Figure 4.15. Multiway multiblock regression problem [297, 556].

variance in Y accounted for by T: a ■ R2XT + (1 — a) • RyT, with 0 < a < 1. The least-squares loss function may be written in terms of the residuals as a minimization problem:

o-(W,Px,Py) =a||X-XWPx||2 + (l-a)||Y-XWPy||2 (4.156)

with the Frobenius matrix norm || • || and constraint TtT = WTXTXW = 1a, where is an A x A identity matrix. The method can be extended to multi-block data. While de Jong and Kiers [119] consider prediction of Yfc, k > 1 from a single X, it is also possible to formulate problems where many X blocks are used to predict Y.

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