# Simultaneous Instance and Attribute Selection for Noise Filtering
## 1 Introduction  
The k nearest neighbor (NN) classifier [1] is currently still a good option when looking for a simple and effective classification model, especially in problems where interpretability and flexibility are important. Its logic is easy to explain to non-technical people, making it easy to communicate results, and it does not assume any specific distribution of data, making it flexible for different types of data. This classification model is easy to understand and implement; it does not require a training process as it is a lazy classifier, and it works well in situations where local similarity is relevant, allowing the use of different distance or dissimilarity functions according to the needs of the user. However, one of the major disadvantages of NN classifiers is their computational cost, which grows as the training data increase. In addition, the existence of mislabeled objects or instances can affect the quality of classification. The existence of noise is inherent to most real data that are collected. There are several well-known sources of noise, such as people giving false information in some scenarios (i.e., increasing salary, decreasing age or weight, lying about health), data having transmission errors for some sensors and leading to outlier values, human errors in manual annotation, and many others. Removing or reducing noisecan help classification algorithms focus on relevant patterns, preventing them from being affected by irrelevant or incorrect information. This can result in more accurate and reliable models, which in turn improves their ability to generalize and make accurate predictions on new data. Thus, noise filtering is essential to ensure data quality and the effectiveness of supervised classification models. Several approaches have been followed for noise removal by instance selection in the context of imbalanced data [2], deep neural networks [3], and regression [4]. Data reduction and noise filtering for instance-based classifiers have been addressed in the literature by selecting features [5], selecting objects or instances [6], and also by selecting both features and instances [7; 8; 9; 10]. This last approach can lead to better results than the sequential selection of features and instances [7] because, in the sequential selection, the first applied method can access the whole training data, but the second can only access the results of the application of the first method. On the other hand, the simultaneous (often called \"dual\") approach can access all training data. Several algorithms for selecting both instances and features have been proposed, mostly following an evolutive approach [10; 11; 12]. However, such methods are focused on reducing the data cardinality and not on noise filtering, sometimes resulting in huge drops in classifier performance. In addition, most methods are specific to certain classifiers and are not directly applicable to others. To address such issues, we use the experimental method, and the main objective of this paper is to propose a novel algorithm for simultaneous instance and feature selection that is able to detect and filter noise and reduce the training data without sacrificing classifier performance. The contributions of this paper are as follows:  
* We introduce ROFS, a deterministic method for simultaneously selecting features and instances in hybrid and incomplete data. * The proposed model does not predefine any supervised classifier and, therefore, can be applied to different supervised classifiers. * We analyze the performance of the compared algorithms under noisy environments and can ensure our proposal overpasses others in recognizing and deleting noisy instances. * The statistical analysis concludes our proposal obtained significantly more accurate results while using a fraction of instances and attributes. The remainder of this paper is as follows: Section 2 presents the datasets and the algorithms used in the experimental analysis, as well as the performance measures.