## 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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