A Method for Reducing the Dimensionality of Data Used for Machine Learning Using the Principal Component Analysis

Despite the constant growth in computational capabilities of modern intelligent data analysis systems, the volume of information being processed grows exponentially and, in some cases, becomes a bottleneck in analytical processes. Consequently, the task of optimizing the dimensionality of the original information space without compromising the analytical value of the obtained results acquires critical importance. The principal component method (PCA) represents one of the most effective tools for solving the data dimensionality reduction problem. This research focuses on the application of this method in analyzing the characteristics of node elements in wireless sensor networks. The key advantages of the method are as follows: first, the method requires no prior assumptions about the nature of the investigated object; second, the linear structure and iterative nature of the algorithm ensure efficient computational implementation on modern computers. As the empirical foundation, we use a dataset characterizing the operational performance of a wireless sensor network comprising one thousand nodes. For each node, samples of observations are compiled for key Quality of Service (QoS) metrics that enable the assessment of the system’s operational characteristics. The research procedure consisted of sequential stages: preliminary cleaning and normalization of the raw observations; construction of the covariance matrix; computation of the eigenvalue spectrum and corresponding eigenvectors; and a linear mapping of the data into the principal component space. The principal components were obtained via an orthogonal transformation of the covariance matrix’s eigenvectors and were used as the basis for subsequent analysis and interpretation of the structure of feature variability. The practical effect of the approach is a substantial reduction of the feature space dimensionality while preserving the representativeness of the original data and the informativeness of the results.