression for 'd' that minimizes the difference between error rates for certain distributions.
Conclusions:
- The (k, l) nearest neighbor method's performance can be directly compared to the Bayes method.
- The derived inequalities offer insights into the trade-offs between the two methods.
- The optimal function 'd' provides a quantitative measure for comparing classification efficiency.
Related Concept Videos
01:13Accuracy and Errors in Hypothesis Testing
Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
01:19Expected Frequencies in Goodness-of-Fit Tests
A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
01:13Standard Error of the Mean
The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
01:03Prediction Intervals
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The...
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The...
00:59Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
01:11Statistical Analysis: Overview
When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...