Finding Curvilinear Features in Spatial Point Patterns: Principal Curve Clustering with Noise
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Solvability of the nonlinear EMS (estimate, maximize, smooth) equations in the nonnegative quadrant is established by the use of the Brouwer fixed point theorem and a priori estimates from Perron--Frobenius theory. Existence of solutions and of an a priori estimate are also proven for a generalization of the EMS equations. The a priori estimates illustrate the quantification shortcomings of the EMS algorithm and should be carefully considered both before applying the algorithm and in the choice of smoothing.