Novel unified framework for latent modeling and its interpretation

• Propose unified framework to better understand and discuss different latent modeling methods.
• Different PLS implementations can be positioned in the unified framework.
• Reduce confusion and better understanding of strengths and weakness of different implementations.
• Towards better interpretation of latent models, and understanding as to why it does not necessarily work for complex data.
• The unified framework allows for better development of latent models for more complex, and big, data.

An important characteristic of chemometrics has been its need to manage the tradeoff between computational, mathematical and statistical performance against data interpretability. Additionally, being mostly seen as a conglomeration of data analytic methods that target the solution to real-world problems, the development of chemometrics as an independent and well-defined field has been hampered by its applied nature. Consequently, the broad range and diversity of application of chemometric tools has hindered the development of a unified theory able to propel it beyond its current use in analytical and industrial chemistry to larger and more complex data problems.In this paper, we provide a mathematical vehicle for the understanding and improvement of current methods popular in chemometrics. Starting from a historical solution to matrix factorization we develop a novel unified framework for the fundamentals of latent variable modeling methods, elucidate major properties and clarify controversies between major PLS implementations and interpretations. The concepts presented in this work aims at contributing to a deeper understanding of the underlying theory of chemometrics methods, and strengthen their use in practice. Furthermore, this effort attempts to bridge the gap between chemometrics and big data problems and contribute to the development and acceptance of chemometrics as a mature and independent scientific field by the broader data analytic community.