The concept of big data has become one of the most important topics in the field of information science and engineering. In this paper, we offer modeling of data and its stability and forecasting by considering anti-symmetric traceless and symmetric models for atmospheric pressure variations. The data sample has been collected every 10 minutes for several years during 2009-2016 at the Weather Station, Max Planck Institute for Biogeochemistry, Jena, Germany. Subsequently, we extend the proposed model with a probabilistic transformation matrix by considering the Google search random surfer matrix with a small damping factor (0 < < 1). Following the Principal Component Analysis (PCA), our study plays a vital role in big data samples and their stability analysis. A comparative discussion is provided for the above transformation matrix and its probabilistic counterpart. Finally, predictions are made towards feature selection, PCA and data compression sensing in the light of big data.

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