Info

Variable Number

Iteration Number 5

Figure 6.33. Percent weight change for the variables after five iterations.

Figure 6.33. Percent weight change for the variables after five iterations.

6.3.3 Curve Registration

The curve registration problem casts the landmark alignment problem in functional data analysis (FDA) framework [495]. FDA involves the estimation of mth order linear differential operators L — wqI + w\D + ... + Wm-iD"1"1 + Dm where Lx = 0, and Dm denotes the mth derivative, and the weights w are functions of the independent variable t. Let N functions Xi be defined on closed real interval [0, To] and hi(t) be a transform of t for case i with domain [0,To]. The time of events must remain in the same order regardless of the time scale. Therefore, the time warping functions hi must be such that hi(t\) > hi(t2) for t\ > t2. Define y{t) to be a fixed (reference) function defined over [0, To] to act as a template (for example a reference batch trajectory) for individual curves xt such that after registration, the features of Xi will be aligned with the features of y. In discrete values yi, k = 1,..., K,

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