Self-Reliant Dimensionality Reduction That Uses Improved Pareto Distribution PCA Framework

An improved Pareto Distribution-based Principal Component Algorithm is a well-known linear technique for reducing the dimensions of any dataset. Essentially, it performs an orthonormal transformation of all the variables, replacing possibly correlated ones with linearly independent ones, referred as principal components, which effectively capture a wider bandwidth of the variance in the data. Many studies have been undertaken to determine the ideal number of principal components for offline PCA. Flowing data, however, constantly changes the optimal number. It is therefore necessary to update both principal components and dimensionality on every time step. Despite the widespread study of continuous updating of the principal components, dimensionality adjustment algorithms are generally restricted to increase of one parameter in neural network featured and incremental PCA. Consequently, existing approaches cannot accommodate predominant fluctuations in the presented data. We present a novel method for updating the optimal number of principal components relative to a neural network based PCA based on several PCA characteristics. A precise calculation of the required dimensionality greatly prevents computation effort while keeping variance within the desired range. It is found that the proposed algorithm has a high computational complexity, and it is benchmarked over any other non-neural network-based and incremental PCA approaches in an experimental study.