BackHistorical remarks
The H-principle was first presented at the 3rd Nordic Workshop in Chemometrics in Tromsø, Norway, in 1992. At the chemometric workshops there were intensive discussions on the measurement situation and the associated modelling tasks. The discussions reminded one on the discussions between Werner Heisenberg and Niels Bohr in 1920s. By replacing the measurement instrument by 'the mathematical model' there appeared a close analogy between the measurement task and the modelling task. The H-principle was then formulated in close analogy with the Heisenberg Uncertainty inequality.
In the 1960s and 1970s there was great interest in large interdependent systems, where each system was represented by a data block of variables. In the context Herman Wold developed the PLS algorithm. It was based on a closed loop of projections. It was shown by von Neumann that such a sequence of projections (actually also for more general transformations) always converges. Herman Wold named the algorithm the NIPALS (Nonlinear Iterative PArtial Least Squares) algorithm. He used arrow diagrams to illustrate his approach and methods of estimation. The algorithms of the H-method in the different fields of analysis have been developed as extensions of the basic views of Herman Wold.
In case of regression analysis there are two data blocks that are connected. In this case the NIPALS algorithm simplifies. Unfortunately the PLS method only selected one set of latent vectors, one for each block. The LISREL method of Jöreskog also only selects one set of latent vector in the causal diagram of (expected) interconnection between the blocks of variables (measured and latent ones). By letting the data decide how many latent vectors are needed at each node in the diagram, these causal methods can be considerably improved. In the regression context Harald Martens and Svante Wold were concerned with how more latent vectors should be selected. In the article Personal Memories of the early PLS developments, Chemometrics and Intelligent Laboratory Systems, 58 (2001) 83-84, Svante made some historical about the early developments. The results of these developments was a NIPALS algorithm that selected as many PLS-latent vectors as needed.