# Enhanced Label Noise Filtering with Multiple Voting
## 2 Related Work  
This work presents an approach to improve multiple-voting based ensemble filters for mislabeled data recognition. As necessary background knowledge, conventional ensemble learning based filters (EnFilter) will be introduced firstly. Then, multiple-voting based filter (MVFilter) will be presented. EnFilter employs an ensemble classifier to detect mislabeled instances by constructing a set of base level classifiers and then using their classifications to identify mislabeled instances. The general approach is to tag an instance as mislabeled if x of the m base level classifiers cannot classify it correctly. The majority filter (MF) and consensus filter (CF) are the representative EnFilter algorithms [27, 28]. MF tags an instance as mislabeled if more than half of the m base level classifiers classify it incorrectly. CF requires that all base level classifiers must fail to classify an instance as the class given by its training label for it to be eliminated from the training data. The reason for employing ensemble classifiers in EnFilter is that the ensemble classifier has better performance than each base level classifier on a dataset if two conditions hold: (1) the probability of a correct classification by each individual classifier is greater than 0.5 and (2) the errors in predictions of the base level classifiers are independent. Algorithm 1 enlists the majority filter (MF) algorithm as a representative EnFilter algorithm. In Step 1, it initializes with the n disjoint subset of the training set E. In Step 2; it initializes the empty set A to reflect the noisy examples. The main loop in Steps 3-6 processes each subset E\({}_{i}\), in an iterative manner. Step 4 establishes subset E\({}_{i}\) having all examples from E except the one existing in E\({}_{i}\). These examples from E\({}_{t}\) are used in an arbitrary inductive learning algorithm in Step 6 to induce a hypothesis (a classifier) H\({}_{j}\). In Step 14, all those examples from E\({}_{i}\) are added to A as potential noisy examples for which the majority of the hypothesis does not hold. CF is more conservative than MF because of the severer condition for noise identification, which ultimately results in fewer instances being eliminated from the training set. With a such property, the CF differs from MF in Step 14, and thus, it considers examples in E\({}_{i}\) as noisy only if all of them are classified incorrectly by the hypothesis. Furthermore, CF has the risk of retaining bad data. As Algorithm 1 shows, the core of EnFilter is adopting a voting mechanism to recognize noises. Training data x, in subset E\({}_{i}\) after data partitioning on E, will be voted on by the multiple classifiers, which are trained based on the data in E \(\backslash\) E\({}_{i}\). Suppose y(x) is the function to determine whether x is mislabeled, then y(x) = vote(classifiers(E\({}_{i}\)), x). Like MF and CF, the conventional EnFilter decides y(x) only based on one-time voting and therefore, is a single-voting based filter (SVFilter). As pointed out in [40], the SVFilter suffers from an instability problem. For data x, if the SVFilter runs twice, the first data random partitioning might assign x to subset E\({}_{i}\), while the second time, it assigns x to subset E\({}_{k}\). Therefore, we have y(x) = vote(classifiers(E\({}_{i}\))) and y(x) = vote(classifiers(E\({}_{k}\))). Note that as there is diversity between E\({}_{i}\) and E\({}_{k}\), the voting results of two SVFilters might be different. Therefore, instead of one-time voting, multiple-voting based filters (MVFilter) have been proposed to address this instability problem. MVFilter consists of t SVFilters. Each SVFilter generates its own decision about suspected mislabeled data index A\({}_{i}\). Finally, all the different decisions A\({}_{i(i=1:t)}\) will be combined by the MVFilter to output the final decision about which data are mislabeled.