# Comparison of Instance Selection and Construction Methods with Various Classifiers
## 5 Conclusions  
In the article we investigated the performance of the popular classical instance selection and prototype generation methods in terms of the obtained compression of the data set and their influence on the performance of various classifiers. To summarize the obtained results we averaged them for each data filtering method over all classifiers. This allowed us to compare all the evaluated data filters. The results are presented in Figure 11. The red line in the plots indicate the methods which belong to the Pareto front, for example, these ones which are not dominated by the other methods. The following methods belong to the front: _ENN_, _HMN-E_, _GLVQ_(0.3), _LVQ2.1_(0.3), _HMN-EI_, _Drop2_, _Drop3_ and _LVQ2.1_(0.1). Some other methods like _k-Means_(0.3) and _LVQ1_ can be considered as the top ones because they lie very close to the Pareto front. From the top methods two algorithms provide compression less than 50%, these are _ENN_ and _HMN-E_. These methods should be considered only when the compression is not the primary need. Figure 10: Results obtained for SVM classifier. (**a**) Average performance ranks. (**b**) Average performance. In theory, as indicated in the beginning of this article, the goal of data filtering methods is to keep the estimated conditional probabilities \(P(c|\mathbf{x})\) unchanged before and after data filtering so that the \(P(c|\mathbf{x})_{\mathbf{T}}=P(c|\mathbf{x})_{\mathbf{p}}\), but in reality each of these classifiers has its own probability estimation technique. So the one used by the decision trees which is based on the instance frequency calculation within the bin, do not match with the one of the nearest neighbor classifier. Moreover, SVM and Random Forest are more robust than \(k\)NN so they can better deal with the noisy samples than the data filters which internally use \(k\)NN to assess training instances. The obtained results indicate that the size of the dataset matters. In general applying any of the examined data filters result in the decrease in accuracy, and a huge drop in prediction performance can be observed between compression 70% and 90%, so that the compression 70% can be considered as a kind of threshold below which we should not compress the dataset. Although, we also observed, that for bigger datasets instance selection methods proved more efficient allowing for higher compression. Interestingly, on average the prediction performance slowly drops even for the noise filters. The exception are 1-NN and Naive Bayes classifiers where some of the tested instance filtering methods (in particular \(ENN\) and the \(LVQ\) family) allowed to increase the accuracy. For the  
Figure 11: Average results over all evaluated classifiers. Red line represents Pareto front. (**a**) Average performance ranks. (**b**) Average performance. \(k\)NN with tuned \(k\) the accuracy may remain unchanged, so the benefit is the execution time of the prediction phase, which requires fewer distance calculations to make the decision. The observed phenomenon can be interpreted taking into account that all of the tested instance selection methods were developed to work with \(k\)NN. As it was indicated in Section 2 instance selection methods can be considered wrappers for the kNN classifier, while for the remaining classifiers they work as filters. Some authors design specific algorithms for particular classifiers. The examples are the works of [PERSON] and [PERSON] who developed memetic [37] and genetic [38] algorithms for SVM, also [PERSON] and others developed an algorithm dedicated for the SVM [39]. In [7] we developed generalized \(CNN\) and \(ENN\) algorithms which work as wrappers in particular with MLP network. But these methods are strictly designed for given classifiers and can not be generalized so they were not considered in this research. In the literature some authors use instance selection methods for balancing the data distribution of unbalanced classification problems [40].