“Principal Component Analysis” (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.

Prescriptive analytics plays an important role in decision making in smart factories by utilizing the available data to gain actionable insights. The planning, integration and development of such use cases still poses manifold challenges. Use cases are still being implemented as standalone versions; the existing IT-infrastructure is not fit for integrative bidirectional decision communication, and implementations only reach low technical readiness levels. We propose a reference architecture for the integration of prescriptive analytics use cases in smart factories. The method for the empirically grounded development of reference architectures by Galster and Avgeriou serves as a blueprint. Through the development and validation of a specific IoT-Factory use case, we demonstrate the efficacy of the proposed reference architecture. We expand the given reference architecture for one use case to the integration of a smart factory and its application to multiple use cases. Moreover, we identify the interdependency among multiple use cases within dynamic environments. Our prescriptive reference architecture provides a structured way to improve operational efficiency and optimize resource allocation.