# Simultaneous Instance and Attribute Selection for Noise Filtering
## 2 Materials and Methods  
### Algorithms for Simultaneous Instance and Feature Selection  
There are three major approaches for simultaneous features and instances selection: evolutionary, embedding editing, and fusion. In the following, we detailed their main characteristics.  
An evolutionary approach to instance and feature selection consists of the application of evolutionary methods, such as Genetic Algorithms, to select simultaneously both features and objects. This is the oldest yet still used approach for simultaneous data processing, dating back to 1994 when Skalak proposed the first method in this strategy, the RMHC-FP1 [13]. It used a Random Mutation Hill-Climbing strategy to choose the best subset of features and instances by generating a binary string of length number of features + number of objects, which represents the inclusion/exclusion of each feature and instance in the result. Then, this initial solution evolves until a termination criterion is fulfilled. With similar representation, several authors used Genetic Algorithms for simultaneously selectingfeatures and instances. These GAs have an encoding strategy similar to the RMHC-FP1 algorithm, an elitist selection strategy, and they usually differ in fitness functions and parameters [7; 8; 11; 12; 14; 15].  
The embedded editing strategy consists of embedding the instance selection process into a feature selection method. It applies an error-based editing method and a condensation method to each candidate feature set into a wrapper feature selection method. [PERSON]'s method [16] (here referred to as DS) combines the Sequential Backward Search (SBS) [17] method with the application of two instance selection methods: the Proximity Graph-based Editing using Relative Neighborhood Graphs (RNG-Edt) [18] and the Minimal Consistent Subset method (MCS) [19]. [PERSON] uses as a fitness function for the SBS method a combined measure of the 1-NN accuracy with respect to a validation set and the amount of instance reduction achieved by the sequential application of the RNG-Edt + MCS methods. To combine the accuracy and reduction, he uses the Euclidean distance between both measures. The sequential application of two instance selection methods allows important instance reduction as well as atypical and mislabeled object filtering. This strategy is time-consuming but has good experimental results.  
Fusion is a deterministic strategy and is based on obtaining small sets of candidate features and instances. Then, it uses different approaches for merging those candidate sets in order to obtain an optimal set of features and instances. The first realization of this strategy is the SOFSA method [20]. Similar to TCCS [21], SOFSA uses the Compact Set Editing [22] and the LEX [23] algorithms for obtaining the small candidate sets of instances and features (called submatrices). It uses a merging strategy based on the individual quality of the submatrices. Other methods of fusion are SHERA [9], designed for educational classification, and AFIS [24], focused on imbalanced data.  
In this paper, we experimentally analyze the performance of different methods for simultaneously selecting features and instances in noisy environments. We choose RMHC-FP1 [13], AKH-GA [12], KJ-GA [7], IN-GA [11] (evolutive approach), DS [16] (embedded editing approach), and SOFSA [20] and TCCS [21] (fusion approach) to ensure the representativity of the different simultaneous attribute and instance selection strategies.