## 4 Experiment and Results  
The experiment was performed on 64 bit Windows, Intel(r) Core CPU i7-6700, 16 GB RAM, and VGA NVIDIA GeForce GTX 1060 6 GB. The data used in the experiments were the handwritten text data of the Extended MNIST (EMNIST) dataset with a size of \(28\times 28\). The learning data of this dataset is 124,800 data points, and the test dataset is composed of 20,800 data points. The PCA used in these experiments compressed 99% of the original data and had data with a size of 331 elements. This environment was designed to identify the features in a more accurate manner, using the highest compression rate of the PCA. The test data were generated by adjusting the parameters of PCA to be equal to the size of the learning data. In this study, the data processed using LFA and PCA were compared and analyzed, and LFA and PCA were analyzed using k-nearest neighbors (KNN) and support vector machine (SVM), which are representative machine learning techniques. In addition, to raise the reliability of the accuracy measurement, other dimensionality reduction techniques, linear discriminant analysis (LDA), independent component analysis (ICA), and t-distributed stochastic neighbor embedding (TSNE), were also performed. This experiment compared and considered the data processed through the suggested LFA and PCA. Figure 9 shows the size of the resulting data according to the compression of the data. The division was made by combining the training and testing data of the EMNIST database and then randomly mixing them and dividing them into the predetermined training and test set sizes. The results in Figure 9 show that the training and testing sizes were different for each compression rate. This is attributed to the linear combination, which is one of the shortcomings of PCA. PCA calculates the principal components by taking a covariance matrix for all inputs. In this process, PCA selects data with a large variance as the principal components without considering the features of the selected principal components. Therefore, PCA can yield different-sized outputs depending on the number and class distribution of the data. One technique to solve this issue is to fix the parameters of the PCA. As such, PCA can generate data of the same size regardless of the inputs. In this case, the selection of parameters for PCA is very critical. In the case of Figure 9, the output data shows a large difference of approximately 90 in the size between 99% and 98% compression. On the other hand, LFA maintains a constant size by identifying the number of linear segments and generating cumulative aggregate data. In addition, because its internal elements are of an integer type, they have relatively light capacities. Figure 10 shows the capacities of the processed data. Figure 9: The size of the resulting data according to the compression of the data (TR: training, TE: test). Since LFA derives an outcome by cumulatively summing up the unique values of all line segments, it only takes an integer value, and its aggregate data is simple count data. Therefore, it requires low memory capacity to store the data. In this experiment, the accuracy of KNN and SVM on LFA, PCA, LDA, ICA, and TSNE was measured. Figure 11 shows the accuracy measurement data using machine learning. The KNN and SVM were used with all parameters to set to their default values. We evaluated the performance of each technique in the same environment, which allowed us to understand the accuracy of each dimensionality reduction algorithms in the default environment. In the analysis in Figure 11, it is shown that the accuracy of each dimensionality reduction algorithms was 90% or above. In terms of accuracy with KNN, LFA showed the highest accuracy (97.5%), which was followed by PCA (96.6%), as shown in Figure 10(a). This was followed by ICA (96.2%), TSNE (93.1%), and LDA (92.3%). On the other hand, in terms of SVM accuracy, LFA showed the highest accuracy (98.9%), which was followed by TSNE (96.4%), ICA (96.1%), PCA (93.8%), and LDA (92.1%), as shown in Figure 10(b).