# Regularized Chained Deep Neural Network Classifier for Multiple Annotators
## 2 Related Work  
As analyzed by the authors in [26], there exists an increasing interest in developing models to deal with multi-labeler data. However, it is possible to identify some problems that are not entirely solved: (i) to code the relationship between the labelers' performance and the input space, and (ii) to identify annotators' interdependencies. In [23], the authors introduced a binary classification algorithm for multiple labelers, where the input data are represented by Gaussian mixture model (GMM)-based clusters. This approach assumes that each annotator exhibits a particular performance concerning a given cluster. Nevertheless, such a model does not consider the information from multiple annotators as an input for the GMM, leading to variations in the labelers' parameters. In [27], the authors propose a binary classification algorithm employing two distributions to compute the annotators' achievement as a function of the input space, namely, Gaussian and Bernoulli. The parameters of such distributions are computed via logistic regression optimization. Still, a linear dependence is assumed between the labeler's expertise and the input space, which may not be appropriate in the presence of non-linear data structures. For example, if we take into account online annotators assessing documents, they may show different labeling accuracies depending on if they are more familiar with some specific topic [28]. On the other hand, the work in [29] uses a multivariate Gaussian distribution to model the annotations, and the experts' interdependencies are coded in the covariance matrix. Besides, in [16], the authors introduce a binary classification method based on a weighted combination of classifiers. The weights are computed using a centered kernel alignment (CKA)-based loss to measure the similarities among the input features and the labels from multiple annotators. Similarly, the authors in [1] proposed a localized kernel alignment-based method, termed LKAAR, to build a classification approach with multiple annotators. However, unlike the work in [16], LKAAR modifies the CKA-based loss to measure the similarities among each input instance and its corresponding set of labels. Thereby, LKAAR measures the annotators' performance as a function of the input space while considering interdependencies among the experts. Our proposal follows the line of the works in [19; 20] in the sense that RCDNN uses a deep-based approach to build a supervised learning model in the context of multiple annotators. However, while such approaches code the annotators' parameters as fixed points, we model them as functions to consider dependencies between the input features and the labelers' behavior. RCDNN is also similar to the LKAAR model introduced in [1]. Both approaches model the annotators' performance as a function of the input instances and consider interdependencies among the labelers. Nonetheless, unlike LKAAR, where it is necessary to use as many classifiers as annotators, our approach only needs to train a single classifier from a deep learning representation, which is advantageous for a large number of labelers. As an illustrative summary, Table 1 shows the key insights of our RCDNN and relevant state-of-the-art works.