## 2 Related Research
### Feature Selection Algorithm for Data Dimensionality Reduction  
A dimensionality reduction technique is applied to reduce input data from a high-dimensional system to a low-dimensional system. The reduced data are divided into existing features and new features created by combining existing features. The technique of selecting only some of the features is called feature selection, and the technique of creating new features from the combination of existing features is called feature extraction. Feature selection is used to select some features for optimal classification, to create a subset, and then to classify target data using this subset. In this way, it is possible to reduce the operational volume and shorten the learning time. Nevertheless, feature selection is a complex process of selecting a subset and requires considerable time [33; 34; 35; 36]. Figure 2 shows a dimensionality reduction technique. Figure 2a shows the feature selection procedure. The first process in feature selection is to extract all features of the learning data, and the next process is to create a subset of selected features. The learning algorithm is executed with the subset, and its performance is analyzed. This procedure is repeated until certain requirements are met. However, when target data are classified with a subject, it is highly likely to lower the performance of classification due to factors such as rotation and size. In addition, when classification is made only with some features, the accuracy is reduced. If the number of features is large, it takes too long to select the best subject. Figure 2: Dimensionality reduction technique. (**a**) Feature selection procedure. (**b**) Principal component analysis process  
Feature extraction is a technique used to convert high-dimensional data to low-dimensional data and to generate new features. There are various methods of feature extraction, including principal component analysis (PCA), linear dimensionality reduction (LDA), independent component analysis (ICA), and non-negative matrix factorization. Among them, PCA is the representative technique [37; 38; 39; 40]. PCA selects the main axis in the direction that has the largest data variance, and it then generates all the data. With data X, the correlation matrix R is calculated. With the use of R, the eigenvector \(\gamma\) and the eigenvalue \(\Lambda\) are calculated. \(\gamma\), known as the largest value of the calculated \(\Lambda\), is the direction with the largest variance in X. The new feature data drawn in this process have reduced dimensions with a minimized error. The components of \(\gamma\) have a direction that has no correlation between the factors. Figure 2b shows the process of projecting data orthographically with the main components. As shown, the data are generally high-dimensional (e.g., three dimensions). The factors constituting an image are located in these dimensions. With the use of the variance value of these factors, the main axis is identified. At this time, the main axis selected has the direction with the largest variance value. Through this process, high-dimensional data are converted to low-dimensional data. Since PCA represents all the inputs in a linear combination, it becomes difficult to explain the process of converting all input variables into a linear combination, and the information about the output data becomes unknown [41; 42; 43]. For example, if there is image A (\(28\times 28\)), PCA will obtain 784 (\(28\times 28=784\)) variables as input. Currently, PCA performs a covariance matrix on A to extract a series of eigenvectors that are principal vectors. In this case, it is difficult to determine the number of elements constituting the main components of the input data and on which features (characteristics) they are covariant. In addition, PCA can derive different output results (data size) even at the same compression rate, depending on the shape of the data (internal features of data).