Trajectory Analysis. The U.S. signatories will provide for a preliminary and a final Trajectory Analysis which will include sequence of events, vacuum impact point prediction, tracking information, and insertion accuracy as well as range safety parameter and lines of sight for down-range acquisition. A summary of the results of these analyses will be presented to the foreign signatories at the appropriate PMR, ICWG, and Progress Reviews.
Trajectory Analysis. The endpoints, MH and QLQ, were treated as continuous variables and unsupervised trajectory clustering was performed by means of a modified k-means algorithm. Specifically, the kmlShape R package was used to cluster individual patient trajectories accounting for the shape of each trajectory using a shape-respecting distance metric. Options regarding the random initialization points and expectation–maximization were kept as default, while the time-slice was set to 0.01. Overall, kmlShape is a variant of k-means where the Fréchet distance, associated with trajectory shape, is used as the distance metric. The Fréchet distance is defined on a continuous interval, so that the real Fréchet distance cannot be obtained in discrete cases, but can be infinitely approximated. In brief, a curve P can be regarded as the mobile trajectory that travels at a speed α. Then, the Fréchet distance between the curve P and another Q considered as a mobile trajectory with speed β, is the smallest possible maximum distance between the two curves after reparameterization of P and Q by α and β, respectively: DistFrechet(P, Q) = dα,β(P, Q). With appropriate approximation, this distance can account for the different number or location of measurement points and missing values in patients. In the implementation of kmlShape, Fréchet distance is also used to determine the cluster centers. A known limitation of k-means algorithm is that the resulting clusters depend on the initial random assignments and, thus, each run with the same number of clusters k, might yield slightly different results. To mitigate this dependence, for each k value, we run the algorithm 10 times with different initial values so as to pick the best result in terms of within-cluster compactness. This was defined as the clustering solution with the lowest within-cluster sum of squares (WSS). The WSS is a commonly used measure of cluster compactness and is defined as the sum of distances between the points and the corresponding centroids for each cluster:
Trajectory Analysis. If the FRET efficiency time traces display temporal fluctuations, the data can be further analyzed to obtain more detailed information on the kinetics of the system using dwell-time analysis or hidden Markov modeling, depending on the type of fluctuation as described below. Regardless of the method of trajectory analysis, only molecules exhibiting single-step photobleaching are analyzed, as this is a unique signature of a FRET interaction between a single donor and single acceptor molecule (Figure 2.7C).
