Bayes Error Estimation Using Parzen and k-NN Procedures

Nearest neighbors in random subspaces

“…To overcome the difficulty with the sparsity of data in such spaces, researchers have investigated using a decision threshold [1] [4] and enhancing the training set by bootstrapping [5].…”

Estimating Cluster Overlap on Manifolds and its Application to Neuropsychiatric Disorders

“…However, such empirical validation largely depends on the feature selection and classifier design, and cannot reveal the underlying overlap between classes. Fukunaga et al use Parzen windows and k-NN to estimate the Bayes error rates [5]. It has been shown that the error rate estimated based on the k-NN rule has upper bound of twice the true Bayes error [3].…”

“…Validation of overlap measurements using Swiss Roll data: (a) the Swiss Roll data with its parameter, i.e., the rolling angle, sampled at clusters; (b) ISOMAP embedding of the data at two dimensional space. Each color represents one cluster; (c) comparing the ground truth with the estimated Bayes error using the presented method; (d) a box and whisker plot of the results in (c); (e) comparing the ground truth with the estimated Bayes error using the k-NN based method [5] in the original data space; (f) a box and whisker plot of the results in (e)…”

“…Therefore it demonstrates that we can use this method to quantify the cluster overlap. For comparison, the original k-NN based method [5] is applied in the original data space. The estimation results are shown in Figure 1.…”

Spatio-temporal pattern recognition using hidden Markov models

“…This sequence is repeated for each piece of data. The leave-one-out method has been described in the literature by (18,26,27,28,38,39,47,71) and is attributed to Lachenbruch (38). This method also appears to have been independently arrived at in the same year by the Russian researchers Lunts and Brailovskiy (47 …”